Weakly commensurable Zariski-dense subgroups of semi-simple groups and isospectral locally symmetric spaces

開催日時: 
2014/07/02 Wed 16:30 - 17:30
場所: 
RIMS110号室
講演者: 
Gopal Prasad
講演者所属: 
University of Michigan
概要: 

I will discuss the notion of weakly commensurable 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 are 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.