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Philadelphia Area Number Theory Seminar

Wednesday, December 11, 2019 - 2:15pm

Mikolaj Fraczyk

Institute for Advanced Study

Location

Bryn Mawr College

Park Science Building, Room 328

Talk is scheduled to begin at 2:40 PM. Tea and refreshments will be served at 2:20 PM in the Math Lounge, Park Science Building, Room 361.

Let G ⊂ GL(N, Q) be a semi-simple linear group and write Γ(N) for the principal congruence subgroup of Γ := G(Z) of level N. DeGeorge and Wallach proved in late 70’s that for any discrete series representation π of G(R), the multiplicity of π in L2(G(R)/Γ(N)) grows roughly linearly in the index [Γ : Γ(N)]. This phenomenon is a special case of the limit multiplicity property which predicts that suitably normalized counting measure on the discrete spectrum of L2(G(R)/Γ(N)) should converge to the Plancherel measure on the unitary dual of G. I will talk about the limit multiplicity property for horizontal (i.e. pairwise non-commensurable) families of arithmetic lattices in semi-simple Lie groups, with particular focus on the rank-1 cases. Talk is based on a joint work with Jean Raimbault.