Postdoc Seminar 2024 – 2025
Postdoc Seminar 2024 – 2025
Organized by James Hotchkiss and Siddhi Krishna
Organized by James Hotchkiss and Siddhi Krishna
October 29, 5 pm in Room 528
Juan Esteban Rodriguez Camargo
In this expository talk I will explain what condensed mathematics is about and why it is both conceptually and practically helpful in different research areas related with geometry, analysis and algebra.
November 7, 5 pm in Room 622
A recurring theme in probability theory is that of universality: when extremely different looking systems have the same large scale statistical behavior. In the last few decades, an important new universality class has been discovered, called the Kardar-Parisi-Zhang (KPZ) universality class, but the universality is only putative as only a handful of "metric" type models have been shown to lie in it in the strongest sense.
In this talk we will discuss a recent proof of membership in the KPZ class of the first non-metric type of model, namely the colored stochastic six-vertex model. The model arises naturally in probability theory and has connections to many areas of statistical physics and quantum integrable systems; e.g., the first form of the six-vertex model was introduced by Pauling in 1935 to model the crystal structure of ice. The Yang-Baxter equation and line ensembles (collections of random non-intersecting curves) will play fundamental roles in our discussion, but no prior background will be assumed. This is based on joint work with Amol Aggarwal and Ivan Corwin.
December 13, 4:30 pm in Room 507
In geometric topology, we study and classify 3- and 4-dimensional manifolds based on their topological and geometric properties. A taut foliation is a special type of geometric structure on a 3-manifold that sheds light on many of its characteristics. These types of structures are predicted to be ubiquitous, but they are famously difficult to construct! In this talk, I'll tell you a bit about why these structures matter, when they may or may not exist, and a bit about how to construct them. No background will be assumed -- all are welcome!
March 24, 5:30 pm in Room 307
James Hotchkiss
The period-index problem is an elementary question about central simple algebras over a field, originating in developments in algebraic number theory from the early part of the twentieth century. I will give an introduction to the problem, and discuss several recent developments based on bringing in ideas from complex algebraic geometry and topology.
April 22, 5:30 pm in Lewisohn 508
Gravitational waves are one of the most striking predictions of General Relativity. Originally proposed by Einstein in 1916, they were first experimentally detected a century later by LIGO. Using spinors and spacetime harmonic functions, we are able to characterize them geometrically.