Tuesday, December 7, 2021
Time | Items |
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All day |
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4:00pm |
12/07/2021 - 4:15pm A result of Mozes-Shah (1995) implies that a sequence of distinct totally geodesic surfaces equidistributes in a closed hyperbolic 3-manifold. Is this also true for a sequence of closed, connected, essential K-quasifuchsian surfaces with K going to one? Not necessarily — we will construct a family of increasingly geodesic connected quasifuchsian surfaces that can accumulate on any finite collection of totally geodesic surfaces. To explain that, we will outline the construction of quasifuchsian surface subgroups, following Kahn, Markovic and Wright. We will also use ideas of Liu-Markovic that ensure that our surfaces are always connected. Location:
LOM 214
12/07/2021 - 4:30pm We explain two connections between Boxer-Pilloni’s higher Coleman theory for modular curves and the completed cohomology of the towers of modular curves. In the first, we use the completed cohomology classes attached to overconvergent modular forms to give a new proof of the slope classicality theorem in higher Coleman theory. In the second, we explain how cup products with the groups in higher Coleman theory furnish a finite level description of (a large chunk of) Pan’s Hodge-Tate decomposition for highest weight vectors in completed cohomology. Location:
Zoom
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