Weibo Fu:Sharp bounds for multiplicities of Bianchi modular forms

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Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	Weibo Fu，Princeton University
Inviter:
Title:	Sharp bounds for multiplicities of Bianchi modular forms
Time & Venue:	2021.06.03 09:00-10:00 Zoom ID: 466 356 2952 Passcode: mcm1234
Abstract:	We prove a degree 1 saving bound for the dimension of the space of cohomological automorphic forms of fixed level and growing weight on SL2 over any number field that is not totally real. In particular, we establish a sharp upper bound on growth of Bianchi modular forms. We transfer our problem into a question over the usual universal envelop- ing algebras by applying an algebraic microlocalisation of Ardakov and Wadsley to completed homology. We solve the representation theoretic question by estimating growth of Poincare–Birkhoff–Witt filtrations on finitely generated modules.