Topological Modular Forms and supersymmetric quantum field theories

by Mayuko Yamashita (Kyoto University)

Wednesday 7 Feb 2024, 14:00 → 16:00 Europe/Zurich

Maximum

In this talk, I explain my works and perspectives on the Segal-Stolz-Teichner program, which is one of the most deep and important topic relating homotopy theory and physics. Mathematically, they propose a geometric model of TMF, the spectrum of Topological Modular Forms, in terms of supersymmetric quantum field theories. My recent works have been motivated by their proposal. I explain my collaborations with Yuji Tachikawa relating the Anderson self-duality of topological modular forms (in homotopy theory) and absence of anomaly in heterotic string theory (in physics), and my recent collaboration with Theo Johnson-Freyd on giving geometric understanding of the 576-periodicity of TMF. I would like to illustrate the exciting interplay between mathematics and physics. In the higher structure seminar on Wednesday I will explain homotopy-theoretical side of the story, and in the RTG colloquium on Thursday I will give a an overall account of my works aimed at a general audience.