Modular forms, supersymmetric field theories, and algebraic topology

Contact for zoom details: Barthel, Ozornova, Ray, Teichner.

Modular forms appear in many contexts in physics and mathematics. In two-dimensional supersymmetric quantum field theories they arise as certain expectation values. In algebraic topology, they emerge in the study of elliptic cohomology theories. A long-standing conjecture suggests that these two appearances of modular forms are intimately related. Specifically, the Stolz-Teichner program predicts that 2-dimensional supersymmetric Euclidean field theories provide a geometric model for the universal elliptic cohomology theory of topological modular forms (TMF). After explaining the ingredients, I’ll describe some recent progress.