Date: June 24, 2023 (Saturday).
Location: online via Zoom.
Plenary speakers
Hoang-Son Do (Đỗ Hoàng Sơn) (Institute of Mathematics, Vietnam)
Duong Ngoc Son (Dương Ngọc Sơn) (Phenikaa University, Vietnam)
Thang Nguyen (Nguyễn Quang Thắng) (Florida State University, USA)
Thuy-Duong “June” Vuong (Vương Nguyễn Thuỳ Dương) (Stanford University, USA)
Organizers: Lê Quang Nẫm (Indiana University), Nguyễn Tiến Khải (NCSU), Phan Văn Tuộc (UTK), Trần Vĩnh Hưng (UW Madison).
Program
Registration link
Talk information
- Hoang-Son Do
- Title: Stability of solutions to complex Monge-Ampère equations
- Abstract: In this talk, we introduce our recent results on the quantitative stability in weighted complex Monge-Ampère energies. Using these results, we prove a quantitative version of the comparison principle and a quantitative stability property in capacity for solutions to complex Monge-Ampère equations. This is a joint work with Vu Duc Viet (University of Cologne).
- Duong Ngoc Son
- Title: On CR maps between real hypersurfaces in complex spaces.
- Abstract: We will discuss the classification problem of CR maps between certain modeled real hypersurfaces in complex space, including the sphere, the tube over the future light cone, and the Winkelman hypersurface.
- Thang Nguyen
- Title: Group actions on manifolds, rigidity and local rigidity
- Abstract: One classical approach to study manifolds and groups is studying their interactions. The basic question whether a certain group can act on a certain manifold was looked at, and is the main theme of Zimmer’s program. Depending on the context of the manifolds, the classes of groups, and the types of actions, many results have been found over the last several decades. The talk will give an overview from old results, even before Zimmer proposed his program, to recent developments. We then focus on some recent local rigidity phenomena discovered in the settings of actions with low regularity.
- Thuy-Duong Vuong
- Title: From Sampling to Optimization on Discrete Domains with Applications to Determinant Maximization
- Abstract: We show a connection between sampling and optimization on discrete domains. For a family of distributions μ defined on size k subsets of a ground set of elements that is closed under external fields, we show that rapid mixing of natural local random walks implies the existence of simple approximation algorithms to find max μ(⋅). We establish the connection between sampling and optimization by showing that an exchange inequality, a concept rooted in discrete convex analysis, can be derived from fast mixing of local random walks.
As the main application of our result, we show a simple nearly-optimal k^{O(k)}-factor approximation algorithm for MAP inference on nonsymmetric DPPs. This is the first nontrivial multiplicative approximation for finding the largest size k principal minor of a square (not-necessarily-symmetric) matrix L with L+L^T⪰0.
Seminar Toan Hoc 