Tuesday, April 19, 2022
Time | Items |
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All day |
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4:00pm |
04/19/2022 - 4:15pm Freedman and Krushkal recently defined the notion of a filling link in 3-manifolds: a link L is filling in M if for any 1-spine G of M which is disjoint from L, pi_1(G) injects into pi_1(M - L). It turns out that proving the existence of filling links is very subtle, even for concrete examples. In this talk we will investigate an intimate relationship between filling links and Kleinian surface groups. We will leverage this connection to prove the existence of filling links in 3-manifolds of small Heegaard genus, using ideas from minimal surfaces, arithmetic groups, and the Hilden-Lozano-Montesinos theory of universal links. Location: 04/19/2022 - 4:30pm For any parahoric $\mathbb Z_{p^2}/ \mathbb Z_p$ hermitian lattice, I will formulate and prove an arithmetic transfer identity relating derived intersection numbers on relevant Rapoport--Zink spaces to derivatives of relevant orbital integrals, including the arithmetic fundamental lemma as a special case. As our moduli spaces are usually singular, we resolve the singularity (similar to the Atiyah flop) to define well-behaved intersection numbers. I will focus on local pictures. These identities have applications towards the arithmetic GGP conjecture for unitary groups, which generalizes the Gross-Zaiger formula on Shimura curves to higher dimensions. Location: |