Speaker: Erik van Erp, Dartmouth College

Date: June 9, 2026

Abstract: Fritz Noether’s index theorem of 1927 expresses the index of a Toeplitz operator on the circle in terms of the winding number of its symbol. In his Ph.D. thesis of 1971, Venugopalkrishna generalized this formula to odd dimensional spheres, using Bott periodicity. In 1979, Boutet de Monvel generalized further to boundaries of strictly pseudoconvex complex domains. Finally, in 1989, Baum, Douglas and Taylor reformulated and deepened Boutet de Monvel’s formula as a statement in K-homology. In this talk I present an equivariant index theorem for Toeplitz operators that generalizes these now classical results to the case where a compact Lie group acts on the manifold. The proof of our equivariant formula requires a fundamentally different approach from those employed in earlier results. In particular, we do not assume or require that the manifold is the boundary of a complex domain. This is joint work with Alexander Gorokhovsky.