### Probability And Data Science ColloquiumTitle: Grothendeick L_p problem for Guaussian matricesSpeaker: Wei-Kuo Chen

Thursday, April 29, 2021
2:00pm – 3:00pm

Storrs Campus
Online

Speaker: Wei-Kuo Chen (University of Minnesota)

Title: Grothendeick L_p problem for Guaussian matrices

Abstract:

The Grothendieck L_p problem is defined as an optimization problem that maximizes the quadratic form of a Gaussian matrix over the unit L_p ball. The p=2 case corresponds to the top eigenvalue of the Gaussian Orthogonal Ensemble, while p=\infty this problem is known as the ground state energy of the Sherrington-Kirkpatrick mean-field spin glass model and its limit can be expressed by the famous Parisi formula. In this talk, I will describe the limit of this optimization problem for general p and discuss some results on the behavior of the near optimizers along with some open problems. This is based on a joint work with Arnab Sen.

Contact:

Zhongyang Li

Discrete Mathematics & Statistical Mechanics Seminar (primary)