Special cycles on $G_2$

Abstract: On the symmetric space for $G_2$, there exist various submanifolds $G_D$ corresponding to the stabilizer of a norm $D$ vector. We show that when a suitable automorphic form is integrated against the $G_D$, the resulting numbers assemble to give a half-integral weight classical modular form. Although this is already implied by a result of Kudla-Millson, we give a simpler proof that avoids the complications in their paper.

number theory

Audience: researchers in the topic

UCSD number theory seminar

Series comments: Most talks are preceded by a pre-talk for graduate students and postdocs. The pre-talks start 40 minutes prior to the posted time (usually at 1:20pm Pacific) and last about 30 minutes.