In-Person and Online Talk 

Zoom link:  https://princeton.zoom.us/j/97126136441

Passcode: The three digit integer that is the cube of the sum of its digits

We study CM cycles on Kuga-Sato varieties over X(N) via theta lifting and relative trace formula.  Our first result is the modularity of CM cycles, in the sense that the Hecke modules they generate are semisimple whose irreducible components are associated to higher weight holomorphic cuspidal automorphic representations of GL_2(Q). This is proved via  theta lifting. Our second result is a higher weight  analog of the general Gross-Zagier formula of Yuan, S. Zhang and W. Zhang.

This is proved via relative trace formula, provided the modularity of CM cycles.