N+8th Southern California Topology Colloquium

 

Saturday, March 26, 2016

 

The Caltech Geometry and Topology Seminar, with funding from Caltech, NSF and the Alfred P. Sloan Foundation, is pleased to sponsor the N+8th Southern California Topology Colloquium (SCTC), to be held on Saturday, March 26th, 2016. All talks will be in 151 Sloan. Coffee and snacks will be available outside the classroom. The speakers are Julie Bergner, Ian Biringer, Ko Honda, and Zhenghan Wang.

 

 

Speaker

Time

Title and Abstract

Coffee and snacks

 9:30  

Ko Honda (UCLA)

10:30-11:30

 Semi-global Kuranishi charts and the definition of contact homology

 

Abstract: In this talk I will explain how to define the full contact homology algebra for any contact manifold and show that it is an invariant of the contact manifold. Our approach uses a simplified version of Kuranishi perturbation theory, consisting of ``semi-global'' Kuranishi charts (for example, if a relevant moduli space of holomorphic maps is compact, then we only need one chart). This is joint work with Erkao Bao.

lunch

11:30-1:30

 

Ian Biringer (Boston College)

1:30-2:30

Growth of Betti numbers via foliated limits

 

Abstract: We study the ratio of the k^th Betti number of a manifold to its volume, and give a strong convergence result for higher rank locally symmetric spaces. The key is a compactification of sets of Riemannian manifolds with constrained geometry (e.g. locally symmetric spaces), where the added limit points are transverse measures on some universal foliated space.

Julie Bergner (UC, Riverside)

2:45-3:45

 
An introduction to homotopical categories

Abstract: Homotopy theory originated with the study of topological spaces up to weak homotopy equivalence. For many purposes, it became convenient to work instead with simplicial sets, which provide a combinatorial model for topological spaces. In recent years, the close relationship between simplicial sets and categories has been further investigated, leading to notions of "topological category up to homotopy". In this talk I'll give an overview of these developments and how they apply back to topology.

Zhenghan Wang (Microsoft Station Q, UCSB)

4:00-5:00

 State-sum (3+1)-TQFTs

 

Abstract: Unitary fusion categories are the algebraic input for the Turaev-Viro type TQFTs in (2+1)-dimensions. We are interested in a generalization to (3+1)-dimensions. Mackaay’s spherical 2-categories are not general enough to include interesting examples such as the G-crossed braided fusion categories. We will discussion some new (3+1)-TQFTs with G-crossed braided fusion categories as input based on the thesis work of Shawn X. Cui.

Party at Francis and Erica's

spouses and children are welcome

 

5:30

 

 

 

Parking:

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

 

Travel:

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.

 

Lodging:

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

 

Support:

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.