Nebraska Conference for Undergraduate Women in Mathematics: Full Schedule

1:30pm CST

Conference General Information Room

If you need technical assistance or have general questions, you can join the Conference Information Meeting Room.

Friday January 22, 2021 1:30pm - 7:00pm CST
Zoom

2:00pm CST

Conference Opening Session

Welcome remarks from Dr. Christine Kelley; Dr. Marco Barker, Vice Chancellor for Diversity and Inclusion, Office of Diversity and Inclusion, University of Nebraska-Lincoln; and Dr. Tom Marley, Professor and Chair, Department of Mathematics, University of Nebraska-Lincoln. Thank you for coming to NCUWM!

Speakers

Christine Kelley

Professor of Mathematics, NCUWM Co-Chair, University of Nebraska-Lincoln

Dr. Christine Kelley has been on the NCUWM Organizing Committee since 2008 and is currently co-chair. Her research area is coding theory. After receiving her Ph.D. from the University of Notre Dame in 2006, she held postdoctoral research positions at the Fields Institute and The Ohio... Read More →

Friday January 22, 2021 2:00pm - 2:15pm CST
Zoom

Zoom Meeting, Opening Session

2:15pm CST

1st Plenary Talk: "From Flying Geometry to Random Forests in the Stars: A Math Story," Cecilia Aragon

From Flying Geometry to Random Forests in the Stars: A Math Story

What do the following two careers have in common: (1) data science professor, and (2) airshow pilot?

Spoiler alert: math.

It turns out it was a good thing Cecilia Aragon was a math major as an undergrad, because math ended up being useful in these two very different careers she pursued during her life. Math was also her personal superpower: she used it to overcome agonizing fears and accomplish life goals.

In this talk she tells her math story, and how math helped her go from painfully shy daughter of immigrants to: working with astronomers and Nobel Prize winners to solve some of the greatest mysteries of the universe; teaching astronauts to fly; and working with NASA to design software for Mars missions. She’ll present examples from her work in aviation, astrophysics, and data science using images, video, and even equations.

As the first Latina full professor in the College of Engineering at the University of Washington, author of over 130 articles and 3 books, and winner of the 2008 Presidential Early Career Award for Scientists and Engineers, she’ll also talk about overcoming stereotypes and low expectations as one of the few women — or Latinas — in both of her careers. For further detail, her recent memoir, FLYING FREE: My Victory over Fear to Become the First Latina Pilot on the US Aerobatic Team, describes how she used math to overcome fear and imposter syndrome to get to where she is today.

Speakers

Cecilia Aragon

Professor and Director, Human Centered Data Science Lab; Professor, Human Centered Design & Engineering, University of Washington

Cecilia Aragon is Director of the Human Centered Data Science Lab, Professor in the Department of Human Centered Design & Engineering, Founding Co-Director of the University of Washington Data Science Master’s Program, and Senior Data Science Fellow at the eScience Institute at... Read More →

Friday January 22, 2021 2:15pm - 3:15pm CST
Zoom

Zoom Meeting, Plenary Talk

3:45pm CST

Panel Discussion: Careers Using Mathematics

Moderators

Jim Lewis

Professor and CSMCE Director, University of Nebraska-Lincoln

Speakers

Kimberly Shurupoff

Director of Mathematics and Statistics Hiring, National Security Agency

Kimberly Shurupoff is the Director of Mathematics and Statistics Hiring at the National Security Agency (NSA). She oversees the hiring process for NSA's three full-time Mathematics Development Programs and three mathematics summer internship programs, as well as coordinates mathematics... Read More →

Julia Read-LaBelle

Global Supply & Inventory Analyst, Nike, Inc.

After graduating with a Bachelor of Science in Mathematics from the University of Nebraska-Lincoln, Julia Read-LaBelle began her career at Texas Instruments working on signal processing algorithms. While working at TI, she obtained her Master of Science in Applied Mathematics from... Read More →

Shanise Walker

Assistant Professor of Mathematics, University of Wisconsin-Eau Claire

Dr. Shanise Walker is an Assistant Professor of Mathematics at the University of Wisconsin-Eau Claire. She received her Ph.D. from Iowa State University. Her research interests lie in combinatorics and graph theory. She has studied various combinatorics and graph theory problems... Read More →

Laura White

Aerospace Engineer, NASA Langley Research Center

Laura White is an Aerospace Engineer at NASA Langley Research Center. She received a bachelors in Mathematics from Arkansas State University in 2013. Her undergraduate research focused on optimal statistical design of experiments for engineering and science applications. In 2018... Read More →

Martha Yip

Assistant Professor of Mathematics, University of Kentucky

Martha Yip is an Assistant Professor of Mathematics at the University of Kentucky. Previously, she served as a Hans Rademacher Instructor of Mathematics at the University of Pennsylvania. She earned her doctorate from the University of Wisconsin-Madison. Her research interests are... Read More →

Friday January 22, 2021 3:45pm - 4:45pm CST
Zoom

Zoom Meeting, Panel Discussion

5:15pm CST

Networking Blitz

Participants will be randomized into breakout rooms with one another. Here's your chance to meet some new people!

Friday January 22, 2021 5:15pm - 5:45pm CST
Zoom

Optional Zoom Meeting, Networking

5:45pm CST

Panel Discussion: Random Bits of Advice

"Random Bits of Advice" panel discussion

Moderators

Judy Walker

Professor of Mathematics and Associate Vice Chancellor for Faculty and Academic Affairs, University of Nebraska-Lincoln

Dr. Judy Walker, Aaron Douglas Professor of Mathematics and Associate Vice Chancellor for Faculty and Academic Affairs at the University of Nebraska-Lincoln, is one of the original co-founders of the Nebraska Conference for Undergraduate Women in Mathematics and chaired or co-chaired... Read More →

Speakers

Cecilia Aragon

Professor and Director, Human Centered Data Science Lab; Professor, Human Centered Design & Engineering, University of Washington

Ruth Haas

Professor of Mathematics; President, AWM, University of Hawaii, Mānoa

Ruth Haas is the President of the Association for Women in Mathematics (AWM). She is a Professor and Graduate Chair of Mathematics at the University of Hawaii, Mānoa. She is also Achilles Professor Emerita in Mathematics and Statistics at Smith College where she co-founded and co-directed... Read More →

Talitha Washington

Director, Atlanta University Center Data Science Initiative

Dr. Talitha Washington is the inaugural Director of the Atlanta University Center Data Science Initiative. This new initiative seeks to provide data-driven solutions to current and emerging societal problems, especially as it pertains to the African American community. Poised to bring... Read More →

Karoline Pershell

COO and Director of Strategy & Evaluation, Service Robotics & Technologies

Karoline Pershell received her B.S. in Mathematics from the University of Tennessee at Martin, where she was a member of the UTM Rodeo Team as the first full time female bull rider in the collegiate circuit. She received her M.S. and Ph.D. in Mathematics from Rice University. Following... Read More →

Friday January 22, 2021 5:45pm - 6:45pm CST
Zoom

Zoom Meeting, Panel Discussion

8:00am CST

Conference General Information Room

If you need technical assistance or have general questions, you can join the Conference Information Meeting Room.

Saturday January 23, 2021 8:00am - 8:00pm CST
Zoom

Optional Zoom Meeting

8:30am CST

Networking Coffee and Conversations

Saturday January 23, 2021 8:30am - 9:15am CST
Zoom

Optional Zoom Meeting, Networking

9:15am CST

Session 1 - A Discrete Event Simulation Model to Overcome Human Trafficking in the U.S. and the State of Nebraska

Human trafficking is a complex issue that affects society and the global economy, which involves the commercial exchange and exploitation of people through forced labor, domestic servitude, and sex trade, and is considered the third-most profitable organized crime in the world. Nebraska and the U.S. are not excluded from this societal issue, and Omaha is one of the main hubs for human trafficking in the state. By analyzing the flow of monetary gains/resources, information, and trafficked people from the perspective of traffickers, police force, and advocacy organizations, this research project develops a discrete event simulation model to represent this complex system. Different scenarios are proposed, and the main goal is to block the monetary flow and minimize the number of trafficked humans within the trafficking ring over the years. To achieve this goal, these scenarios study how an increase in government funds and private organizations can maximize information and resources within the police force and advocacy organizations. The solution of this model can assist governmental organizations to create public policies to diminish the number of trafficked individuals in the U.S. and the state of Nebraska over the years.

Speakers

Sydney Meier

Junior, University of Nebraska at Omaha

Sydney Meier, contacted at sydneymeier@unomaha.edu, is pursuing a double degree in Mathematics and Women’s and Gender Studies and minors in Human Rights and Information Management Systems. Sydney is very passionate about humanitarian issues and hopes to apply Operations Research... Read More →

Meier Human Trafficking Simulation pptx

Saturday January 23, 2021 9:15am - 9:30am CST
Zoom

Zoom Meeting Room A, Undergraduate Talk

Talk Subject Applied Mathematics

9:15am CST

Session 1 - Using Modeling to Characterize Patients with Pulmonary Hypertension

Pulmonary hypertension is a deadly disease characterized by high blood pressure above 25 mmHg in the pulmonary arteries. For this study, we use mathematical modeling to simulate and analyze right heart catheterization data from five patients diagnosed with pulmonary hypertension. To assess hemodynamics, we develop a compartment model analogous to an electric circuit in order to predict the flow, pressure, and volume of the cardiovascular system. This closed-loop cardiovascular system estimates model parameters that minimize the difference between model predictions and right-heart catheterization data from 5 patients. We use sensitivity analysis, covariance analysis, and parameter subset selection in order to determine a set of identifiable parameters that are fitted specific to each data from each of the 5 patients. Results show that hypertensive patients have increased pulmonary vascular resistance and decreased compliance compared to normotensive control patients. By simulating pulmonary hypertension treatments, we can achieve normotensive pressure values in both the right ventricle and pulmonary artery, while simultaneously reducing the pressure in the right atrium and systemic arteries. Since pulmonary hypertension is a chronic and progressive disease, recognizing the distinguishing features of a hypertensive network can facilitate diagnosis and improve treatment strategies.

Speakers

Mariam Kharbat

Senior, North Carolina State University

Saturday January 23, 2021 9:15am - 9:30am CST
Zoom

Zoom Meeting Room B, Undergraduate Talk

Talk Subject Applied Mathematics

9:15am CST

Session 1 - Critical groups of directed cones over cycle graphs

For any graph, we can determine a group known as the critical or Jacobian group, which takes the form of a Cartesian product of cyclic groups. The cone of a graph is the graph formed when a vertex is added and connected by an undirected edge to each existing vertex. We look at a specific class of directed graphs and the affect on the Jacobian group when we take the nth iterated cones of such graphs.

Speakers

Gabrielle Stokely

Junior, Lawrence University

Saturday January 23, 2021 9:15am - 9:30am CST
Zoom

Zoom Meeting Room C, Undergraduate Talk

Talk Subject Graph Theory

9:15am CST

Session 1 - Elliptic Curves and the Probability of Prime Torsion

Elliptic Curves are the research focus of several disciplines. But what are they? And why are they so special? It turns out that depending on how you define an elliptic curve, they are particularly interesting to those who study them in the context of cryptography. A commonly considered question in public-key cryptography is the discrete logarithm problem. As with many cryptography problems, one is particularly interested in groups for which there is no efficient way to solve it. One example is the groups of rational points on elliptic curves over finite fields.

In this talk, I will discuss the probability that an elliptic curve defined over a finite field has a rational point of prime order. In order to do so, we will review some key concepts and background material to gain a fundamental understanding of elliptic curves. Then, I will lead you through the derivation of combinatorial formulas to describe this probability.

Speakers

Zoe Daunt

Tutor/Mentor, Bridge to Calculus

Elliptic Curves NCUWM pdf

Saturday January 23, 2021 9:15am - 9:30am CST
Zoom

Zoom Meeting Room D, Undergraduate Talk

Talk Subject Algebra

9:35am CST

Session 1 - A Quantitative Analysis on Bitcoin Perpetual Inverse Futures Contract

The perpetual inverse futures contract is a recent and popular cryptocurrency derivative on crypto exchanges. Though the contract is perpetual, exchanges implement a liquidation mechanism that terminates positions that no longer fulfill maintenance requirements. Therefore, understanding liquidation will help investors optimize the use of leverage for maximizing profitability and minimizing risks; it will also benefit researchers in understanding the design of crypto derivatives. In this study, I used both theoretical and empirical approaches to quantify how factors such as the leverage of a position and volatility of Bitcoin/USD exchange rate increase the risks of liquidation. To do so, I used regression, stochastic calculus, and simulation methods to estimate the expected time and probability of liquidation.

Speakers

Yue Wu

Senior, Carnegie Mellon University

Research Slides Yue Wu v2 pdf

Saturday January 23, 2021 9:35am - 9:50am CST
Zoom

Zoom Meeting Room A, Undergraduate Talk

Talk Subject Applied Mathematics

9:35am CST

Session 1 - Analysis of Monte Carlo Tree Search Methods in a 2D Lattice Search Detection Problem

Monte Carlo Tree Search (MCTS) is an artificial intelligence game player method that uses many simulations to learn about a decision space and choose the best move based on a balance of exploration and exploitation. We apply this theory to a simple game of search and detection, using one stationary target and one moving searcher in a 2D lattice with periodic boundaries. Through simulated data and theoretical proofs we show that the MCTS performs optimally when the target is from a known delta distribution and it performs as a nearly self-avoiding random walk when the target distribution is uniform.

Speakers

Elana Kozak

Senior, United States Naval Academy

Saturday January 23, 2021 9:35am - 9:50am CST
Zoom

Zoom Meeting Room B, Undergraduate Talk

Talk Subject Combinatorics

9:35am CST

Session 1 - Finding Minimum Dominating Sets on Three-Dimensional Grid Graphs

A dominating set in a graph is a set of vertices with the property that every vertex in the graph is either in the set or is adjacent to a vertex in the set. A minimum dominating set of a graph is one whose cardinality is as small as possible, and the cardinality of such a set is called the domination number of the graph. In general, finding the domination number of large graphs can be computationally difficult. In this project, we considered a specific family of graphs: three-dimensional grid graphs. Our method was to create integer programming models that would attempt to optimize placement of dominating vertices in the grid. The results led to the identification of patterns, and the patterns in some cases led to proofs of exact numbers. In this talk, I will discuss our models, demonstrate some interesting patterns, establish some exact results, and conjecture several others.

Speakers

Devon Waskiewicz

Senior, Furman University

Saturday January 23, 2021 9:35am - 9:50am CST
Zoom

Zoom Meeting Room C, Undergraduate Talk

Talk Subject Graph Theory

9:35am CST

Session 1 - Coxeter groups and the Bruhat Order

We examine Coxeter groups, specifically the symmetric group, through a combinatorial lens. Furthermore, we present properties of intervals in posets on type A Coxeter groups. In Type A (the symmetric group), it is known how and when a principal order ideal of some permutation w is isomorphic to a generic interval. In particular, if w is decomposable, then w does not force a factor. We investigate whether this same property also holds for type B Coxeter groups (the group of signed permutations).

Speakers

Lisa Johnston

Senior, Kalamazoo College

Coxeter Groups and the Bruhat Order pdf

Saturday January 23, 2021 9:35am - 9:50am CST
Zoom

Zoom Meeting Room D, Undergraduate Talk

Talk Subject Algebra

9:55am CST

Session 1 - An Unstructured Mesh Approach to Nonlinear Noise Reduction

In any type of data acquisition, the event of gathering undesirable noise along with desirable data is inevitable. To denoise signals originating from smooth, chaotic attractors, the Air Force Research Laboratory (AFRL) adapted the time-delay embedding theory of Takens' Theorem (1981) and the causation-detecting method of Convergent Cross Mapping (CCM) to develop a grid-based denoising technique. Given a clean signal from such a dynamical system, AFRL’s technique attempts to denoise a corrupted signal observed from the same system. To improve this grid-based method, we implement an unstructured mesh based on triangulations and Voronoi diagrams that better distributes data over mesh cells and improves the accuracy of the reconstructed signal. Our method achieves statistical convergence with known test data and reduces synthetic noise on experimental signals from Hall Effect Thrusters (HETs) with greater success than the grid-based strategy.

Speakers

Megan Osborne

Senior, University of Scranton

Saturday January 23, 2021 9:55am - 10:10am CST
Zoom

Zoom Meeting Room A, Undergraduate Talk

Talk Subject Applied Mathematics

9:55am CST

Session 1 - Economic Drivers in Modeling Pandemics

Kermack and McKendrick’s SIR model is a standard basis for epidemiological models. The model uses parameters, such as social distancing, vaccines, and treatments for a disease, to account for the aspects of our life that can affect the spread of a disease. Using this model, we find that social distancing is the most important factor in limiting the spread of a disease outbreak preventing an epidemic. Given the importance of social distancing, we expand the standard SIR epidemic model so it divides the population into three groups to account for the differences in possible disease exposure given an individual’s occupation and economic status. Next, we worked to create a model of the economy that could be coupled to our expanded SIRD model. The levels of social distancing and economic activity for various groups of the population vary based on socioeconomic status. As such, our model will show that an individual’s financial situation is an important predictor of how their health and future financial situation will be impacted by an epidemic. This helps us investigate whether public health policies are reasonable and effective in curbing an epidemic and mitigating its impact on the population as a whole.

Speakers

Miranda Reed

Senior, Western Washington University

Saturday January 23, 2021 9:55am - 10:10am CST
Zoom

Zoom Meeting Room B, Undergraduate Talk

Talk Subject Applied Mathematics

9:55am CST

Session 1 - Graph Coloring for the Assignment of Seats to Fans

Graph coloring, in which labels are assigned to elements of a graph in such a way that specified conditions are met, has many variations. We consider an application of graph coloring to the assignment of seats to sports fans. Each seat is represented by a vertex, and pairs of vertices associated with adjacent seats are connected by edges. Each team has a unique color. The vertices of the graph are colored, subject to certain constraints, to indicate the placement of fans in seats. For various families of graphs, we determine which collections of fans can be seated under the stated compatibility conditions, and we provide optimal assignments in the feasible cases. Fans supporting more than one team are also considered; this results in multi-colored vertices when seating arrangements are determined.

Speakers

Lam Doan

Senior, La Salle University

Hi,I'm a senior majoring in Mathematics and Secondary Education at La Salle University. I'm interesting in Geometry - Topology, Algebra, and Analysis. My career goal is working in academia, soI'm currently applying for graduate program. Besides math, I also like cooking, baking and... Read More →

Saturday January 23, 2021 9:55am - 10:10am CST
Zoom

Zoom Meeting Room C, Undergraduate Talk

Talk Subject Graph Theory

9:55am CST

Session 1 - Minimal Base Sizes of Symmetric Groups

This research explores how symmetric groups interact with different sets including: 2-sets, 3-sets, and 4-sets. More specifically, it seeks to find the minimal base size of symmetric groups acting on 2-sets, 3-sets, and 4-sets.

To achieve this goal, the project focuses on the number of elements necessary to form a base for each set. Using this idea, lower bound formulas were created. Looking at the arrangements of elements within the set allowed for the creation of upper bound formulas. Manipulating these formulas led to the development of the greatest lower bounds and least upper bounds. Through the use of these formulas minimal base sizes for 2-sets, 3-sets, and 4-sets were found.

Speakers

Ally Wilson

Senior, College of Saint Benedict

Saturday January 23, 2021 9:55am - 10:10am CST
Zoom

Zoom Meeting Room D, Undergraduate Talk

Talk Subject Algebra

10:15am CST

Session 1 - Analyzing, Predicting, and Mitigating Defect Formation in Metal Additive Manufacturing

Recent advances in metal additive manufacturing have made this technique a promising direction in industry for printing metal parts, such as for biomedical devices and automobile machinery. Despite its ability to efficiently print highly specific parts, this process is prone to errors during printing, causing pores to form in the metal part. These pores weaken the metal by increasing the likelihood of internal cracks forming. With current techniques implemented by HRL Laboratories, these defects are only able to be detected after printing, which impedes any efforts to correct these errors in real-time. In order to provide a real-time quality control framework, we developed a machine learning model that inputs the laser printing parameters and predicts whether a defect will form at a given location, which is informed by the X-ray images of the metal scanned after printing. This model provides an in-situ prediction for the formation of defects in real-time so that corrections can immediately be made. In addition to building this predictive model, we provide a semi-automated process for preprocessing and registering the X-ray images with the in-situ laser data.

Speakers

Julie Fucarino

Junior, IPAM/Wellesley College

DefectsMetalAM pdf

Saturday January 23, 2021 10:15am - 10:30am CST
Zoom

Zoom Meeting Room A, Undergraduate Talk

Talk Subject Applied Mathematics

10:15am CST

Session 1 - Digitizing Maine's Voting History with a Statistical Analysis of Error Rate

The purpose of my project, completed remotely via Bowdoin Summer Research Fellowships, was to digitize Maine voting data and analyze the error rate using three statistical tests. This research was done under the umbrella of my advisor's project: to create a single online resource for researchers that stores election data throughout Maine's history. Voting records were digitized through an Optical Character Recognition Software (OCR), ABBYY Finereader, and then converted to files that could be made public.

In the second part of the project, I plotted election results from different columns against one another, as the proportion of "yes" and "no" votes per town remained largely proportional (a column represents vote totals per question, and a row represents vote totals per town). I then used RStudio to create a line of best fit using a least squares regression which allowed me to identify original outliers in this patterns. I also calculated the p-values of each row of data, and flagged vote totals that fell out of the traditionally "acceptable range" for this test. The second test involved summing columns of voting results by town and comparing the result to the vote total noted on the original voting record, while the third used random-selection code on RStudio to check randomized entries.

My results suggest that the first two tests were very effective when used in tandem, as there were few errors identified in the third across all county sheets.

Speakers

Gillian King

Junior, Bowdoin College

Hello everyone! I am a junior at Bowdoin College in Brunswick, Maine. I am a Mathematics Major & Physics Minor, and am interested in studying Biostatistics in graduate school. I am giving a talk about my Summer 2020 research with Professor Jack O'Brien (Associate Professor of Mathematics... Read More →

Digitizing Maine’s Voting History with a Statistical Analysis of Error Rate (2) pptx

Saturday January 23, 2021 10:15am - 10:30am CST
Zoom

Zoom Meeting Room B, Undergraduate Talk

Talk Subject Statistics

10:15am CST

Session 1 - Jacobian Groups of Bipartite Digraphs

With a graph we can associate an algebraic structure called the Jacobian group, which can be expressed as a Cartesian product of cyclic groups. Patterns exist among the Jacobian groups of graphs within a given type. Some of these patterns are readily discovered and proven, while some require more investigation. We present one new such pattern regarding the Jacobian groups of complete bipartite digraphs on n,n vertices that were modified by removing a single directed edge.

Speakers

Miriam Syvertsen

Junior, Lawrence University

I'm a Junior math major at Lawrence University in Appleton, Wisconsin. I'm excited because this is my first experience at a larger undergraduate conference, and I look forward to connecting with others who share a main one of my interests. When I'm not doing math I like to play... Read More →

Saturday January 23, 2021 10:15am - 10:30am CST
Zoom

Zoom Meeting Room C, Undergraduate Talk

Talk Subject Graph Theory

10:15am CST

Session 1 - Forms of Golden-type Recursive Polynomials

In this talk we will present some properties of Fibonacci-type recursive polynomials. After introducing the classical Fibonacci-like polynomials and the so-called Golden polynomials, we introduce recursive polynomial sequences defined by G_{n+1}(x) = x^k G_{n}(x) + x^ℓ G_{n-1}(x), where k and ℓ are positive integers, G_{0} = -1, and G_{1} = x-1.

We discuss Binet forms, Pascal-like triangle representations, and matrix representations for G_{n}. We derive interesting sequences and identities.

Lastly, we present analytic and numerical results on the nature of the real roots of G_{n}. Our work extends known results for Fibonacci-like polynomials.

Speakers

Kristen Hallas

Student Assistant, The University of Texas Rio Grande Valley

Joan Mattle

Junior, Ithaca College

Deanna Perez

Junior, california state university, fullerton

Recursive Polynomials pdf

Saturday January 23, 2021 10:15am - 10:30am CST
Zoom

Zoom Meeting Room D, Undergraduate Talk

Talk Subject Algebra, Number Theory

11:00am CST

Session 2 - Assessment of mitigation strategies for Sars-CoV-2 using a mathematical epidemiological model

The first reported case from COVID-19 in Puerto Rico occurred on March 13, 2020, after the Costa Luminosa Cruises arrived. As the epidemic progresses, the governor implemented various executive orders to safeguard the citizens' lives. SMICRC was established by a group of young epidemiologists and statisticians to contact trace and cut transmission chains by identifying infected cases and possible contacts. All these measures are considered non-pharmaceutical interventions, and they directly affect the course of the epidemic. We aim to analyze the effectiveness of the actions taken to mitigate the virus based on data behavior. An epidemiological mathematical model was developed to understand the epidemic evolution. The data was retrieved directly from the Health Department to determine new cases and deaths per day. As preliminary results, after applying releasing measures in the executive orders, an increase in new cases is evident. In six months, April to September 2020, the month with more confirmed new cases was in August and more confirmed deaths in September. As data and the decisions taken re-shape the epidemic curve, we are not close to being over on this battle against the COVID-19 epidemic in Puerto Rico.

Speakers

Frances Aponte-Caraballo

Senior, University of Puerto Rico at Cayey

Frances M. Aponte Caraballo has a BA in biology and a minor in Mathematics, in progress, at the University of Puerto Rico in Cayey. Also, certified in ethics, HIPAA, and IRB. She currently serves as president of T-MED, a student organization in the Department of Biology, specializing... Read More →

Saturday January 23, 2021 11:00am - 11:15am CST
Zoom

Zoom Meeting Room A, Undergraduate Talk

Talk Subject Applied Mathematics

11:00am CST

Session 2 - Random Walk on the English Language Dictionary

The English language dictionary, consisting of approximately 171,000 words, is a common tool for linguists, writers, and Scrabble players everywhere. We take the English language dictionary and study it from a mathematical perspective by phrasing it as a random walk problem. A random walk on the dictionary would consist of a random walk on a graph where nodes represent words that are connected if they share some property. For example, we could define two words to be connected if they share any common letters. In order to create and study such graphs, we begin by analyzing random walks on a much smaller subset of words. We analyze such properties of the random walk as time to stationarity, hitting time, commute time, and cover time. These properties provide understanding toward answering questions such as what percentage of words our random walk covers and where we would have to start to cover a maximum number of words. We talk about our progress toward extending these smaller problems to a random walk on the entire English language dictionary.

Speakers

Shraddha Shankar

Senior, Denison University

Saturday January 23, 2021 11:00am - 11:15am CST
Zoom

Zoom Meeting Room B, Undergraduate Talk

Talk Subject Statistics

11:00am CST

Session 2 - On Deleting Directed Graphs

Sylver Slayer is a 2-player game played on directed graphs, inspired by Conway’s game Sylver Coinage, with the goal being to eliminate the digraph. We will present new results on families of digraphs that can be eliminated by any initial choice of vertex.

Speakers

Chloe Frechette

Senior, Northern Arizona University

Saturday January 23, 2021 11:00am - 11:15am CST
Zoom

Zoom Meeting Room C, Undergraduate Talk

Talk Subject Graph Theory

11:00am CST

Session 2 - Lie-derivations of three-dimensional Leibniz algebras

The concept of derivations play an important role in understanding algebraic structures such as Leibniz algebras, which are a generalization of Lie algebras in which the bracket operation is not necessarily skew symmetric. A new notion of derivations, namely L-derivations, was recently introduced as a generalization of the notion of derivations for non-L Leibniz algebras, relying on the fact that the quotient space g/b(g) of a Leibniz algebra g by the two-sided ideal b(g) is a Lie algebra, where b(g) := <[x,x]~x∈ g> is referred to as the Leibniz kernel of g. In this talk, we will discuss how to determine the Lie algebras of \Lie-derivations of non-Lie Leibniz algebras. Our calculations will focus on the case of three-dimensional non-Lie Leibniz algebras in which we completely determine the basis of the Lie algebras of \Lie-derivations and classify the basis elements as inner or outer derivations.

Speakers

Emily Howe

Senior, Georgia College and State University

I'm Emily, a mathematics student at Georgia College and State University. I'm honored to be speaking at the Conference for Undergraduate Women in Mathematics about my research!

Saturday January 23, 2021 11:00am - 11:15am CST
Zoom

Zoom Meeting Room D, Undergraduate Talk

Talk Subject Algebra

11:20am CST

Session 2 - Effects of Mars' Obliquity on Ice Cover: A Budyko Model Approach

Studies suggest that the evolution of Mars' rotational axis is chaotic and may have varied by as much as 60 degrees over its history. This large and unpredictable range in the orientation of the planet makes Mars' climate history uncertain. A planet's climate largely depends on the characteristics that describe the planet's specific orbit. Specifically, in the case of Mars, its obliquity, which refers to the angle of the tilt of its rotational axis, has a prominent role in the extent of ice cover on the Martian surface. Ice cover is particularly interesting due to its potential implications from geological and biological perspectives. To observe how Mars' changing obliquity potentially impacted ice cover dynamics over time, we use an obliquity-dependent energy balance model examining the incoming and outgoing energy. In this talk, we will discuss our simulations of Mars climate and the different resulting ice regimes. We find that as obliquity changes, there are large oscillations in polar ice cover. We see certain regions of parameter space where the model indicates stable oscillations between partial ice cover and ice-free states. The model also shows no stable partial ice cover on the Martian surface with the poles being ice-free.

Speakers

Anushka Narayanan

Junior, Cornell University

Saturday January 23, 2021 11:20am - 11:35am CST
Zoom

Zoom Meeting Room A, Undergraduate Talk

Talk Subject Applied Mathematics

11:20am CST

Session 2 - Using statistical models to analyze trap color and location for effective capture of Velvet Longhorn

Velvet Longhorned Beetles, an invasive species native to Asia, have spread to North America and are causing damage to orchards, forests, and other plant life. In order to mitigate their destructive habits, we worked with researchers to evaluate different traps used to capture the beetles. Specifically, we compared the trap color (black, purple, green) and trap location (ground versus raised). To assess which traps were most effective, negative binomial mixed effects models were fit to these data, which indicated that black traps and high traps proved to be the most effective. The United States Department of Agriculture funded this research, and the results of this study will be submitted for publication early next year.

Speakers

Ashley Weeks

Senior, Furman University

Saturday January 23, 2021 11:20am - 11:35am CST
Zoom

Zoom Meeting Room B, Undergraduate Talk

Talk Subject Statistics

11:20am CST

Session 2 - Spectral Touching Points in 2 Dimensional Materials

In recent years, graphene has gained significant popularity as a building material and energy storage medium with a wide variety of applications. One of graphene’s most unique properties is its conductivity, which is enhanced by mass-less fermions that enable loss-less electron transfer across a graphene sheet. Previous researchers [Novoselov (2011)] have conjectured a potential relation between a special type of spectral touching point, Dirac conical points, and the unique properties of graphene, although this has yet to be formally proven. Further research from T. Weyand (2014) and R. Martin (2017) found that variations of graphene also have these touching points. I expand upon this idea by searching for other materials possessing spectral touching points, which may indicate the presence of properties similar to those of graphene. I verify the existence of these touching points by modeling a material as a 2-dimensional infinite periodic graph, the spectrum of which can be found using Floquet-Bloch theory. I find the fundamental domain of this graph, find the corresponding magnetic flux Schrodinger operator, and then take the union over all possible values of magnetic flux. This allows me to graph the infinite spectrum and search for touching points, which indicate repeated eigenvalues. I then verify touching points by calculating the eigenvalues and eigenvectors at probable locations to show that there exist linearly independent eigenvectors for the same eigenvalue. In my presentation, I will explain how, using the methods described above, I found examples of these materials and proved the existence of various types of touching points within them under different symmetry conditions.

Speakers

Andrea Wynn

Junior, Rose-Hulman Institute of Technology

Hi! My name is Andrea. I’m a junior at Rose-Hulman studying Computer Science, Software Engineering, and Mathematics (Discrete Mathematics Concentration). My goal is to put my skills to use in a challenging, rewarding environment and make a meaningful impact while learning more about... Read More →

Saturday January 23, 2021 11:20am - 11:35am CST
Zoom

Zoom Meeting Room C, Undergraduate Talk

Talk Subject Graph Theory

11:20am CST

Session 2 - Chains and Antichains in the Bipartite Cambrian and Tamari Lattice

Dillworth's Theorem states that the maximal size of an antichain is equal to the minimal number of chains needed to cover the partially ordered set. We study the Greene-Kleitman partition of c-Cambrian lattices of type A. We partially compute the Greene-Kleitman partition of the Bipartite Cambrian Lattice. We also study the Greene-Kleitman partition for the Tamari Lattice, a popular poset given by triangulations of polygons and the Catalan numbers. We give a lower bound for the size of a largest antichain for the Tamari Lattice.

Speakers

Rose Silver

Senior, Northeastern University

Saturday January 23, 2021 11:20am - 11:35am CST
Zoom

Zoom Meeting Room D, Undergraduate Talk

Talk Subject Combinatorics

11:40am CST

Session 2 - Image Segmentation via Hypergraphs using k-Means Clustering

Image processing techniques have continued to advance to keep up with complex data sets generated by experimental facilities. The Advanced Light Source at Lawrence Berkeley National Laboratory houses a micro-tomography instrument which uses X-rays to visualize cross-sections of the object and recreate it as a virtual 3D model. Medical imaging utilizes this technique due to its ability to see inside an object without destroying it. Segmentation is an image processing technique used to create a simplified representation of the image so that it is more meaningful and easier to analyze. This research develops a hypergraph-based image segmentation algorithm that can be parallelized to handle large volumes of data. This algorithm is built off the Parallel Markov Random Field (PMRF) graph-based image segmentation algorithm. We build a hypergraph model of the image using the k-means clustering algorithm. The hyperedges are then augmented to respect the graph partitions used in the PMRF model, which allows for parallel computations. When optimizing the associated energy function, we incorporate a higher-order term which calculates the energy from the hypergraph model. When applied to micro-CT images from the Berkeley Sandstone Data Set, this algorithm shows improved accuracy compared to previously tested algorithms.

Speakers

Darcy Brunk

Senior, California State University, Stanislaus

Saturday January 23, 2021 11:40am - 11:55am CST
Zoom

Zoom Meeting Room A, Undergraduate Talk

Talk Subject Applied Mathematics

11:40am CST

Session 2 - Accordion Solitaire

Accordion Solitaire is a complex single player card game in which the player aims to consolidate a standard 52-card deck into one pile. To begin, the player randomly deals all 52 cards face up in a straight line. Throughout the game, cards that meet certain conditions shift leftward to cover other cards, thus compressing the deck like an accordion. The game concludes when there are no more available moves. We use mathematical concepts from areas such as graph theory, algebra, and statistics to develop winning strategies and algorithms for this game.

Speakers

Samantha Dukes

Senior, Furman University

Hello, my name is Samantha and I am a senior Applied Mathematics and Music double major at Furman University in Greenville, SC. At Furman, I am a leader in many extracurricular activities. I am the Music Director of the FUTones coed acapella group, the New Member Chairman for the... Read More →

Saturday January 23, 2021 11:40am - 11:55am CST
Zoom

Zoom Meeting Room B, Undergraduate Talk

Talk Subject Recreational Mathematics

11:40am CST

Session 2 - Throttling for standard zero forcing on directed graphs

Zero forcing is a coloring process performed on a graph with initially blue and white vertices. The color change rule is applied repeatedly: a blue vertex u can force a white vertex w to become blue if w is the only white neighbor of u. This coloring procedure has connections to the inverse eigenvalue problem and has applications to PMU placement in electrical engineering and quantum control in physics. Throttling is a process that gives the optimal balance of resources and time when zero forcing. In particular, the throttling number of a graph minimizes the sum of the number of vertices initially blue and the number of time steps needed to color every vertex blue. The process of zero forcing can also be extended to directed graphs in which a white vertex w can be forced if it is the only white out-neighbor of a blue vertex u. In this talk, we demonstrate how this extension motivates throttling for directed graphs and present some recent results.

Speakers

Emily Cairncross

Senior, Oberlin College

I am a senior Mathematics major at Oberlin college with minors in Computer Science, Hispanic Studies, and Linguistics. So far, I've done some work in coding theory/algebraic geometry, graph theory (zero forcing and throttling), and extremal combinatorics. This is my second time at... Read More →

Emily Lopez

Junior, University of California, Santa Barbara

I am a third year mathematics major at UC Santa Barbara (UCSB) College of Creative Studies (CCS) from Santa Clarita, California and a first generation college student. I am also a McNair Research Fellow working on a linear optimal transport project with UCSB Mathematics Professor Katy Craig. My research interests are in optimal transport, applied mathematics, and graph theory... Read More →

Ashley Zhuang

Sophomore, Harvard University

Hi! I'm an undergraduate student at Harvard University studying Computer Science and Mathematics.

Saturday January 23, 2021 11:40am - 11:55am CST
Zoom

Zoom Meeting Room C, Undergraduate Talk

Talk Subject Graph Theory

11:40am CST

Session 2 - Enumerating "Good" Permutations

Two permutations π and σ are said to be order isomorphic if they are equivalent after pattern reduction, in other words, if they are in the same relative order. We call a permutation “good” if its first ℓ entries are order isomorphic to the last ℓ entries. Given a k, we wish to enumerate all good permutations on [k]. This will enable us to enumerate those pairs of permutations that overlap consecutively and which are order isomorphic. We do this for whenever ℓ ≤ k/2 and via experimentation we conjecture that whenever ℓ > k/2 the number of good permutations is polynomial in k - ℓ. We also make a connection of enumerating good permutations to the problem of explicitly determining the expected number of distinct permutation patterns contained in a random permutation.

co-authors: Austin Allen, Sebastian Papanikolaou-Costa, Christopher Soto

Speakers

Vonnie Dobbs

Marquette University

Lino Yoshikawa

Junior, University of Hawaii at Hilo

Saturday January 23, 2021 11:40am - 11:55am CST
Zoom

Zoom Meeting Room D, Undergraduate Talk

Talk Subject Algebra, Combinatorics

12:00pm CST

Session 2 - Influential nodes detection on complex networks via network topology

Identifying influential nodes in complex network is an important graph mining problem that has wide applications in many areas such as market advertising and rumor controlling. Nodes in a network can have varying roles in information diffusion. In this research project, we use the diffusion Frechet function (DFF), a function that leverages network topology and is robust to noise in data, to identify the most influential nodes in networks. We apply our method to various real-world network datasets to identify influential nodes. Its performance is then compared to that of the classical graph-theoretic centrality measures using the Susceptible-Infected-Recovered (SIR) simulation model. Our experimental results suggest that our method is promising in influential nodes detection and more effective than the classical centrality measures.

Speakers

Sidra Jawaid

Undergraduate Presenter, University of Central Oklahoma

Saturday January 23, 2021 12:00pm - 12:15pm CST
Zoom

Zoom Meeting Room A, Undergraduate Talk

Talk Subject Applied Mathematics

12:00pm CST

Session 2 - Not Your Normal Fibonacci Sequence

The Fibonacci sequence is perhaps the most well-known sequence in the field of mathematics. In the Fibonacci sequence each element in the series is the sum of the previous two numbers. We will denote the first two numbers in the series as a and b, where a is less than or equal to b. Given a number n, we seek to find the smallest positive value b such that n appears in the Fibonacci series starting with a and b. One can determine a and b given n by performing an exhaustive search for various combinations of a and b. We investigate quicker methods than this brute force approach for n values with certain properties.

Speakers

Montana Ferita

Senior, Westminster College (PA)

Hello! I am a senior at Westminster College in Pennsylvania. In addition to being a mathematics major, I have a minor in data science and theater. Currently, I am in the process of applying to PhD programs to study mathematical biology.

Saturday January 23, 2021 12:00pm - 12:15pm CST
Zoom

Zoom Meeting Room B, Undergraduate Talk

Talk Subject Recreational Mathematics

12:00pm CST

Session 2 - Total Roman Domination of Kneser Graphs

In graph theory, Total Roman Domination (TRD) colors every vertex in a graph with a 0, 1, or 2 by specific rules that originate from Roman military strategy. The TRD-number γ_{tR}(G), or "weight" of a graph, is the smallest possible sum of all the vertices' numbers that follow TRD rules. In this talk, we discuss strategies for finding the TRD-number of generalized Kneser graphs, a type of graph of which the Petersen graph is a well-known example, and we will demonstrate some explicit bounds. We will begin with some basic definitions of graphs, domination, and the "rules" for Total Roman Domination.

co-authors: Sviatlana Kniahnitskaya, Benjamin Nored, Dr. Katharine Shultis, Dr. Hays Whitlatch

Speakers

Amanda Mallott

Senior, Gonzaga University

Hello! I'm a senior at Gonzaga University majoring in math with a minor in communication studies. I'm intending to go on to graduate school next year, and hope to eventually teach undergraduate-level mathematics. I hope to meet you at the conference!

Saturday January 23, 2021 12:00pm - 12:15pm CST
Zoom

Zoom Meeting Room C, Undergraduate Talk

Talk Subject Graph Theory

12:00pm CST

Session 2 - Games of Best Choice: The Hiring Problem

We explore the strategies to solve the classical version of the scenario called the Secretary Problem, in which an administrator is looking to hire the best candidate from a pool of applicants. After interviewing each candidate individually, the administrator must immediately make a decision to hire or reject the current applicant. The Secretary Problem asks us to consider the probability that the administrator hires the best candidate given the above constraints. Our project focused on first understanding the classical scenario and the known optimal 37% solution and proof. We then explored concepts of incentive compatibility and top t choices. Incentive compatibility was used to look at the optimal solutions to stay and go probabilities, as well as to compare strategies to each other. Whereas the classical Secretary Problem looks at the probability of choosing the best or top one candidate, we looked at how strategies changed when top two, three, or more candidates were considered desirable. Python was used to look at larger probability trees in order to avoid human error and provide a faster computation device for the probabilities.

Speakers

Uyanga Naranbaatar

Junior, Concordia College, Moorhead

Eliana Rutherford

Sophomore, Concordia College - Moorhead

Saturday January 23, 2021 12:00pm - 12:15pm CST
Zoom

Zoom Meeting Room D, Undergraduate Talk

Talk Subject Combinatorics

2:00pm CST

2nd Plenary Talk: "Reconfiguration in Graph Coloring," Ruth Haas

Reconfiguration in Graph Coloring (and other contexts)

In mathematics, as in life, there are often multiple solutions to a question. Reconfiguration studies whether it is possible to move from one solution to another following a given set of rules. Is it possible? How long will it take? In this talk, we will consider reconfiguration of graph coloring as well as reconfiguring a mathematical life.

Here's a mathematical description of the graph theory part of the talk: A proper coloring of a graph is an assignment of a color to each vertex of the graph so that neighboring vertices have different colors. Suppose we change the color of just one vertex in a graph coloring. Can we get from one coloring to another by a sequence of vertex changes so that each step along the way is a proper coloring? The answer is yes, if we are allowed an unlimited number of colors. But, what is the fewest colors we can have for this to work? How many steps might it take? We will look at this, related questions and variations.

Speakers

Ruth Haas

Professor of Mathematics; President, AWM, University of Hawaii, Mānoa

Saturday January 23, 2021 2:00pm - 3:00pm CST
Zoom

Zoom Meeting, Plenary Talk

3:30pm CST

Breakout Session 1: Full Listing with Zoom Links

Undergraduates can choose to attend any breakout but if a Zoom room has more than 80 people already in attendance we encourage you to select a different breakout to get a small-group experience. Faculty and graduate students are welcome to attend any of the breakout sessions or have been asked to facilitate a session.

Applying to Grad School I: If you have not yet applied to graduate programs, this discussion will give you details of the application process, information about the general and math subject Graduate Record Examinations, and the types of courses you should be taking at your undergraduate institution to prepare for graduate school. https://unl.zoom.us/j/96235376693

Careers with a Bachelor's Degree I: Discover your career options with a Bachelor's Degree in Mathematics, and how your mathematical background can help you get a job in industry or the government sector. This session will also cover the logistics of how to go back to school to pursue a graduate degree after working in industry. https://unl.zoom.us/j/93079306855

Getting Ready for Grad School I: Have you decided that graduate school is the path you are going to pursue? This discussion will cover how to make the most of recruitment visits and understanding the logistics of accepting offers. https://unl.zoom.us/j/96643356699

Research in Mathematics I: Learn about the differences between mathematical research at the graduate level, mathematical research encountered as part of an undergraduate research experience, and coursework. This session will also cover how to choose a research topic and help to define what progress is in regard to research. https://unl.zoom.us/j/98961161108

Summer Opportunities for Undergraduates I: If you think the summer is a time to continue your educational journey, this session will provide information about summer programs all over the country for undergraduates at various stages of their educational careers. https://unl.zoom.us/j/95807155286

The Confidence Gap I: This session will discuss the findings from the article and give strategies on how to build and strengthen mathematical confidence in an historically male-dominated field. https://unl.zoom.us/j/95991965846

Being a Mathematician from an Underrepresented Group: Join a discussion about being a mathematician from an underrepresented group in a graduate program or workplace, and how to succeed in that environment. https://unl.zoom.us/j/93454399944

Being a Non-Traditional Student: This session is for those who consider themselves a nontraditional student and are interested in hearing how other students in similar situations have transitioned into graduate school. https://unl.zoom.us/j/99239578784

Juggling Graduate School and Your Social Life: Most students find that graduate coursework is much more demanding than undergraduate coursework. This session will discuss how to maintain a healthy balance between work and play while in graduate school, and how to avoid burnout. https://unl.zoom.us/j/99192821069

Math Club Activities: Join a discussion covering how to start a math club, how to recruit members and how to plan appropriate activities for your math club. https://unl.zoom.us/j/94217159202

Opportunities in Math Education: This session will cover opportunities in mathematics education ranging from pursuing graduate-level work in math education to finding jobs in industry specifically geared toward those interested in math education. https://unl.zoom.us/j/96402268142

Writing a Resume or CV: This session will explore the similarities and differences between a resume and CV, when one is more appropriate to submit than the other, and outline proper formatting and content. https://unl.zoom.us/j/92238637731

Saturday January 23, 2021 3:30pm - 4:30pm CST
Zoom

Zoom Meeting, Breakout

4:40pm CST

Breakout Session 2: Full Listing with Zoom Links

Applying to Graduate School II: If you have not yet applied to graduate programs, this discussion will give you details of the application process, information about the general and math subject Graduate Record Examinations, and the types of courses you should be taking at your undergraduate institution to prepare for graduate school. https://unl.zoom.us/j/92722120259

Careers with a Bachelor's Degree II: Discover your career options with a Bachelor's Degree in Mathematics, and how your mathematical background can help you get a job in industry or the government sector. This session will also cover the logistics of how to go back to school to pursue a graduate degree after working in industry. https://unl.zoom.us/j/99013746561

Getting Ready for Grad School II: Have you decided that graduate school is the path you are going to pursue? This discussion will cover how to make the most of recruitment visits and understanding the logistics of accepting offers. https://unl.zoom.us/j/98164134107

Research in Mathematics II: Learn about the differences between mathematical research at the graduate level, mathematical research encountered as part of an undergraduate research experience and coursework. This session will also cover how to choose a research topic and help to define what progress is in regard to research. https://unl.zoom.us/j/95990277280

Summer Opportunities for Undergraduates II: If you think the summer is a time to continue your educational journey, this session will provide information about summer programs all over the country for undergraduates at various stages of their educational careers. https://unl.zoom.us/j/91459015792

The Confidence Gap II: A 2014 article in The Atlantic states, "Evidence shows that women are less self-assured than men; and that to succeed, confidence matters as much as competence." This session will discuss the findings from the article and give strategies on how to build and strengthen mathematical confidence in an historically male-dominated field. https://unl.zoom.us/j/94336244810

Being a Graduate Student and a Parent: Are you concerned about how to balance graduate school and a family? This discussion will allow you to hear about others' experiences and their solutions to issues such as the "two-body problem" and childcare. https://unl.zoom.us/j/98576214990

Building on Online Presence: Having an online presence can be beneficial in finding jobs and sharing research ideas. This session will explore different platforms of social media and blogs for scholars and discuss social media etiquette as well as how to have an effective account or website. https://unl.zoom.us/j/92911964170

Identifying Microaggression in the Mathematical Community: Microaggressions are described as the everyday slights, insults, put-downs, and assumptions that communicate some sort of bias toward historically marginalized groups. The difference between microaggressions and overt discrimination is that people who commit microaggressions might not even be aware of them. https://unl.zoom.us/j/97573332663

Leading a Happier College Life: This discussion helps to identify the signs and symptoms of common mental health issues for college students and where and when to seek help when experiencing emotional troubles. https://unl.zoom.us/j/94843382553

Opportunities in Statistics: This session will cover opportunities in statistics ranging from pursuing graduate-level work in statistics to finding jobs in industry specifically geared toward those interested in statistics. https://unl.zoom.us/j/96785231285

Various Teaching Opportunities: This session will cover the general requirements needed to teach mathematics at the high school level, community college level, small college/university level and large research institution level. This session will also cover the differences in teaching load and types of courses at each type of institution. https://unl.zoom.us/j/94651652339

Saturday January 23, 2021 4:40pm - 5:40pm CST
Zoom

Zoom Meeting, Breakout

7:00pm CST

Faculty Networking

Faculty and guests not hosting a breakout room in the undergraduate event during this same time are invited to stop by our faculty networking Zoom room!

Moderators

Christine Kelley

Professor of Mathematics, NCUWM Co-Chair, University of Nebraska-Lincoln

Saturday January 23, 2021 7:00pm - 8:00pm CST
Zoom

Zoom Meeting, Networking

7:00pm CST

Networking with Invited Guests: Breakout Room Listing

Read bios for each of the breakout room hosts here: https://www.math.unl.edu/~ncuwm/23rdAnnual/resources/

Breakout Rooms by Number
1 - Cecilia Aragon, Plenary Speaker, University of Washington, Seattle
2 - Ruth Haas, Plenary Speaker, University of Hawaii, Mānoa
3- Talitha Washington, Plenary Speaker, Atlanta University Center Data Science Initiative, and Clark Atlanta University
4 - Karoline Pershell, Panelist, Service Robotics & Technologies
5 - Julia Read-LaBelle, Panelist, Nike, Inc.
6 - Shanise Walker, Panelist, University of Wisconsin-Eau Claire
7 - Laura White, Panelist, NASA Langley Research Center
8 - Martha Yip, Panelist, University of Kentucky
9 - Hayley Bertrand, Invited Grad, Indiana University Bloomington
10 - Nicole Buczkowski, Invited Grad, University of Nebraska-Lincoln
11 - Maryam Khaqan, Invited Grad, Emory University
12 - Rachel Knak, Invited Grad, The University of Arizona
13 - Gage Martin, Invited Grad, Boston College
14 - Mackenzie Simper, Invited Grad, Stanford University
15 - Alexandra Seceleanu, Faculty, University of Nebraska-Lincoln and Susan Hermiller, Faculty, University of Nebraska-Lincoln
16 - Alex Zupan, Faculty and NCUWM Co-Chair, University of Nebraska-Lincoln
17 - Kimberly Shurupoff, Panelist, NSA
18 - Tomek Bartoszynski, Invited Guest, NSF, and Eun Heui Kim, Invited Guest, NSF
19 - Lara Ismert, Invited Guest, Embry-Riddle Aeronautical University
20 - Undergraduate Networking (hosted by UNL graduate student Vince Longo)

Speakers

Cecilia Aragon

Professor and Director, Human Centered Data Science Lab; Professor, Human Centered Design & Engineering, University of Washington

Ruth Haas

Professor of Mathematics; President, AWM, University of Hawaii, Mānoa

Talitha Washington

Director, Atlanta University Center Data Science Initiative

Karoline Pershell

COO and Director of Strategy & Evaluation, Service Robotics & Technologies

Julia Read-LaBelle

Global Supply & Inventory Analyst, Nike, Inc.

Shanise Walker

Assistant Professor of Mathematics, University of Wisconsin-Eau Claire

Laura White

Aerospace Engineer, NASA Langley Research Center

Martha Yip

Assistant Professor of Mathematics, University of Kentucky

Hayley Bertrand

Graduate Student (Invited), Indiana University

Hayley Bertrand is a fourth-year graduate student at Indiana University studying algebra, especially in the topological setting, under Dr. Ayelet Lindenstrauss. She received her bachelor’s in mathematics from St. Norbert College in 2017 and her master’s in mathematics from Indiana... Read More →

Nicole Buczkowski

Graduate Student (Invited), University of Nebraska-Lincoln

Nicole Buczkowski is a fourth-year graduate student at UNL and is advised by Petronela Radu and Mikil Foss studying nonlocal models. She obtained her B.S. in mathematics and mechanical engineering in 2017 from Jacksonville University. In her free time, Nicole likes to play with her... Read More →

Maryam Khaqan

Graduate Student (Invited), Emory University

Maryam Khaqan is a Ph.D. candidate at Emory University working under the supervision of Dr. John Duncan on moonshine and related aspects of number theory. Maryam grew up in Lahore, Pakistan, where she finished her undergraduate studies in physics and mathematics at Lahore University... Read More →

Gage Martin

Graduate Student (Invited), Boston College

Gage Martin is a fourth-year graduate student at Boston College working in the field of low-dimensional topology and knot theory, advised by Dr. J. Elisenda Grigsby. She received her B.A. in mathematics from Marlboro College in 2016. When she isn't working on math, Gage enjoys cooking... Read More →

Mackenzie Simper

Graduate Student (Invited), Stanford University

Mackenzie Simper is a fourth-year graduate student at Stanford, focusing on applied probability with Persi Diaconis. Her hometown is Salt Lake City, where she graduated from Salt Lake Community College and the University of Utah. After undergrad, she spent one year at Cambridge as... Read More →

Rachel Knak

Graduate Student (Invited), University of Arizona

Rachel Knak is a fourth-year graduate student at the University of Arizona studying algebraic number theory under Dr. Brandon Levin. She earned her B.A. in Mathematics and Statistics and her B.A. in Religious Studies from Grinnell College in 2017. In her spare time Rachel enjoys cooking... Read More →

Lara Ismert

Faculty, Embry-Riddle Aeronautical University, Prescott

Lara Ismert is an Assistant Professor of Mathematics at Embry-Riddle Aeronautical University in Prescott, Arizona. She earned her Ph.D. in Mathematics from the University of Nebraska in 2019, where she began her research career in the exciting field of operator algebras. Dr. Ismert's... Read More →

Susan Hermiller

Professor, University of Nebraska-Lincoln

Prof. Susan Hermiller has been the director of the graduate program at UNL since 2011. In her research she explores connections between geometric properties and the complexity of computational algorithms for groups. She became a Fellow of the American Mathematical Society in 2019... Read More →

Alex Zupan

Faculty, University of Nebraska-Lincoln

I'm in my seventh year on the NCUWM Organizing Committee and am currently co-chair. My research is in geometry and topology. In particular, I study 3- and 4-dimensional manifolds and the theory of knots in these dimensions. Before arriving at UNL, I earned my Ph.D. from the University... Read More →

Alexandra Sececleanu

Assistant Professor of Mathematics, University of Nebraska-Lincoln

Alexandra Seceleanu is an assistant professor at the University of Nebraska-Lincoln, where she also serves as graduate program recruitment coordinator. After spending her formative years in Romania, she received her Ph.D. in Mathematics from the University of Illinois at Urbana-Champaign... Read More →

Kimberly Shurupoff

Director of Mathematics and Statistics Hiring, National Security Agency

Eun Heui Kim

Program Director, National Science Foundation

I have a Ph.D. from the University of Connecticut, and am a full professor at the California State University, Long Beach. I am currently a program director at NSF and my work website ishttps://www.nsf.gov/staff/staff_bio.jsp?lan=eukim&org=NSF&from_org=NSF... Read More →

Tomek Bartoszynski

Program Director, National Science Foundation

Tomek Bartoszynski is a program officer in the Division of Mathematical Science (DMS) at the National Science Foundation. His research interests are in set theory and its applications. At NSF he works with the disciplinary programs Foundations, Combinatorics and Probability. Prior... Read More →

Saturday January 23, 2021 7:00pm - 8:00pm CST
Zoom

Zoom Meeting, Networking

8:00am CST

Conference General Information Room

If you need technical assistance or have general questions, you can join the Conference Information Meeting Room.

Sunday January 24, 2021 8:00am - 3:30pm CST
Zoom

Optional Zoom Meeting

8:30am CST

Networking Coffee and Conversations

Sunday January 24, 2021 8:30am - 9:15am CST
Zoom

Optional Zoom Meeting, Networking

9:15am CST

Session 3 - Recurrent Neural Network Models for Predicting Ordinary Differential Equation Dynamics

Recurrent neural networks (RNN) are a class of graph-theoretic machine learning models loosely inspired by neurobiological processes. RNNs, which “learn” via vector inputs of variable length, have remarkable capabilities in applications modeling sequential data ranging from machine translation to speech and image recognition. In this talk, we apply RNN techniques to the numerical solution of certain systems of ordinary differential equations, and address whether claims of model stability made in published and unpublished work in the field can be rigorously defended.

Speakers

Camille Renaud

Senior, Marist College

My name is Camille Renaud and I am a senior at Marist College in Poughkeepsie, New York majoring in Applied Mathematics with a double minor in Data Science and Environmental Science. My research and educational experience has been quite multidisciplinary and broad so far, and I am... Read More →

Sunday January 24, 2021 9:15am - 9:30am CST
Zoom

Zoom Meeting Room A, Undergraduate Talk

Talk Subject Applied Mathematics

9:15am CST

Session 3 - Generalizations of Alder's Conjecture via a Conjecture of Kang and Park

Integer partitions have long been of interest to number theorists, perhaps most notably Ramanujan. Here, we focus on partitions with gap conditions and partitions with parts coming from fixed residue classes.

Let Δ_{d}^{(a,b)}(n) = q_{d}^{(a)}(n) - Q_d^{(b)}(n) where q_{d}^{(a)}(n) counts the number of partitions of n into parts with difference at least d and size at least a, and Q_{d}^{(b)} counts the number of partitions into parts ≡ b mod (d + 3). In 1956, Alder conjectured that Δ_{d}^{(1,1)}(n) ≥ 0 for all positive n and d. This conjecture was proved partially by Andrews in 1971, by Yee in 2008, and was fully resolved by Alfes, Jameson and Lemke Oliver in 2011. Alder's conjecture generalizes several well-known partition identities including Euler's theorem.

In 2020, Kang and Park constructed an extension of Alder's conjecture which relates to the second Rogers-Ramanujan identity by considering Δ_{d}^{(a,b,-)}(n) = q_{d}^{(a)}(n) - Q_{d}^{(b,-)}(n) where Q_{d}^{(b,-)}(n) counts the number of partitions into parts ≡ b mod (d + 3) excluding the d + 3 - b part. Kang and Park conjectured that Δ_{d}^{(2,2,-)}(n) ≥ 0 for all d ≥ 1 and n ≥ 0 and proved this for d = 2^r - 2 and n even.

We prove Kang and Park's conjecture for all but finitely many d. Toward proving the remaining cases, we adapt work of Alfes, Jameson and Lemke Oliver to generate asymptotics. Finally, we present a generalized conjecture for higher a = b and prove it for infinite classes of n and d.

Speakers

Adriana Duncan

Senior, Tulane University

Simran Khunger

Junior, Carnegie Mellon University

Sunday January 24, 2021 9:15am - 9:30am CST
Zoom

Zoom Meeting Room B, Undergraduate Talk

Talk Subject Number Theory

9:15am CST

Session 3 - An Empirical Study on Minimal Generators of Topological Features from Persistent Homology

This work provides an empirical study of the computational cost and effectiveness of several common optimization procedures applied to homological generators in dimension one, including algorithms to minimize L_{0} and L_{1} norms, bounding area, and “volume.” We conduct these optimizations via standard linear programming methods, applying general-purpose solvers to optimize over column bases of simplicial boundary matrices. Our key findings are (i) the computational cost of optimizing a basis of generators exceeds the cost of computing such a basis, for each of the tested general-purpose solvers, (ii) optimization is generally effective in reducing the size of generators, though the extent of the reduction varies according to the distribution of the underlying data, and (iii) the space of L_{1} optimal solutions properly contains that of L_{0} optimal solutions in the majority of Vietoris-Rips complex studied, though none of these complexes had totally-unimodular boundary matrices in degree one, a sufficient condition found in other studies.

Speakers

Lu Li

Senior, Macalester College

Sunday January 24, 2021 9:15am - 9:30am CST
Zoom

Zoom Meeting Room C, Undergraduate Talk

Talk Subject Topology

9:15am CST

Session 3 - Numerical Range of Composition Operators on the Hardy Space of the Unit Ball

The numerical range of a bounded operator T on a Hilbert space is defined as W(T) = {<Tx,x> : |x| = 1}.

We explore the numerical range of a composition operator C_{A} on the Hardy space, H^2(𝔹_{n}), of the open unit ball 𝔹_{n} of ℂ^n, induced by an n x n matrix A that is a self-map of 𝔹_{n}. The composition operator C_{A} is defined by C_{A} f = f ○ A for all f ∈ H^2(𝔹_{n}).

We show that spaces of homogeneous polynomials of degree k, denoted H_{k}(𝔹_{n}), are invariant under C_{A}. We find a matrix representation of C_{A} restricted to H_{k}(𝔹_{n}). We then characterize the numerical range of C_{A} induced by a variety of matrices, including forward shift, backward shift, circular shift, anti-diagonal, and arbitrary permutation matrices. For example, we show that W(A) ⊆ W(C_{A}) in general, and W(A)=W(C_{A}) when A is the circular shift matrix. To achieve this, we compute the invariant subspaces of C_{A} |_{H_{k}(𝔹_{n})} and decompose the matrix representation of C_{A} |_{H_{k}(𝔹_{n})} as a direct sum of matrices. We then use combinatorial and computational methods and well-known numerical range results to characterize the numerical ranges of the composition operator.

co-authors: Elisha Dayag, Gerardo Gonzalez

Speakers

Cassandra Lem

Senior, University of California - Santa Barbara

Ivan Matos

Senior, North Carolina State University

Sunday January 24, 2021 9:15am - 9:30am CST
Zoom

Zoom Meeting Room D, Undergraduate Talk

Talk Subject Analysis

9:35am CST

Session 3 - Relativistic Brownian Motion

The displacements of a particle from classical Brownian motion forms a Gaussian distribution. However, the distribution of variables drawn from a distribution with infinite variance as opposed to a finite variance in classical Brownian motion is not Gaussian. We show that the sum of a large number of log-normal variables tends to a Levy sub-ordinator distribution. This distribution is surprisingly common in real-life stochastic systems such as the stock market and relativistic Brownian motion.

Speakers

Yue Wang

Senior Undergraduate Student, University of Rochester

I am a physicist, mathematician, and classical pianist.

BrownianMotion YW 0120 pptx

Sunday January 24, 2021 9:35am - 9:50am CST
Zoom

Zoom Meeting Room A, Undergraduate Talk

Talk Subject Applied Mathematics

9:35am CST

Session 3 - Comparing Virtual and Concrete Manipulatives

Defined as “an object that can be handled by an individual in a sensory manner during which conscious and unconscious mathematical thinking will be fostered,” (2010, p. 14) manipulatives are used in mathematic classrooms all across the United States and other countries. Stein and Bovalino state that manipulatives provide a concrete way to link abstract information to already established knowledge thus giving new concepts a deeper meaning (2001). The purpose of this study is to compare concrete and virtual manipulatives to see if one fosters a deeper conceptual understanding of the FOIL Method. Students in a Middle Grades Cohort at Georgia College were given both a pre- and post-assessment to assess their level of understanding of the FOIL Method after a lesson using either virtual or concrete manipulatives. They then were taught using the other type of manipulative to assess whether students prefer virtual or concrete manipulatives.

Speakers

Kristen Hartley

Senior, Georgia College and State Univeristy

Sunday January 24, 2021 9:35am - 9:50am CST
Zoom

Zoom Meeting Room B, Undergraduate Talk

Talk Subject Math Education

9:35am CST

Session 3 - Exploring Solvability of the String Link Concordance Group using Milnor's Invariants

Suppose you have n knotted-up pieces of string tangled together. Is there a mathematical way to describe just how tangled they are? The Milnor's invariants of a string link provides us with information about how "linked" components are. In this talk, we'll discuss two ways to calculate the Milnor's invariants of a string link: a group-theoretic method and a method that involves generating surfaces bounded the link. Then, we'll discuss some results concerning the solvability of the string link group; by calculating the Milnor's invariants of string link commutators, we can learn more about how things commute in the string link group.

Speakers

Madison Ford

Senior, Wayne State University

Sarah Pritchard

Junior, Georgia Institute of Technology

Sunday January 24, 2021 9:35am - 9:50am CST
Zoom

Zoom Meeting Room C, Undergraduate Talk

Talk Subject Topology

9:35am CST

Session 3 - Local Properties of Difference Sets

Erdős and Shelah asked what we can learn about a large and complicated object X from properties that are satisfied by each small piece of X. We study the following variant of this problem, first studied by Erdős and Sós. Given a set of real numbers A, we consider the difference set A - A = {|a - b| : a, b ∈ A}. While a random set A is expected to have |A - A| = Θ(|A|^2), arithmetic progressions satisfy |A - A| = Θ(|A|).

Let g(n,k,ℓ) denote the minimum size of |A - A|, taken over all sets A of n numbers that satisfy the following local property: every subset A' ⊂ A of k numbers satisfies |A' - A'| ≥ ℓ. Intuitively, every k numbers from A span many differences. We derive several new bounds for g(n,k,ℓ). We now state two of our results.

Erdős and others were interested in linear thresholds of local properties problems: the smallest ℓ for which the size of the global property is superlinear. We establish the linear threshold of the differences problem. We prove that for every k, we have g(n,k,k-1) = n - 1 and g(n,k,k) ≫ n. The following is the simplest of a family of bounds that we derive. When k is a power of two, we have g(n,k, (k^{\log_2(3)}+1)/2) = Θ(n^{1+1/(k-1)).

Speakers

Anqi Li

Sophomore, Massachusetts Institute of Technology

I am broadly interested in theoretical computer science and discrete mathematics. Currently, I am very interested in the areas of discrete geometry that deal with polyhedral combinatorics. I would be very happy to chat about any of these or any related ideas!

Sunday January 24, 2021 9:35am - 9:50am CST
Zoom

Zoom Meeting Room D, Undergraduate Talk

Talk Subject Algebra, Combinatorics

9:55am CST

Session 3 - Solving the Navier Stokes Equation

The Navier Stokes equations are used to model fluid flow. Examples include fluid-structure interactions in the heart, climate and weather modeling, and flow simulations in computer gaming and entertainment. The Navier Stokes equations date back to the 1800s, and research and development of numerical approximation algorithms and finite element methods continue to be an active area. Using C++ and the academic software library dealii, we implement a least-squares finite element algorithm to approximate solutions to the Navier Stokes equations. We review the Navier Stokes equations, we derive the least-squares method algorithm, and we discuss its implementation.

Speakers

Taylor Boatwright

Junior, Francis Marion University

Sunday January 24, 2021 9:55am - 10:10am CST
Zoom

Zoom Meeting Room A, Undergraduate Talk

Talk Subject Applied Mathematics

9:55am CST

Session 3 - Informing the Need of Critical Thinking in Mathematics

Based on the National Assessment of Educational Progress, it seems that the public education system in California is failing to provide students with essential problem solving and critical thinking skills in mathematics. Many studies have proven that students do not rationally think about mathematics word problems. Though, it comes to question that this issue may come from outdated and unrelatable terminology, or context of mathematics problems. Using a survey that contains the original and modernized version of the “How Old is the Sheppard?” problem (which states “There are 125 sheep and 5 dogs in a flock. How old is the shepherd?”) in schools in California’s Central Valley, this research discovered that word choice does not play a role in students’ performance on nonsensical mathematics problems; students significantly increase their critical thinking skills from middle school to high school; and performance on traditional mathematics problems has no correlation to their performance on nonsensical problems. We speculate possible distractions in their testing environment and psychological tendencies that may have influenced our data, such as talking in the classroom and how math is commonly taught, and recognize that students' critical thinking has improved from about 35 years ago (when the original study was done), but it still needs to be improved. This information may help teachers, textbook authors, and others invested in mathematics education create better material for students.

Speakers

Arlena Liryce Gavino

Senior, California State University, Stanislaus

I'm a mathematics and economics major in my last year of my undergraduate.

Sunday January 24, 2021 9:55am - 10:10am CST
Zoom

Zoom Meeting Room B, Undergraduate Talk

Talk Subject Math Education

9:55am CST

Session 3 - Classifying toric 3-fold codes of dimensions 4 and 5

A toric code, introduced by Hansen to extend the Reed-Solomon code as a k-dimensional subspace of (𝔽_q*)^m, is determined by a toric variety or its associated integral convex polytope P, where k = |P ∩ ℤ^m|. Previous authors have classified toric surface codes with dimension up to k=7. We classify all 4-dimensional toric codes of polytopes in ℝ^3 using White's description of polytopes with 4-lattice points, and we present progress toward the same for dimension 5 codes using work by Blanco and Santos. In particular, for k=4 we first prove formulae for the minimum distances of codes coming from empty tetrahedra of the form T(s,t) = conv {(0,0,0),(1,0,0),(0,0,1),(s,t,1)}, where gcd(s,t) = 1, which occurs as a subpolytope for each subsequent case. We then uncover which disagreements in parameters s and t two polytopes may have while still yielding codes which are generated by matrices identical up to scaling and reordering their columns. Likewise, for k=5 we prove bounds on the minimum distances of each class and indicate where uncertainty in a total classification remains.

Speakers

Tori Braun

Senior, Ripon College

Jenna Gorham

Junior, The University of Arizona

Sunday January 24, 2021 9:55am - 10:10am CST
Zoom

Zoom Meeting Room C, Undergraduate Talk

Talk Subject Algebra

9:55am CST

Session 3 - Periodic Infinite Friezes of Type Λ_{p_{1},...,p_{n}} and Dissections on Annuli

Frieze patterns are arrays of shifted rows of numbers that satisfy the unimodular property and are related to polygon dissections, quivers, and cluster algebra. Finite frieze patterns of positive integers are first defined by Coxeter and have been extended to infinite cases by Baur, Parsons, and Tschabold. Finite friezes are generalized to algebraic integers by Holm and Jørgensen, which we called friezes of type Λ_{p_{1},...,p_{n}}. We extended these Holm-Jørgensen friezes to their infinite cases and discussed their geometric interpretations and the corresponding realization criterion. We proved that for all friezes that are realizable, their entries are in the form of the sum of path weights. This property allows us to prove that all friezes that have normal dissected annulus interpretations are positive and to find combinatorial interpretations of other statistics of frieze patterns such as the growth coefficients.

Speakers

Jiuqi Chen

Senior, Dartmouth College

Sunday January 24, 2021 9:55am - 10:10am CST
Zoom

Zoom Meeting Room D, Undergraduate Talk

Talk Subject Combinatorics

10:15am CST

Session 3 - Statistical Dashboard for Categorizing Particle Movement in Cells

At the intersection of nanoscience and biology lies the question of precisely how particles move within cells. In contrast to in vitro particle tracking experiments, wherein there are great controls on particle and environmental homogeneity, live cell tracking features tremendous diversity in particle movement. Within this research area, the use of mathematics has allowed for a better description of movement categorizations and quantitative methods to differentiate between them. In this work, we have developed a first-pass statistical dashboard to categorize disparate types of particle trajectories. The tools we developed for the categorization process include the correlation between consecutive increments and effective diffusivity from a maximum likelihood estimation. The standard deviation for the major and minor axis and the creation of a parameterized path to represent a fictional moving anchor employed principal components analysis. This anchor estimation allowed the computation of the average distance the particle deviated from the anchor. Based on these data measures, K-means clustering was utilized to distinguish between free diffusion, stuck diffusion, directed transport, tracker error, subdiffusion, and skating diffusion. This automated categorization process proved to be successful on data simulated using stochastic differential equations and provided interesting results on the live cell data.

Speakers

Riley Juenemann

Senior, Tulane University

Undergraduate senior passionate about research at the intersection of mathematics, computer science, and biology.

Sunday January 24, 2021 10:15am - 10:30am CST
Zoom

Zoom Meeting Room A, Undergraduate Talk

Talk Subject Applied Mathematics

10:15am CST

Session 3 - The Gender Gap of Doubt

In an effort to measure the effectiveness of their calculus courses, APSU mathematics faculty administered the "Calculus Challenge" assessment designed with an atypical, penalized scoring method, which unintentionally produced an achievement gap between men and women. The penalized scoring structure discouraged guessing by deducting 1 point for incorrect answers, while awarding 0 for unanswered questions. Analyzing two years of historical data revealed that, on average, women answered significantly fewer questions and scored far lower than men on this particular test. These findings motivated the hypothesis that penalized scoring adversely affects the prevalence to which women experience self-doubt, their willingness to guess, and overall score. To test this, we enlisted 287 participants to complete an anonymous survey and mathematics assessment utilizing the Calculus Challenge's penalized scoring structure. Preliminary analysis of the collected data supports the hypothesis and suggests a need to develop a more equitable assessment method.

Speakers

Sara Grey

Senior, Austin Peay State University

I am a Mathematics major at Austin Peay State University in Clarksville, TN. My concentration is Secondary Education and I am currently in my student teaching semester of my education. I will graduate in May, 2021. I have also completed a minor in Women and Gender Studies that has... Read More →

Sunday January 24, 2021 10:15am - 10:30am CST
Zoom

Zoom Meeting Room B, Undergraduate Talk

Talk Subject Math Education

10:15am CST

Session 3 - Knotris Gameplay and Probability

Knotris is a new game we have developed based on mosaic knot theory. In this talk, I will discuss probabilities related to gameplay and how they give us insight into game strategies. I will also describe how coding has helped us to determine both strategy and which game states are more difficult to play within. This analysis has informed how scoring works in the game.

Speakers

Kelemua Tesfaye

Senior, Seattle University

Hey there, I'm studying Applied Mathematics at Seattle University, and am deeply invested developing my skills to create mathematical models that highlight inequity and support the development of community based solutions. I look forward to meeting you!

Sunday January 24, 2021 10:15am - 10:30am CST
Zoom

Zoom Meeting Room C, Undergraduate Talk

Talk Subject Knot Theory

10:15am CST

Session 3 - Symmetries of linear systems on graphs

In the divisor theory of graphs, a finite, connected graph is viewed as a discrete analog of a Riemann surface. A divisor D on a graph is an assignment of integers to each vertex of the graph. An important statistic in this setting is the complete linear system of D, which is the collection of effective (e.g. non-negative) divisors linearly equivalent to D via the discrete Laplacian operator. Recently, S. Brauner, F. Glebe, and D. Perkinson characterized all complete linear systems on a finite graph G. We extend their results by computing the subset of divisors in any complete linear system that are fixed by a symmetry of G. When G is the cycle graph, we present a bijection between certain effective divisors and a subposet of Young’s lattice defined by R. Suter; using the combinatorics of these divisors, we give an alternate proof of a result by H. Thomas and N. Williams that Suter’s poset exhibits the cyclic sieving phenomenon (CSP).

Speakers

Annika Christiansen

Junior, University of Minnesota Twin Cities

Nhung Pham

Junior, University of Minnesota - Twin Cities

I'm a junior in Mathematics and Computer Science at the University of Minnesota - Twin Cities. Currently, I'm interested in Combinatorics but still in the journey to explore other areas.

NCUWM talk pdf

Sunday January 24, 2021 10:15am - 10:30am CST
Zoom

Zoom Meeting Room D, Undergraduate Talk

Talk Subject Combinatorics

11:00am CST

Poster Session A

Poster presenters in Room A will be available to talk about their posters. Please post abstracts in your personal profile.

View their posters and introductory videos at: https://padlet.com/stephanielvendetti/uni2rhu3cg4t6ti3

Zoom with them live at https://unl.zoom.us/j/99129576039.

Speakers

Holly Abrams

Junior, Austin Peay State University

Title: Measuring Gerrymandering: Improving Upon the Efficiency GapGerrymandering is the prominent issue of drawing voting district boundaries in a way that favors one political party over another. It has been an issue since 1812, and in recent history, the US courts have relied heavily... Read More →

Lillian Baker

Senior, United States Naval Academy

Poster title: Exploring Links between Climate Shocks and MigrationPoster abstract: This project explores increased migration from Mexico into the U.S. as it relates to climate change in Mexico and Central America. Fluctuating rainfall patterns reflect climate shocks that damage... Read More →

Jessica Bennett

Undergraduate Presenter, Brown University

Allison Cruikshank

2nd Year Graduate Student, Duke University

I am a second-year math PhD student at Duke University pursuing mathematical biology. I went to UNL for undergrad and attended this conference in my junior and senior year. I plan to go into industry after receiving my PhD to work at a pharmaceutical company.

Annabelle (Anna) Eyler

Senior, Hood College

Hello! My name is Anna and I am a senior Mathematics Major and Chemistry Minor at Hood College in Maryland. When not in the classroom, you can find me on a pool deck coaching athletes with intellectual disabilities or catching up on a good show series. Activities such as President... Read More →

Penelope Fiaschetti

Junior, Boston University

Catherine Huang

Junior, University of California, Berkeley

Connecting Graph Spectral Clustering and PDEsAbstract: Visualizing and interpreting a dataset can be a difficult task for high dimensional data. Clustering and dimensionality reduction help us extract important features and make the data more manageable to interpret. One approach... Read More →

Ariba Khan

Junior, Georgia Tech

Chloe Makdad

Undergraduate Presenter, Butler University

Hi! I'm Chloe, my pronouns are she/her/hers, and I'm a senior at Butler University majoring in mathematics, statistics, and computer science. After presenting a poster at this conference last year, I am excited to be giving a talk about my work on algorithms to count smooth numbers... Read More →

Maati McKinney

Senior, Spelman College

Poster Title: Modeling Cooperation between SpeciesMaati McKinney & Laura StemmlerAbstract: Population dynamics informs our knowledge of ecological interactions and influences our conservation laws and wildlife management. A central model in population dynamics is the Lotka-Volterra... Read More →

Shannon Murphy

Senior, Montana State University

Poster Title: Mathematical Modeling of a Biphasic Isothermal DNA Amplification ReactionAbstract: Isothermal DNA amplification has many possible applications; nearly all the capabilities of standard PCR, including clinical diagnostics, environmental monitoring, and forensic testing... Read More →

Kaleigh Rudge

Junior, Colorado School of Mines

Simulating Nonlinear Waves on Vortex Rings in Ideal FluidsVortex filaments are a fundamental structure in fluid dynamics for transferring energy. Understanding their motion and the relationship between the transfer of energy and the helical patterns of the vortex lines are crucial... Read More →

Delaney Scheiern

Senior, Colgate University

Poster title: Genetic Algorithms for Cluster Analysis: Health Insurance Coverage and PollutionAbstract: This poster explores Genetic Algorithms for Cluster Analysis, aided by a discussion of more simplistic clustering techniques such as k-Means and Gaussian Mixture Model clustering... Read More →

Laura Stemmler

Sophomore, Carnegie Mellon University

Myka Terry

Senior, Morgan State University

I will be presenting my research entitled Rainbow Cells: Tracking Trends in Cell Division Using Motzkin Paths, in poster session A. I am a first-generation college student who is currently a senior mathematics major at Morgan State University. I conduct research funded by the NIH-RISE... Read More →

Gabriella Torres Nothaft

Junior, University of Minnesota Twin Cities

Hello! I am a Junior from the University of Minnesota Twin Cities, and I am majoring in Mathematics with a minor in Chemistry. I am very excited to be able to share my research with all of you and to learn more about what is being researched right now! In math, I have an interest... Read More →

Christina Tran

Senior, Harvard University/IPAM

About: I am a senior mathematics major at Harvard University with a minor in Educational Studies. I intend to go to graduate school and pursue a Ph.D. in Applied Mathematics, with a focus in research related to developing algorithms for use on networks. I enjoy dancing and gaming... Read More →

Kenna Zimmerman

Junior, Arizona State University

My poster title is Utilizing Statistics and Machine Learning to Detect Events and Summarize Basketball Game Footage. The NBA (National Basketball Association) yields billions of dollars each year and serves as a past-time and hobby for millions of Americans. However, many of us simply... Read More →

Sunday January 24, 2021 11:00am - 12:00pm CST
Zoom

Zoom Meeting, Poster Session

11:00am CST

Poster Session B

Poster presenters in Room B will be available to talk about their posters. Please post abstracts in your personal profile.

View their posters and introductory videos at: https://padlet.com/stephanielvendetti/uni2rhu3cg4t6ti3

Zoom with them live at: https://unl.zoom.us/j/99121094978

Speakers

Evan Alexander

Junior, Southwestern University

Heather Baranek

Junior, University of Wisconsin-Eau Claire

Title: Game of Cycles: Extended. Abstract: The study of graphs provides an answer to questions in a variety of disciplines through the process of modeling the problem onto a graph. The Game of Cycles is a newly developed impartial mathematical game, introduced by Francis Su in his... Read More →

Ruth Butters

Junior, Kalamazoo College

My poster is Exploring Why The Conway Knot Is Not Slice: In 2018, Lisa Piccirillo wrote a proof about the famous 11-crossing Conway knot. This knot, named for mathematician John Horton Conway who passed away in 2020 due to Covid-19, had been stumping knot theorists... Read More →

Ivy Collins

Senior, Berry College

My name is Ivy and I am a senior at Berry College. I am studying Mathematics and Computer Science. I am excited to attend this year's NCUWM conference as it has been highly recommended by many of my professors and leaders in the STEM community. The title of my poster and abstract... Read More →

Elaine Danielson

Sophomore, University of Florida

Hi, I'm Elaine and I'm a second year math major at the University of Florida. Within math, I'm most interested in combinatorics and algebra. I enjoyed taking part in the Polymath REU last summer as part of the Explorer-Director group and I'm so grateful for all the kind people I met... Read More →

Kenzie Fontenot

Senior, University of North Texas

Kimberly Hadaway

Senior, Williams College

Title: An Introduction to Parking FunctionsAbstract: In 1966, Alan G. Konheim and Benjamin Weiss defined “parking functions” as follows: We have a one-way, one-lane street with n parking spaces, numbered in consecutive order from 1 to n, and we have n cars in line waiting to park... Read More →

Toni Hinskton

Senior, University of Denver

Angela Li

Sophomore, The Ohio State University

Hello! I'm Angela and I'm a 2nd year majoring in computer science and mathematics at The Ohio State University. I enjoy graph theory and am currently exploring Lean proof assistant. I also enjoy studying English and French at OSU, and I miss rock climbing before COVID. In my profile... Read More →

Marcella Manivel

Senior, Carleton College

Andrew Nguyen

University of Michigan

Deniz Ozbay

Junior, Lafayette College

Hi everyone! My name is Deniz and I am a junior at Lafayette College studying mathematics and theater. I am really excited to share my research with you! More information about my poster can be found below. I am looking forward to learning more about math research in general!Title... Read More →

Thi Phuong Anh Pham

Junior, University of Texas at Dallas

Hello! I'm an junior Math major at the University of Texas at Dallas. I love Algebra and Geometry! I'm currently doing research in Knot Theory with my professor and one other student. In my free time, I like playing the piano, reading, and writing stories.

Madelynn Roche

Junior, Vanderbilt University

I am a junior at Vanderbilt studying math and education. I’m undecided in a research area, but particularly interested in Algebra at the moment. I am the co-founder of my university’s student chapter of the Association for Women in Math, and am passionate about amplifying under-heard... Read More →

Marguerite Shaya

Senior, Carleton College

Riley Stephens

Junior, The University of Texas at Dallas

I am Riley Stephens, a junior at the University of Texas at Dallas majoring in pure mathematics. After graduating, I intend to pursue a Ph.D. relating to pure math, possibly in differential geometry, though I have not made a firm decision on what subject I would like to focus on yet... Read More →

Yuki Takahashi

Undergraduate Presenter, Grinnell College

I am a senior at Grinnell College, majoring in Mathematics and Philosophy. I am generally interested in combinatorics, discrete mathematics, and mathematical logic, and I plan to pursue a PhD in mathematics after graduation.

Zariah Whyte

Senior, Southwestern University

AliAnn Xu

Senior, University of Georgia

I am a fifth-year math major and a history minor at the University of Georgia. I have a particular interest in Abstract Algebra, Analysis, Foundations of Math, European and American hitory, Music Theory, and molecular biology. Outside of juggling my classwork, I enjoy reading, biking... Read More →

Zhichun Zhang

Junior, Swarthmore College

Laura Zinnel

Senior, University of Wisconsin-La Crosse

I am a Mathematics and Psychology major at the University of Wisconsin-La Crosse, and I plan to enroll in a Computational Neuroscience Ph.D. program next fall. My mathematics research is in combinatorics and this project specifically falls within the field of anti-Ramsey Theory, or... Read More →

Knot Poster pdf

Sunday January 24, 2021 11:00am - 12:00pm CST
Zoom

Zoom Meeting, Poster Session

12:30pm CST

Panel Discussion: Choosing a Graduate Program

Speakers

Hayley Bertrand

Graduate Student (Invited), Indiana University

Nicole Buczkowski

Graduate Student (Invited), University of Nebraska-Lincoln

Maryam Khaqan

Graduate Student (Invited), Emory University

Rachel Knak

Graduate Student (Invited), University of Arizona

Gage Martin

Graduate Student (Invited), Boston College

Mackenzie Simper

Graduate Student (Invited), Stanford University

Sunday January 24, 2021 12:30pm - 1:30pm CST
Zoom

Zoom Meeting, Panel Discussion

2:00pm CST

3rd Plenary Talk: "Be the ‘Square Root of Possible'," Talitha Washington

Be the ‘Square Root of Possible’

Beginning to navigate the mathematical community can feel abstract and vague. As a first-year undergraduate student, Talitha Washington withdrew from a mathematical proof course because of the rigorous demand. Now, she is a full professor of mathematics who leads a major initiative to develop data science that is grounded in ethics and addresses topics in Black America. She will share how she rose above obstacles to become a mathematician because “the square root of impossible is possible” in us all.

Speakers

Talitha Washington

Director, Atlanta University Center Data Science Initiative

Sunday January 24, 2021 2:00pm - 3:00pm CST
Zoom

Zoom Meeting, Plenary Talk

3:00pm CST

Closing Remarks and Evaluation

Please join us for the closing remarks by NCUWM co-chairs Christine Kelley and Alex Zupan of the University of Nebraska-Lincoln.

An email message will be forthcoming from the external evaluation team with a link to the survey.

Please complete the survey within a few days of the end of the conference, while your experience is still fresh. The survey is intended to help the conference planning committee and evaluators understand what worked well, what participants gained from participating in the conference, and what might be enhanced to make any future conferences more useful and beneficial for participants. Questions gather information on your perceptions on whether goals were met, your satisfaction with different facets of the sessions, opportunities to network, conference logistics, what you were able to take away from the conference, and your recommendations. The survey does not collect identifying information. You will be asked to create a unique number that will only be used to track responses. Data from the survey will be seen by conference organizers and the conference evaluators, and may be used to plan future conferences. The information collected will be incorporated into conference reports, which will be publicly available. However, no individual identifying information will be published in any reports. Thanks for your consideration and participation in the conference evaluation survey.

Speakers

Christine Kelley

Professor of Mathematics, NCUWM Co-Chair, University of Nebraska-Lincoln

Alex Zupan

Faculty, University of Nebraska-Lincoln

Sunday January 24, 2021 3:00pm - 3:15pm CST
Zoom

Zoom Meeting, Closing Session