Constraint Satisfaction Problems and Probabilistic Combinatorics II

Fotios Illiopoulos
Member, School of Mathematics
November 26, 2019

The tasks of finding and randomly sampling solutions of constraint satisfaction problems over discrete variable sets arise naturally in a wide variety of areas, among them artificial intelligence, bioinformatics and combinatorics, and further have deep connections to statistical physics.

In this second talk of the series, I'll cover some results regarding random constraint satisfaction problems and their connection to statistical physics.

Unique and 2:2 Games, Grassmannians, and Expansion

Irit Dinur
Weizmann Institute of Science; Visiting Professor, School of Mathematics
November 20, 2019

The unique games conjecture gives a very strong PCP theorem, which, if true, leads to a clean understanding of a broad family of approximation problems. We will describe recent progress on the conjecture and how certain type of expansion and hypercontractivity of the Grassmannian complex plays a key role.

Nonconvex Minimax Optimization

Chi Jin
Princeton University; Member, School of Mathematics
November 20, 2019

Minimax optimization, especially in its general nonconvex formulation, has found extensive applications in modern machine learning, in settings such as generative adversarial networks (GANs) and adversarial training. It brings a series of unique challenges in addition to those that already persist in nonconvex minimization problems. This talk will cover a set of new phenomena, open problems, and recent results in this emerging field.