Description: This course introduces how to develop deep generative models (DGMs) by integrating probabilistic graphical models and deep learning to generate realistic data including images, texts, graphs, etc. Course contents include 1) basics of probabilistic graphical models, including Bayesian network and Markov random field; 2) posterior inference methods, including message passing, variat...
AbstractA powerful technique in representation theory is localization, wherein one identifies categories of modules for an algebra of interest with categories of D-modules or perverse sheaves. After reviewing the classical Beilinson”ŖBernstein theorem, which introduced localization for semisimple Lie algebras, we will describe some analogues for certain vertex algebras, notably W-algebras and...