New Mexico State University

February 25

Zachary Letterhos, NMSU

Random Walks and The Gambler's Ruin

If a gambler decides to play a series of fixed-stakes games until they either double their money or go broke, how likely are they to succeed? This is the gambler's ruin problem, one of the oldest questions studied in modern probability theory. Answering it will lead us to random walks, a simple model for random motion with a wide variety of applications. We will then discuss some of the classic results on random walks, including the celebrated contributions of George Polya and Shizuo Kakutani. No prior experience with probability or gambling is required.

December 3

Adaline De Chenne, NMSU

It’s Just Multiplication, Right?

The multiplication principle is a fundamental tool in combinatorics, and it can be applied in surprisingly nuanced ways. We will use the multiplication principle to find all ways to represent real numbers using positional representations with positive integers (e.g., the binary system or the factorial system). We will then use combinatorics as a way to introduce research in mathematics education, particularly that which explores student thinking. The only math you will need to know for this talk is addition and multiplication.

November 12

Boyu Li, NMSU

Hilbert's Hotel, Shift Operators, and Semigroup Representations

Hilbert’s Hotel has infinitely many rooms and is already full. Yet, with a clever strategy, the manager can still make space for new guests — even infinitely many of them. This classic paradox, introduced by David Hilbert in 1925, highlights a surprising aspect of infinity. In this talk, we will step into the manager’s shoes and explore different ways to accommodate these demanding guests and see how these ideas connect to shift operators and representations of semigroups.

October 16

Selvi Kara, Bryn Mawr College

Meet a Mathematician, Edge Ideals and Beyond

I will begin this talk by introducing my passion project, MΣΣT a Mathematician, a collection of video interviews that highlight the experiences of mathematicians, particularly from diverse and historically excluded backgrounds in the mathematical sciences. I will then transition to an overview of my research, which focuses on monomial ideals arising from combinatorial and visual objects, such as graphs (e.g., edge and cover ideals). I will discuss how monomial ideals can be studied through minimal free resolutions, which encode important invariants. By examining the interplay between algebra and combinatorics, I will show how graph data can be used to express algebraic information, sharing results that illustrate these connections and discussing open questions that continue to drive my work.