2021 Talks

Student Research Presentations

A1 Working Backwards.mp4

Brianna Louie - Working Backwards

Abstract: Working backwards is a beneficial took in mathematical problem solving. This concept is applicable to the real world in many game settings. Learning this concept of working backwards can be applied to help you create some winning strategies when playing games with your friends. In this talk I will go over some example problems to demonstrate how this concept works and provide some extra problems if students are interested and want to challenge themselves.

B1 Finding a Path The Beginnings of Tsuro Research.mp4

Raul Reynoso & Luis Vega - Finding a Path: The Beginnings of Tsuro Research

Abstract: In this presentation, we will share our findings and progress in understanding the board game Tsuro. We will first explain the basic rules and properties of the board game, including its limitations. We will then share how we created smaller variants of Tsuro in an attempt to discover winning strategies that could be applied to the study of the main game. We will end our presentation with our current focus of research and future plans.

A2 On a Characterization of Convergence in Banach Spaces with a Schauder Basis.mp4

Olivia Soghomonian - On a Characterization of Convergence in Banach Spaces with a Schauder Basis

Abstract: We extend the well-known characterizations of convergence in the spaces $l_p (1\leq p < \infinity)$ of $p$-summable sequences and $c_0$ of vanishing sequences to a general characterization of convergence in a Banach space with a Schauder basis and obtain as instant corollaries characterizations of convergence in an infinite-dimensional separable Hilbert space and the space $c$ of convergent sequences.

B2 The topological symmetry group of the graph G_3.mp4

Miguel Baza - The topological symmetry group of the graph G_3

Abstract: Spatial graph theory is the study of graphs embedded in $\mathbb{R}^3$. Given a graph and its automorphism group, we show how studying fixed vertices and edges allows us to determine the possible symmetries that a graph embedding may have in $\mathbb{R}^3$. In particular, we show which elements of the automorphism group for the graph $G_3$, a member of the $K_7$ family of graphs, allow symmetry preserving embeddings and which do not. Ongoing work on other graphs in the same family will also be presented at the end, together with possible avenues for future work.

A3 A Three-Part Model of a Two-Dimensional Heart.mp4

Anthony Cortez - A Three-Part Model of a Two-Dimensional Heart

Abstract: The common understanding of the heart describes it as a pump that works to move blood around the body. While conceptually accurate, the function of the heart is far more complicated than this. The goal of this work is to add a level of detail to this everyday view by forming a two-dimensional numerical model to provide a deeper qualitative understanding of the heart. In its completed state, the model will depict the propagation of electrical waves that trigger the contraction of simulated muscle, which pumps simulated fluid through the virtual heart. Electrical wave propagation, muscle contraction, and fluid flow constitute the three parts of the model that we are proposing. These processes will be modeled with the FitzHugh-Nagumo(FHN) model, a mass-spring model, and Smoothed Particle Hydro-dynamics (SPH), respectively. Thus far the electrical wave and fluid simulations have been implemented independently to run in real-time. Once the mass-spring model is completed, work will begin to couple the methods into the final version of the simulation. Coupling these popular methods should produce a real-time simulation that provides a good qualitative picture of the specified processes and gives a framework for scaling the program to three dimensions.

B3 Multiplier Sequences Over the Fields of Order 2, 3 and 4.mp4

Grace Burton - Multiplier Sequences Over the Fields of Order 2, 3 and 4

Abstract: If after reading the title you are wondering: What is a field of order 4? What are multiplier sequences, and why are we trying to find them all? Why is this talk not about all of the fields? Then come and listen to my interesting talk about multiplier sequences over the fields of order 2, 3 and 4, in which you will learn how sequences of field elements can interact with polynomials while maintaining the types of zeros they have.

A4 Preferential and K-Zone Parking Functions.mp4

Parneet Gill - Preferential and K-Zone Parking Functions

Abstract: Parking functions are vectors that describe the parking preferences of $n$ cars that enter a one-way street containing $n$ parking spots numbered 1 through $n$. A list of each car’s preferences is compiled into vectors in which we denote as ($a_{1}, \ldots , a_{n}$), such that $a_i$ is the parking preference for car $i$. The classical parking rule allows cars to enter the street one at a time going to their preferred parking spot and parking, if that space is unoccupied. If it is occupied, they then proceed down the one-way street and park in the first available parking spot. If all cars can park, we say the vector ($a_{1}, \ldots , a_{n}$) is a parking function. In this presentation, we introduce new variants of parking function rules with backward movement called $k$-Zone, preferential, and inverse preferential functions.

B4 Extending Classical Link Invariants to Singular Links.mp4

Matthew Nuyten - Extending Classical Link Invariants to Singular Links

Abstract: In the field of knot theory, quantum invariants such as the HOMFLY-PT polynomial are tools used to distinguish links in the 3-sphere. The goal of this talk is to discuss methods used by Luis Paris in defining a HOMFLY-PT polynomial invariant for singular links by means of skein modules and Hecke algebras. I will relate this to my ongoing research and share how this can be used in extending the Kauffman 2-variable polynomial to an invariant for singular links.

A5 Cheeger constants of planar trivalent graphs and fully augmented links.mp4

Audrey Baumheckel - Cheeger constants of planar trivalent graphs and fully augmented links

Abstract: Fully augmented, a class of hyperbolic links, can be associated with perfect matchings on planar trivalent graphs. This presentation will give some results about Cheeger constants of planar trivalent graphs, and make some initial connections between the Cheeger constant of such a graph and the Cheeger constant of its associated fully augmented link.

A6 An Invariant of Colored Links.mp4