Elizabeth Collins-Woodfin (McGill)

Probability Seminar

Wednesday, March 22nd, 2023

Time: 12:00 p.m.  Place: Jeffery Hall, Room 234

Speaker: Elizabeth Collins-Woodfin (McGill)

Title: Phase transitions in spherical spin glass models

Abstract: This talk will focus on a series of recent results involving phase transitions in the spherical Sherrington-Kirkpatrick (SSK) spin glass model. In addition to their physical meaning, these phase transitions can be interpreted in the context of statistics, random matrix theory, and optimization problems. In the first half of the talk, I will discuss the transition between SSK with an external field and SSK without an external field (based on my joint work with Baik, le Doussal, Wu). In the second half of the talk, I will discuss the transition between high and low temperature SSK. Recent papers by Landon and by Johnstone-Klochkov-Onatski-Pavlyshyn have analyzed the free energy fluctuations of SSK at the critical temperature. I will summarize these papers and then discuss my current work to extend their result to a bipartite spin glass model (joint with Le). While the context for all of these works is spin glass, my focus is primarily theoretical and draws on tools from random matrix theory, as well as contour integral analysis.