Consortium Distinguished Lecture Series
Michael Douglas
Coassociative fibrations
Michael R. Douglas, Harvard University
Thursday, June 29 & 30, 2023
ICMS Sofia, Bulgaria
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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.
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