Current Schedule

9/11/26

Tony Vuolo

Title: On B-Colorings in Planar Graphs

Abstract: Gy\'arf\'as and S\'ark\"ozy [Studia Sci. Math. Hungar., 2023] defined a B-coloring of a graph to be a proper coloring of the edge set in which any $C_4$ is totally multicolored. Let $q_B(G)$ denote the minimum number of colors sufficient for a B-coloring of a graph $G$. In this talk, we prove that any planar graph $G$ with $\Delta=\Delta(G)$ and $\Delta_2=\Delta_2(G)$ has $q_B(G)\leq\Delta+\max\{\Delta_2,38\}$, refining a bound by Kong, Wang, and Zheng [J. Graph Theory, 2026].

9/18/26

Matt Burnham

Title: Small q-kernels in digraphs

Abstract: An independent set $Q$ of a digraph $D$ is called a $q$-kernel if all vertices of $D$ are reachable from $Q$ via a directed path of length at most $q$. The small quasikernel conjecture of Erdős and Székely posits that every digraph $D$ with minimum in-degree $\delta = 1$ has a $2$-kernel of size at most $\frac{1}{2}|V(D)|$. In 2024, Spiro posed a more general question: What is the smallest constant $c_{\delta,q}$ such that every digraph $D$ with minimum in-degree $\delta$ has a $q$-kernel of size at most $c_{\delta,q}|V(D)|$? We present new upper bounds for the constants $c_{\delta,q}$ and conjecture that a simple lower bound construction is tight when $q\geq 3$.

9/25/26

Billy Duckworth

Title: From Entropy to Continued Fractions and Knot Theory 

Abstract: Starting with an attempt to define a notion of entropy for almost periodic dynamical systems, we will be forced to go on an unexpected journey into such topics as continued fractions and knot theory. Come ready to get tangled up in tangents! 

10/9/26

Khiem Nguyen

Talk title: Combinatorics in topology

Abstract: A Hausdorff space is called a P-space if every countable intersection of open sets is open. A Hausdorff space is called extremally disconnected if the closure of any open set is open. Both properties generalize certain property of discrete spaces when it comes to the ring of real valued continuous functions. Are there nondiscrete extremally disconnected P-spaces? The answer turns out to involve the combinatorics of cardinals!

10/16/26

Sophia Child

Title: Matroids Crash Course

Abstract: A brief introduction to matroids, their equivalent definitions, and constructions! I will attempt to make matroids and their connections to different fields of mathematics as understandable as possible. If we have time, we'll get to discuss some of my favorite results. The audience will hopefully leave less fearful of matroids. 

10/23/26

Micah Coats

Title: Fixed point theorems and their applications with a focus on Analysis and PDEs

Abstract: Fixed point theorems are theorems of the form that for a function f and set X there exists x in X such that f(x)=x. These theorems range over many fields of mathematics, with broad applications to topology, analysis and PDEs, economics, linear algebra, and combinatorics. This talk will be an overview of some of the more famous theorems, their proofs, and their applications- especially to PDEs and topology.

10/30/26

Clay Higgins

Title: Knot Colorings in the Petaluma Model

Abstract: This will be an abbreviated version of the presentation I gave for my master's thesis. We will discuss the basics of knot theory and Fox colorings, and how these relate to a relatively new type of knot model: the Petaluma model. Our main result is that we show a method to create a coloring system of equations for any knot based on some petal diagram of that knot (we will also discuss the theory of random knots if time allows). There will be lots of pretty hand-drawn pictures!

11/6/26

Ben Bridenbaugh

Title: Introduction to flag algebras and extremal numbers. 

Abstract: The first portion of this talk will focus on providing a high-level introduction to flag algebras, and how they are applied. Then we will introduce the extremal number of (hyper)graphs, some of the seminal results in the field, and some of what remains open. To tie everything together, we will finish with a new result, which is characterizing ex(n, F5) (for n < 33).

11/13/26

Nick Layman

Title: On OpenAI's Proof of Bipartite Crossing Numbers

Abstract: On October 6, 2026 OpenAI released a preprint of a paper claiming to have exactly determined the crossing number of all complete bipartite graphs. This problem, and the conjectured answer by Zerankiewicz, has been actively worked on since 1954 when Zerankiewicz first proposed a proof which was later found to contain an error. Small examples and families with one part small were solved, but global progress was restricted to incrementally improving asymptotic lower bounds. OpenAI's paper develops new tools in linear algebra to solve the problem outright in its entirety. I will attempt to describe how those tools are applied to graph drawings and crossing numbers, but I will not be describing the proofs of those tools themselves. 

11/20/26

Nate Schacherl

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11/27/26

Thanksgiving break!

12/4/26

Double Feature! Sycamore Herlihy and Austin Longin

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12/11/26

Hope Pungello

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