Colloquium - Gopal Prasad

October 2, 2014

4:30PM - 5:30PM

CH 240

Add to Calendar 2014-10-02 16:30:00 2014-10-02 17:30:00 Colloquium - Gopal Prasad Title: Weakly Commensurable Zariski-Dense Subgroups of Semi-Simple Groups and Isospectral Locally Symmetric SpacesSpeaker: Gopal Prasad, University of MichiganAbstract: I will discuss the notion of weakly commensurability of Zariski-dense subgroups of semi-simple groups. This notion was introduced in my joint work with Andrei Rapinchuk (Publ. Math. IHES 109(2009), 113-184), where we determined when two Zariski-dense S-arithmetic subgroups of absolutely almost simple algebraic groups over a field of characteristic zero can be weakly commensurable. These results enabled us to prove that in many situations isospectral locally symmetric spaces  of simple real algebraic groups are necessarily commensurable.  This settled the famous question "Can one hear the shape of a drum?" of Mark Kac for these spaces. CH 240 Department of Mathematics math@osu.edu America/New_York public

Title: Weakly Commensurable Zariski-Dense Subgroups of Semi-Simple Groups and Isospectral Locally Symmetric Spaces

Speaker: Gopal Prasad, University of Michigan

Abstract: I will discuss the notion of weakly commensurability of Zariski-dense subgroups of semi-simple groups. This notion was introduced in my joint work with Andrei Rapinchuk (Publ. Math. IHES 109(2009), 113-184), where we determined when two Zariski-dense S-arithmetic subgroups of absolutely almost simple algebraic groups over a field of characteristic zero can be weakly commensurable. These results enabled us to prove that in many situations isospectral locally symmetric spaces of simple real algebraic groups are necessarily commensurable. This settled the famous question "Can one hear the shape of a drum?" of Mark Kac for these spaces.

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