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
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
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
David Wang & Jack Lee
Title: Seven Shuffles Is Enough