Mathematical Sciences
Departmental Weekly Events
January 20 – January 24, 2025
AGENDA
Monday, January 20
- Martin Luther King Jr Holiday – Offices and campus closed
Tuesday, January 21
- No Events
Wednesday, January 22
- No Events
Thursday, January 23
- No Events
Friday, January 24
- No Analysis Seminar
- Algebra Seminar, "Ehrhart Fans". Dustin Ross, San Francisco State University. 10:00AM – 11:00AM. Zoom and SH 235. Link: 897 6549 4169.
Abstract: Motivated both by lattice point counting in polytopes and by Euler characteristics of sheaves on algebraic varieties, we introduce a new class of polyhedral fans that we call Ehrhart fans. In this talk, we will familiarize ourselves with Ehrhart fans and discuss how they provide a setting in which Euler characteristics of matroids, which were recently introduced by Larson, Li, Payne, and Proudfoot, can be generalized and studied alongside Euler characteristics of sheaves on smooth complete toric varieties. Using a classical lattice point counting interpretation of the latter, we will discuss how ideas from Ehrhart theory can be used to study positivity of Euler characteristics of matroids. This is joint and ongoing work with Melody Chan, Emily Clader, and Carly Klivans.
- Colloquium, "A Geometer’s Guide to Log-concavity". Dustin Ross, San Francisco State University. 12:00PM refreshments | 12:30PM – 1:20PM talk. Zoom and SH 107. Link: 821 4637 5616.
Abstract: Chromatic polynomials count the number of ways to color a graph’s vertices so that no two adjacent vertices have the same color. One of the great combinatorial conjectures of the 20th century claimed that the chromatic polynomial of any graph is log-concave, meaning that the square of each of its interior coefficients is at least as big as the product of its neighbors. This conjecture remained unresolved for over 50 years until, in a major breakthrough, June Huh finally resolved it in 2012. In this talk, we’ll explore chromatic polynomials, log-concavity, and a recently-discovered method by which we can view Huh’s result through the lens of classical ideas in geometry.
- No Geometry and Topology Seminar
Notes:
None
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