Lecture Hall 5F, Cosmology Building, NTU

(臺灣大學宇宙學大樓 五樓演講廳)

Equivariant Fixed Point Formulae and Toeplitz Operators under Hamiltonian Torus Actions

Andrea Galasso ()

Abstract:

Suppose given a holomorphic and Hamiltonian action of a compact torus on a polarized Hodge manifold. Assume that the action lifts to the quantizing line bundle, so that there is an induced unitary representation on the associated Hardy space which decomposes into isotypes. In this talk we consider the description of asymptotics along rays in weight space of traces of equivariant Toeplitz operators composed with quantomorphisms for torus actions. The main ingredient in the proof is the microlocal analysis of the equivariant Szegö kernels. As a particular case we obtain a simple approach for asymptotics of the Lefschetz fixed point formula and traces of Toeplitz operators in the setting of ladder representations.