# Analysis Seminar

#### Global-in-time Solvability of Mean-Field Control Problems and Related Equations

**Speaker:**
Tak Kwong Wong, The University of Hong Kong

**Location:**
Warren Weaver Hall 1314

**Date:**
Wednesday, April 3, 2024, 3:30 p.m.

**Synopsis:**

Mean-field theory provides an effective approximation of interactions among a

huge amount of agents, and hence, makes the study of optimal control

problems with numerous agents becoming feasible in both mathematical

analysis and numerical simulations. The mean-field type control problems arise

from various real-world applications, in which all the numerous agents

collaborate to optimize a single ultimate objective function, and play a crucial

role in understanding social planner problems, electricity networks, residual

neural networks (ResNet) with batch normalization, etc. In this talk, we will

first introduce the first-order mean-field type control problems in a generic

setting, and then discuss the global-in-time solvability of these problems and

their differential equations. If time permits, new results in mean field games

will also be discussed.

This is a joint work with Alain Bensoussan, Phillip Yam, and Hongwei Yuan.

**Notes:**

**Special Analysis Seminar**