Geometric and arithmetic theta correspondences

Abstract

Geometric/arithmetic theta correspondences provide correspondences between automorphic forms and cohomology classes/algebraic cycles on Shimura varieties. We give an introduction focusing on the example of unitary groups and highlight recent advances in the arithmetic theory (also known as the Kudla program) and their applications. These are expanded lecture notes for the IHES 2022 Summer School on the Langlands Program.

29 pages. final version. To appear in the proceedings of the IHES 2022 Summer School on the Langlands Program