Seminar| Institute of Mathematical Sciences
Time: Friday, January 30th, 2026,13:30-15:00
Location: IMS, RS408
Speaker: Xiaolong Han, Shanghai Institute for Mathematics and Interdisciplinary Sciences(SIMIS) and Fudan University
Abstract: Let M be an arithmetic hyperbolic manifold of type I with dimension at least 3. We explain how to use the rigidity of unipotent flow to upgrade Thurston’s bending construction to construct a sequence of hypersurfaces in M that are asymptotically geodesic, asymptotically dense in the Grassmann bundles, non-arithmetic, strongly filling, and quasi-convex. We then explain a current exploration between a right notion of asymptotically geodesic hypersurfaces of a hyperbolic manifold M and the property that the fundamental group of M is at least virtually a subgroup of integer-valued matrix groups. This is a joint work with Ruojing Jiang.