Jesus Sanchez Jr
(Washington University in St Louis)
February 17, 2023
Organized by Americas GNCG Seminar.

Equivariant Local Index Theory for Lie Groupoids

 In recent work, Higson and Yi developed a new perspective on Getzler’s symbol calculus, reinterpreting the latter in terms of a convolution algebra of sections of a multiplicative vector bundle over the tangent groupoid of a spin manifold. In joint work with S. Liu, Y. Loizides, and A.R.H.S. Sadegh we generalize the construction in two directions; to the equivariant setting, and to the adiabatic groupoid of any Lie groupoid. We discuss applications including an equivariant longitudinal local index theorem for Lie groupoids with a closed space of units.

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