Beijing Institute of Mathematical Sciences and Applications

Stephen S-T. Yau

Jiayi Kang

Monday, August 21, 2023 2:30 PM - 3:00 PM

数学系理科楼A-203

The primary aim of this report is to introduce the complexity of the task of sampling: given a target probability density π ∝ exp(−V ) on R^d , how expensive is it to generate random variables whose law is close to π in suitable metrics? Since the dawn of the Markov chain Monte Carlo (MCMC) revolution, sampling has been the algorithmic cornerstone of Bayesian inference and scientific computing. How do we design fast samplers, and how can we develop a theory of complexity for this task?

Jiayi Kang received his Ph.D. in Mathematics from Tsinghua University in 2024. He joined the Beijing Institute of Mathematical Sciences and Applications (BIMSA) as an Assistant Researcher in July 2024, and became an Assistant Professor at the Hetao Institute for Mathematical and Interdisciplinary Sciences (HIMIS) in November 2025. His research focuses on the intersection of deep learning, nonlinear filtering, and computational biology. His main research interests include: neural network-based filtering algorithms and their mathematical foundations, sampling methods in Wasserstein geometry, nonlinear filtering theory (including the Yau-Yau method) and its applications in climate science and other fields, as well as computational genomics and evolutionary system modeling. He is committed to solving complex problems in science and engineering using mathematical and machine learning methods.