Geometry and Topology Seminar
|August 29||Yuanqi Wang||Liouville theorem for complex Monge-Ampere equations with conic singularities.||Wang|
|September 12||Chris Davis (UW-Eau Claire)||L2 signatures and an example of Cochran-Harvey-Leidy||Maxim|
|September 19||Ben Knudsen (Northwestern)||TBA||Ellenberg|
|October 3||Kevin Whyte (UIC)||Quasi-isometric embeddings of symmetric spaces||Dymarz|
|October 10||Alden Walker (UChicago)||Transfers of quasimorphisms||Dymarz|
|October 31||Jing Tao (Oklahoma)||TBA||Kent|
|November 1||Young Geometric Group Theory in the Midwest Workshop|
|November 7||Thomas Barthelmé (Penn State)||TBA||Kent|
Liouville theorem for complex Monge-Ampere equations with conic singularities.
Following Calabi, Pogorelov, Evans-Krylov-Safanov, and Trudinger's pioneer work on interior regularities and liouville theorems for Monge-Ampere equations, we prove the Liouville theorem for conic Kähler-Ricci flat metrics. We also discuss various applications of this Liouville theorem to conic Kähler geometry.
Chris Davis (UW-Eau Claire)
L2 signatures and an example of Cochran-Harvey-Leidy
Ben Knudsen (Northwestern)
Rational homology of configuration spaces via factorization homology"
The study of configuration spaces is particularly tractable over a field of characteristic zero, and much effort has gone into producing chain complexes simple enough for explicit computations, formulas for Betti numbers, and homological stability results. I will discuss recent work identifying the homology of the configuration spaces of an arbitrary manifold M with the homology of a certain Lie algebra constructed from the compactly supported cohomology of M. The aforementioned results follow immediately from this identification, albeit with hypotheses removed; in particular, one obtains a new, elementary proof of homological stability for configuration spaces.
Kevin Whyte (UIC)
Alden Walker (UChicago)
Rotation quasimorphisms on free groups coming from hyperbolic surface realizations are a particularly nice class of quasimorphisms. I'll describe a transfer construction which lifts rotation quasimorphisms from finite index subgroups, and I'll give an infinite family of examples of group chains for which this construction produces an extremal quasimorphism. Though dynamics and geometry underlie this construction, my talk will be primary combinatorial and should be accessible to anyone at all familiar with geometric group theory. This is joint work with Danny Calegari.
Jing Tao (Oklahoma)
Thomas Barthelmé (Penn State)