TOPOLOGICAL MODULAR FORMS AND VANISHING OF HETEROTIC ANOMALY

In this talk, based on my work with Yuji Tachikawa, I will explain how to use algebraic topology to solve the physical problem of vanishing anomalies in heterotic string theories. We translate this physical problem into the mathematical problem of showing that a certain transformation of generalized cohomology theories from Topological Modular Forms (TMF) to the Anderson duals of string bordisms vanishes. TMF is related to 2d-superconformal field theories via the Stoltz-Teichner conjecture, and the Anderson duals are related to the classification of anomalies via the Freed-Hopkins conjecture. I will explain these ingredients, as well as related works on Anderson duals.