Columbia / Courant Joint Probability Seminar

Columbia University, Friday May 3, 2019



9:30-10:10 Coffee and tea (Room 508)
10:10-11:00 Jason Fulman [Central limit theorems for character values of symmetric groups]
11:10-12:00 Timo Seppäläinen [Geometry of the corner growth model]
12:00-1:00 Lunch will be provided in Room 508
1:00-1:50 Eliran Subag [Optimization of random polynomials on the sphere in the full-RSB regime]
  Practical Information
The talks will take place at Columbia University Mathematics building in Room 520, on May 3, 2019. No registration necessary.

Directions to Columbia.

For further information, please contact the organizers.

  Titles and Abstracts

Jason Fulman (Univ. of Southern California)
Central limit theorems for character values of symmetric groups

Abstract: We study central limit theorems for random character values of the symmetric groups. We describe three approaches: the method of moments, martingales, and Stein’s method. Although the objects studied are of algebraic origin, this talk is aimed at probabilists and no background in algebra is needed.

Timo Seppäläinen (Univ. of Wisconsin-Madison)
Geometry of the corner growth model [Slides]

Abstract: The corner growth model is a last-passage percolation model of random growth on the square lattice. It lies at the nexus of several branches of mathematics: probability, statistical physics, queueing theory, combinatorics, and integrable systems. It has been studied intensely for almost 40 years. We review properties of the geodesics, Busemann functions and competition interfaces of the corner growth model and present new qualitative and quantitative results on the overall geodesic picture and the joint distributions of the Busemann functions. Based on collaborations with Louis Fan (Indiana), Firas Rassoul-Agha and Chris Janjigian (Utah).

Eliran Subag (NYU Courant)
Optimization of random polynomials on the sphere in the full-RSB regime

Abstract: The talk will focus on optimization on the high-dimensional sphere when the objective function is a polynomial with independent Gaussian coefficients. Such random processes are called spherical spin glasses in physics, and have been extensively studied since the 80s. I will describe certain geometric properties of spherical spin glasses unique to the full-RSB case, and explain how they can be exploited to design a polynomial time algorithm that finds points within vanishing error from the global minimum.