08/31/2026 – Gavin Dooley: Monsky’s Theorem
Abstract: In this talk, we prove Monsky’s theorem, which states that it is impossible to dissect a square into an odd number of triangles of equal area. The only known proof of Monsky’s theorem uses the concept of valued fields and appears in Aigner and Ziegler’s book Proofs from THE BOOK.
09/07/2026 – Chen-Kuan Lee: The Hopf product conjecture
Abstract: The Hopf product conjecture is a classical open problem in differential geometry that asks whether the product of two 2-spheres admits a Riemannian metric with strictly positive curvature. In this talk, we will survey the history of the conjecture and discuss its significance in differential geometry.
09/14/2026 – Tony Yan: A Taste of Free Probability
Abstract: In the 1990s, D. Voiculescu developed the theory of free probability, a noncommutative analog of classical probability that proves to be useful in the study of operator algebras and random matrices. In this talk, I discuss motivations for this theory, some central concepts, and several important results related to this field of study.
09/21/2026 – Atticus Stonestrom: A case against AI use in mathematics
Abstract: I will present a number of arguments against “substantial use” of AI in mathematics (I will make precise what I mean by substantial use). The talk will have more-or-less two parts; in the first I will argue that substantial AI use is detrimental to the discipline of academic mathematics as a whole, and in the second I will argue that one is ill-served by substantial AI use at an individual level.
09/28/2026 – Tan Özalp: Shelah’s proof of the Hales–Jewett theorem
Abstract: We present Matet’s variant of Shelah’s proof of the Hales–Jewett theorem.
10/05/2026 – Akash Narayanan: Insolvability of the general quintic
Abstract: Abel proved that there is no solution in radicals to a general polynomial of degree five or higher. We will discuss a topological proof of Abel’s theorem due to Arnold.
10/12/2026 – Fuxiang Yang: An Introduction to Twisted Commutative Algebra
10/19/2026 – FALL BREAK: NO TALK
10/26/2026 – Noa Hunter: Line Bundles over CP^2 and Bézout’s Theorem
Abstract: We will give an introduction to line bundles over CP^2, then use the theory of Chern classes to give a “proof” of Bézout’s Theorem, a classical result in Algebraic Geometry on the intersection of plane curves.
11/02/2026 – Yuyan He: Fun with Indiscernibles
11/09/2026 – Dominic Scarcelli: TBA
Abstract: TBA
11/16/2026 – Emma Dooley: TBA
Abstract: TBA
11/23/2026 – Luis Atzin Franco-Reyna: TBA
Abstract: TBA
11/30/2026 – Leon Menger: TBA
Abstract: TBA
12/07/2025 – Audriana Houtz: TBA
Abstract: TBA