N+10th Southern California Topology Colloquium


Saturday, April 6, 2019


The Caltech Geometry and Topology Seminar, with funding from Caltech and NSF, is pleased to sponsor the N+10th Southern California Topology Colloquium (SCTC), to be held on Saturday, April 6th, 2019. All talks will be in 310 Linde Hall. Coffee and snacks will be available outside the classroom. The speakers are Richard Bamler, Matthew Durham, Jen Hom, and Yi Liu.





Title and Abstract

Coffee and snacks


Yi Liu (Peking University, BICMR)


Title: On virtual homological eigenvalues of surface automorphisms

Abstract: Given a mapping class of a closed orientable surface, we look at any lift of the mapping class to any finite cover of the surface. An eigenvalue of the induced homological action of the lift will be called a virtual homological eigenvalue. How much about the mapping class can we learn through virtual homological eigenvalues? In this talk, I will discuss some results related to this question. In particular, I will present some ways to combine the Nielsen fixed point theory with the more recent virtual specialization techniques in 3-manifold topology.





Richard Bamler (UC, Berkeley)


Title: Classification of diffeomorphism groups of 3-manifolds through singular Ricci flow
Abstract: I will present recent work of Bruce Kleiner and myself in which we classify the diffeomorphism groups of all spherical and hyperbolic 3-manifolds up to homotopy, except for RP^3. This partially resolves the Generalized Smale Conjecture in the spherical case and reproves a theorem due to Gabai in the hyperbolic case.

Our proof is based on a new uniqueness theorem for singular Ricci flows, which we have established in previous work. Singular Ricci flows were introduced by Kleiner and Lott and are similar to Perelman’s Ricci flows with surgery, as used in his resolution of the Poincaré and Geometrization Conjectures. In contrast to Perelman’s surgery process, which is carried out at a positive scale and depends on a number of auxiliary parameters, a singular Ricci flow is more canonical, as it "flows through surgeries" at an infinitesimal scale. Our uniqueness theorem allows the study of continuous families of singular Ricci flows, providing important information on the diffeomorphism group of the underlying manifold.

Matthew Durham (UC, Riverside)


Title: Almost hyperbolic surface bundles over surfaces
Abstract: Whether there exists a hyperbolic surface bundle over a closed surface is a well-known open problem in low-dimensional topology, even when one only requires hyperbolicity at the level of fundamental groups.  In this talk, I will give some background on this family of problems and explain how to reframe them in terms of the geometry of subgroups of the mapping class group.  Then I will describe new examples of nearly hyperbolic surface bundles over naturally interesting surfaces coming from Teichmuller dynamics, namely Veech surfaces and Leininger-Reid combinations thereof.   This is based on joint work with Spencer Dowdall, Chris Leininger, and Alessandro Sisto.

Jen Hom (Georgia Tech)


Title: Heegaard Floer and homology cobordism

Abstract: We show that the three-dimensional homology cobordism group admits an infinite-rank summand. It was previously known that the homology cobordism group contains an infinite-rank subgroup and a Z-summand. The proof relies on the involutive Heegaard Floer homology package of Hendricks-Manolescu and Hendricks-Manolescu-Zemke. This is joint work with I. Dai, M. Stoffregen, and L. Truong.


Party at Avery Courtyard,

spouses and children are welcome







Parking is free in the Caltech lots on weekends. The nearest parking lot to the Linde Hall is Structure #3.



Information about driving directions and public transportation can be found here. If you come by flight, you may fly to Burbank (BUR), Los Angeles (LAX), Ontario (ONT), Long Beach (LGB), or Orange County (SNA), then take a supershuttle to Caltech. BUR is the closest airport, and LAX has the most flights.



If you need a hotel, the Saga Motor Hotel and Vagabond Inn are close and affordable.



Limited travel and lodging support is available for graduate students (especially those coming from Northern California). To apply, please contact Yi Ni and have your advisor send a brief (1 or 2 paragraphs) email of reference.


History of the SCTC.