Modularity of generating functions of special cycles on unitary Shimura varieties

Abstract: Special cycles on orthogonal and unitary Shimura varieties are analogues of Heegner points on modular curves in higher dimensions. Following work of Hirzebruch--Zagier, Gross--Zagier, Gross--Keating, and Kudla--Millson, Kudla predicted the modularity of generating functions of these special cycles in the 1990s.

I will review some historic development of this conjecture, and summarize recent results built upon earlier work of Borcherds and Zhang. I will also talk about arithmetic applications, especially the recent work of Li--Liu on arithmetic inner product formula. Time permitting, I will sketch the method of Bruinier--Raum and discuss its scope.

number theory

Audience: researchers in the topic

Algebra and Number Theory Seminars at Université Laval