For Attendees' Attention: This lecture will be held on-site at LT-K and online via zoom.

Abstract

We consider the problem of minimizing an objective function without any derivative information. Such optimization is called zeroth-order, derivative-free, or black-box optimization.

The remarkable empirical performance of Generative Adversarial Networks (GANs) in generating high-quality samples have attracted enormous attention in the past few years. In this talk, we discuss how well can GANs approximate and learn high-dimensional distributions.

We study the existence of positive functions K in C^1(S^n) such that the conformal Q-curvature equation Pm(v) = K v^{n*} on S^n has a singular positive solution v whose singular set is a single point, where m is an integer sa