Number Theory Seminar

Speaker: Antonio Cauchi (Concordia University)

Title: Algebraic cycles and functorial lifts from G2 to PGSp(6)

Abstract: The relation between the poles of automorphic L-functions and the non-vanishing of automorphic periods is often linked to questions in Langlands functoriality. In the case when the L-function is motivic, this correspondence can have applications to the arithmetic of the motive in question. In this talk, we examine an instance of this phenomenon in the case where the spin L-function of cuspidal automorphic representations of PGSp(6) has a simple pole at s=1. In particular, we describe the construction of certain algebraic cycles in the Siegel sixfold, whose regulator is related to the residue at s=1 of the spin L-function, and explain their role in the proof of a conjecture of Gross and Savin on the construction of seven dimensional motives with Galois group of type G2. This is joint work with Francesco Lemma and Joaquin Rodrigues Jacinto.

The talk will take place on Zoom. If you are interested in attending and not on the Number Theory Seminar mailing list, please contact the organizer to obtain the link