By Viatcheslav Kharlamov
By Michele Ancona
By Olivier Benoist
By Chao Li
Appears in collection : Summer School on the Langlands Program
Geometric/arithmetic theta correspondences provide correspondences between automorphic forms and cohomology classes/algebraic cycles on Shimura varieties. I will 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.