Abstract 

In this talk, I will explain the work "Topological modular forms and the absence of all heterotic global anomalies" (https://arxiv.org/abs/2108.13542) with Yuji Tachikawa from a mathematical point of view. That work is aimed at settling a physical problem to show the vanishing of anomalies in heterotic string theories. We translate the problem into a mathematical problem to show that a certain transformation of generalized cohomology theories from TMF (Topological Modular Forms) to the Anderson dual to String bordism vanishes, and prove that it is indeed the case. Here, the Anderson dual of a generalized homology theory plays the crucial role in the classification of anomalies by a conjecture of Freed and Hopkins. I will also explain this point, as well as related works on the Anderson duals.