Faculty/Graduate Speaker Session

Clostridioides difficile, also known as C. difficile, is a prevalent cause of infectious diarrhea in United States healthcare facilities. Spread through the fecal-oral route and primarily through contact with spores on contaminated surfaces, C. difficile can cause severe diarrhea, stomach pain, and colitis. Most individuals can mount an effective immune response, but older populations, immunocompromised individuals, and those taking antibiotics have an increased risk of being colonized by C. difficile. While extensive research has been conducted in hospital-based settings to improve understanding of the transmission of this bacteria, few studies apply mathematical models in the context of long-term care facilities. Residents in these settings require care from staff for many activities of daily living, and often have a more social and active environment than in hospitals since residents may stay in their private rooms or visit common areas, especially during meal times. This talk will focus on two mathematical models aimed at quantifying the transmission of C. difficile in long-term care facilities. Our work, completed in collaboration with undergraduate student researchers, introduces a system of ordinary differential equations and an agent-based model to represent C. difficile transmission dynamics in long-term care facilities, with their interactive nature and high-risk factors. We used data from the Emerging Infections Program at the Centers for Disease Control and Prevention for parameter estimations and performed sensitivity analyses to quantify the impact of varying these parameters on incidence. Mitigation strategies such as frequent disinfection, increased handwashing compliance, and a lower ratio between residents and healthcare workers had the greatest impact on reducing the incidence of colonization with C. difficile in these facilities.
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Logical thinking is at the heart of studying mathematics. Mathematicians must be able to think logically and present their ideas using flawless mathematical logic. As a mathematician, how logical do you think you are? We can find out through a simple logical puzzle. In this talk, we'll solve the puzzle, dive through its history, and show historical results when the puzzle has been presented to math students, math professors, and the non-math students.
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In this talk, I will share an interactive classroom activity designed to introduce students to the Central Limit Theorem (CLT) and sampling distributions. Using a simple and relatable context, students engage with an online simulation app that allows them to draw repeated samples from a known population distribution. Through this process, they actively observe the variability of sample means and discover how sampling distributions emerge and converge toward normality. The activity emphasizes active engagement, guiding students from hands-on exploration to a formal understanding of the CLT. I will discuss the structure of the activity and some strategies for adapting it across different course levels.
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This talk examines how GPT-5 can serve as both a learning aid for students and a teaching tool for instructors in a calculus-based undergraduate probability course. We begin by assessing GPT-5’s ability to address a wide variety of probability problems, including standard textbook exercises, mathematical reasoning and proof-based questions, coding tasks for problems that require simulations, and challenging non-routine problems, including Putnam competition-type questions. Based on this evaluation, we propose strategies for students to effectively engage GPT-5 to improve their problem-solving skills and understanding of the material, with particular emphasis on developing critical thinking skills by analyzing, questioning, and refining the model’s output. In addition, we also discuss ways instructors can leverage GPT-5’s strengths to create course materials, design assessments, and enhance classroom engagement.
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Two important types of distributions of permutation statistics are Mahonian and Eulerian. Mahonian statistics include the major index (maj) and the number of inversions (inv), while Eulerian statistics include the number of descents (des) and excedances (exc). Some statistic pairs share the same distribution as (des, maj); these are called Euler-Mahonian pairs. We define a Stirling statistic as one that has the same distribution as the number of right-to-left minima (rlmin), and a Stirling-Euler-Mahonian triple as a triple of statistics with the same joint distribution as (rlmin, des, maj). We present several well-known statistics that form these triples, and we describe a general bijective method for proving such results for any Mahonian statistic that can be represented using a permutation code.
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In the semigroup $M_2(\mathbb{N}_0)^\bullet$ of two-by-two matrices with non-negative integer entries and non-zero determinant, we study the factorization of matrices into atoms, or irreducible matrices. In 2022, Baeth et al. discovered classes of atoms in this semigroup; however, the factorability of most matrices in $M_2(\mathbb{N}_0)^\bullet$ remains unknown. As the result of joint work with Eva Goedhart and Gregory Heilbrunn, I will discuss two additional classes of atoms: a class of atoms with determinant p, 2p, or 4p, where p is prime, and a class of atoms where the main diagonal is much “larger” than the off-diagonal (or vice-versa). In addition, we classify the bisymmetric atoms of $M_2(\mathbb{N}_0)^\bullet$ with minimum entry up to 100 and conjecture that a special subset of bisymmetric matrices is divisor-closed.
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For a graph $G$, a configuration space of $G$ can be thought of as the set of all possible configurations of "robots" which can move throughout $G$, subject to some constraints. In this talk, we introduce a type of configuration space which we call "Grouped Stirling Complexes," in which the robots are placed in groups, and the configurations are subject to two constraints. First, there must be at least one robot on each vertex of $G$, and second, any two robots from the same group must be separated by at least one full "open edge" of $G$. We will focus on the cell structure of these configuration spaces, showing how we can "build up" the configuration space using "cells" of various dimensions.
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