Activities This Week

This is part 1 of the speaker’s talk from last semester, expanded into a two-part series.

The functoriality conjecture is a key ingredient in the theory of automorphic forms and the Langlands program. Given two reductive groups G and H, the principle of functoriality asserts that a map r:G^->H^ between their dual complex groups should naturally give rise to a map r*:Rep(G)->Rep(H) between their automorphic representations. In this talk, I will describe the idea of functoriality, its connection to L-functions and recent work on weak functorial lifts to the exceptional group of type G_2.

We will consider a class of groups defined by their action on Cantor space and use the invariant of finiteness properties to find among these groups an infinite family of quasi-isometry classes of finitely presented simple groups.

This is a joint work with Stefan Witzel and Matthew C. B. Zaremsky.