# Algebra/Topology seminar

Speaker: Pavel Safronov (Zurich).

Title: Categorified Grothendieck—Riemann—Roch theorem.

Abstract: The Grothendieck--Riemann--Roch theorem compares the Chern character of pushforward of a coherent sheaf along a smooth and proper map of varieties to the pushforward of the Chern character. Following the work of several people, it was understood in terms of functoriality of traces in symmetric monoidal categories. In this talk I will describe a categorification of the GRR theorem where one replaces coherent sheaves by quasi-coherent sheaves of categories. This is joint work with Marc Hoyois, Sarah Scherotzke and Nicolo Sibilla.