ICMS-Sofia and IMSA-Miami

presents

Consortium Distinguished Lecture Series

June 30, 2023, 15:30 (EEST, Sofia time),
“Prof. Marin Drinov” Hall, Bulgarian Academy of Sciences
1, “15th November” Str., Sofia
and via Zoom

Michael R. Douglas, Harvard University, CMSA

Michael R. Douglas received his PhD in Physics in 1988 under the supervision of John Schwarz, one of the developers and leading researchers in superstring theory.

Douglas is best known for his work in string theory, for the development of matrix models (the first nonperturbative formulations of string theory), for his work on Dirichlet branes and on noncommutative geometry in string theory, and for the development of the statistical approach to string phenomenology. He has influenced the developments of modern mathematics by finding interpretations of branes on the language of derived categories and introducing the theory of stability conditions for categories.

Douglas received the 2000 Sackler Prize in theoretical physics and has been a Gordon Moore Visiting Scholar at Caltech, a Louis Michel Visiting Professor at the IHES, and a Clay Mathematics Institute Mathematical Emissary. He is a fellow of the American Mathematical Society and a member of the American Physical Society, and has served as the editor of the Journal of High Energy Physics and of Communications in Mathematical Physics.

June 30, 2023, 15:30 (EEST, Sofia time) June 30, 2023, 17:00 (EEST, Sofia time)

Lecture 1: Tameness and quantum field theory

Abstract: I will discuss the notion of a space of quantum field theories, and explain various approaches to its definition and some of its expected properties. I will then cover joint work with Thomas Grimm and Lorenz Schlechter on tameness of quantum field theories.  This is based on the mathematical concept of o-minimal structures, which has been very powerful for proving finiteness results. Given a QFT or a space of QFTs, we define a corresponding structure, and conjecture in many cases that it is tame (o-minimal).  We also show that Feynman amplitudes at any fixed loop order are tame.

Lecture 2: Numerical methods for differential geometry

Abstract: State of the art machine learning techniques can be adapted to many problems in scientific and mathematical computation. In this talk, I will explain how this can be done for problems such as finding a numerical approximation to a Ricci flat metric, and discuss results for Calabi-Yau and G2 manifolds as well as exploratory studies on other manifolds.