Events

May 7 - May 14, 2023

Monotonicities and master equations in mean field games - Part 3

Alpar Meszaros, Assistant Professor, Department of Mathematical Sciences, Durham University (UK)

May 11, 10:30 - 12:00

B1 L4 R4102

The theory of mean field games (MFG for short) aims to study limiting behavior of Nash equilibria of (stochastic) differential games when the number of agents tends to infinity. While in general existence of MFG Nash equilibria can be established under fairly general assumptions, uniqueness is the exception rather than the rule.
A brief introduction to the obstacle problem regularity theory - Part 3

Eduardo Teixeira, Full Professor, Department of Mathematics, University of Central Florida (USA)

May 11, 08:30 - 10:00

B1 L4 R4102

How does an elastic membrane lie on a given obstacle? This naive looking question hides a beautiful mathematical theory integrating powerful tools with far-reaching applications. In this mini-course we will discuss the obstacle problem as a free boundary model. All necessary tools will be carefully constructed from scratch. We will mainly focus on: optimal regularity of solutions, non-degeneracy estimates, weak geometric-measure properties of the free boundary, classification of global profiles, and differentiability of the free boundary.
Monotonicities and master equations in mean field games - Part 2

Alpar Meszaros, Assistant Professor, Department of Mathematical Sciences, Durham University (UK)

May 9, 10:30 - 12:00

B1 L4 R4102

The theory of mean field games (MFG for short) aims to study limiting behavior of Nash equilibria of (stochastic) differential games when the number of agents tends to infinity. While in general existence of MFG Nash equilibria can be established under fairly general assumptions, uniqueness is the exception rather than the rule.
A brief introduction to the obstacle problem regularity theory - Part 2

Eduardo Teixeira, Full Professor, Department of Mathematics, University of Central Florida (USA)

May 9, 08:30 - 10:00

B1 L4 R4102

How does an elastic membrane lie on a given obstacle? This naive looking question hides a beautiful mathematical theory integrating powerful tools with far-reaching applications. In this mini-course we will discuss the obstacle problem as a free boundary model. All necessary tools will be carefully constructed from scratch. We will mainly focus on: optimal regularity of solutions, non-degeneracy estimates, weak geometric-measure properties of the free boundary, classification of global profiles, and differentiability of the free boundary.
Monotonicities and master equations in mean field games - Part 1

Alpar Meszaros, Assistant Professor, Department of Mathematical Sciences, Durham University, UK

May 8, 10:30 - 12:00

B1 L4 R4102

The theory of mean field games (MFG for short) aims to study limiting behavior of Nash equilibria of (stochastic) differential games when the number of agents tends to infinity. While in general existence of MFG Nash equilibria can be established under fairly general assumptions, uniqueness is the exception rather than the rule. For finite horizon mean field games uniqueness typically holds if the time horizon is small (or the data satisfies other smallness conditions).
A brief introduction to the obstacle problem regularity theory - Part 1

Eduardo Teixeira, Full Professor, Department of Mathematics, University of Central Florida (USA)

May 8, 08:30 - 10:00

B1 L4 R4102

How does an elastic membrane lie on a given obstacle? This naive looking question hides a beautiful mathematical theory integrating powerful tools with far-reaching applications. In this mini-course we will discuss the obstacle problem as a free boundary model. All necessary tools will be carefully constructed from scratch. We will mainly focus on: optimal regularity of solutions, non-degeneracy estimates, weak geometric-measure properties of the free boundary, classification of global profiles, and differentiability of the free boundary.