Colloquium Fest 2025, Monday January 27

Colloquium Fest 2025 

Please join us for the 2025 Colloquium Fest hosted by the department of Mathematics & Statistics. Please find the schedule below:

9:00 – 9:25: Light breakfast & refreshments served in the Frank Morgan Library

9:30 – 10:10am:  Ava Irons (NSB 113), 

10:15 – 10:55am: Jarin Sutton (NSB 113), Munguldei Batsaikhan (NSB 015)

11:00 – 11:50am: Raymond Liu & Matthew Wu (NSB 113), Gabe Miller & Oscar Nobel (NSB 015)

12:00 – 1:00pm: Pizza lunch served in the Frank Morgan Library

1:00 – 1:40pm: Nicole Albright (NSB 113), Isaac Becker (NSB 015)

1:45 – 2:25pm: Carter Anderson (NSB 113), Rauan Kaldybayev (NSB 015)

2:30 – 3:20pm: Harrison Cross & Harry Appelt (NSB 113), David Wang & Jack Lee (NSB 015)

 

Ava Irons

Title: Dynamic Mode Decomposition: Making Sense of Big Data

Abstract: A newer tool in data science, dynamic mode decomposition (DMD) takes a large data set and reduces the dimension to find the best linear approximation of the system. To do this, DMD uses methods from linear algebra, most notably the singular value decomposition, as well as topics from differential equations. Differing from similar methods such as principal component analysis, DMD is time-centric and relatively easy to adjust as the system changes. DMD has applications in physics, most notably fluid dynamics, as well as epidemiology, neuroscience, and video processing

Jarin Sutton

Title: Counting Orbits Using Burnside’s Theorem

Munguldei Batsaikhan

Title: Coupling and Mixing in Markov Chains: a Case Study on the n-Cycle
Abstract: Markov chains are a cornerstone of probability theory with applications ranging from statistical physics to machine learning. To understand their behaviour, we look at mixing time — the time required for a chain to reach equilibrium. This presentation explores coupling as a method to bound mixing time, with focus on lazy random walks on the n-cycle and the d-dimensional torus.

 

Raymond Liu & Matthew Wu

Title: Cantor and the Uniqueness of Fourier Series

Abstract: The uniqueness problem of Fourier series is a well-known topic among mathematicians, but it is less widely recognized that Cantor addressed this issue as early as the 1870s. This talk will present Cantor’s original proof and its modern extensions. A key part of these extensions is to discuss sets of uniqueness, a weaker version of the uniqueness problem that leads to many exciting results in analysis.

Gabe Miller & Oscar Nobel

Title: Six Thousand One Hundred Seventy Four
Abstract: Six thousand one hundred and seventy four. This number, affectionately known as Kaprekar’s Constant, has a unique property: it is the single fixed point (and attractor!) for a simple process applied to any four-digit number (provided all four digits are not equal). What this unintuitive and seemingly gimmicky process lacks in real-world applications it makes up for in surprising aesthetic wonders. In this talk, Gabe and Oscar explore the nuances of this process and uncover hidden structures in the Kaprekar constant and the Kaprekar function, while expanding these findings to other relevant and interesting spaces.

 

Nicole Albright

Title: Toward Clinical Applications: Exploring Coupled Dynamics in Cardiovascular and Respiratory Systems

Abstract: Heart disease, the leading cause of death among adults in the United States, presents significant challenges in diagnosis and treatment due to the complexity of the cardiovascular system. Mathematical models can be valuable tools for predicting cardiac dysfunction and guiding therapeutic interventions. However, achieving a balance between physiological accuracy and computational simplicity — critical for use in clinical settings — remains a key challenge. This talk will examine Bram W. Smith’s ‘minimal model’ of the cardiovascular system, which captures fundamental hemodynamics in a closed-loop framework. It will also introduce two modifications to the model that improve its ability to account for cardiopulmonary interactions and variable heart rate, increasing its accuracy and clinical relevance.

Issac Becker

Title: Gödel’s Incompleteness Theorem

Abstract: For centuries, logicians and mathematicians have sought to create an axiomatic system for all of mathematics that is sound, complete, and consistent. In 1931, Kurt Gödel demonstrated that any system capable of representing basic arithmetic will be either incomplete or inconsistent. In this talk, we will present and discuss a proof of this celebrated theorem.

Carter Anderson

Title:  The Finite Difference Method, an Introduction to Numerical Methods

Abstract:  Through a discussion of the Finite Difference method, I will briefly introduce numerical methods—what they are, why mathematicians and scientists need them, and how I use them to study black holes and neutron stars.

Rauan Kaldybayev

Title: Exploring p-adic numbers and dynamics on the p-adics

Abstract:  A real number can be specified by a sequence of rational numbers that get progressively closer together. But “closer” in what sense? Thinking about the real number line, we use the Euclidean notion of distance. A remarkable result of Ostrowski shows that there are, in a sense, only two reasonable notions of “closeness”: the Euclidean one and a number-theoretic, p-adic one. This leads us to define p-adic numbers for each prime p = 2, 3, 5, 7, …. The p-adics have some properties quite unlike the reals, for example: every point inside a ball is a center of that ball; every point is disconnected from every other point; and the sum 1 + p + p^2 + … converges to -1 / (p – 1).  The p-adics are an interesting setting for dynamics, which is the study of how points evolve under iterative processes. I will introduce so-called rank-one maps and discuss my research under Professor Silva into the dynamics of continuous rank-one maps.

Harrison Cross & Harry Applet 

Title: Modeling Tumor Progression: From Early Models to Advanced Frameworks
Abstract: This presentation explores the evolution of mathematical models for tumor growth. From simplistic early models to advanced frameworks like the Reaction-Diffusion-Advection (RDA) model, differential equations have been used to model and predict tumor growth over time. While early models lacked the complexity to accurately reflect the tumor microenvironment (TME), advanced models now incorporate interactions among cancer cells, immune cells, and surrounding tissues, which enhances the ability to predict treatment outcomes and therapeutic strategies. We will discuss these models’ progression, limitations, and possible future research directions.

David Wang & Jack Lee

Title: Seven Shuffles Is Enough

Abstract: This talk explores the ideas of randomness and achieving a “fully shuffled” state within the framework of Markov Chains, focusing on different card shuffling techniques.