N+7th Southern California Topology Colloquium


Saturday, March 30, 2013


The Caltech Geometry and Topology Seminar, with funding from Caltech, NSF and the Alfred P. Sloan Foundation, is pleased to sponsor the N+7th Southern California Topology Colloquium (SCTC), to be held on Saturday, March 30th, 2013. All talks will be in 151 Sloan. Coffee and snacks will be available outside the classroom. There will also be a Leonidas Alaoglu Memorial Lecture given by Ian Agol on Monday, April 1st, 2013.





Title and Abstract

Coffee and snacks


Francis Bonahon

University of Southern California


Hitchin representations

The talk will be centered around certain group homomorphisms from the fundamental group of a surface S to a Lie group G. Over the past thirty years, much of low-dimensional topology and hyperbolic geometry has been based on the cases where G = SL_2(R) or SL_2(C). Hitchin, and more recently Fock, Goncharov, Labourie and others have shown how to extend some of the corresponding properties to more general Lie groups such as G = SL_n(R). I will discuss additional results in this direction, obtained in collaboration with Guillaume Dreyer. 




Ciprian Manolescu

University of California,

Los Angeles


Floer homology and the Triangulation Conjecture

Using finite dimensional approximation and Conley index theory, we define Pin(2)-equivariant Seiberg-Witten Floer homology for rational homology 3-spheres equipped with a spin structure. The analogue of Frøyshov’s correction term in this setting is an integer-valued invariant of homology cobordism whose mod 2 reduction is the Rokhlin invariant. As an application, we show that the 3-dimensional homology cobordism group has no elements of order 2 that have Rokhlin invariant one. By previous work of Galewski-Stern and Matumoto, this implies the existence of non-triangulable high-dimensional manifolds.

Lenny Ng

Duke University


Knot contact homology and the augmentation polynomial
Knot contact homology is a package of invariants of knots and links that 
comes from counting holomorphic curves in the cotangent bundle to R^3 
with boundary on the conormal bundle. Recently, one part of this 
package, the augmentation polynomial, has shown up in some surprising 
places, including relations to the A-polynomial, colored HOMFLY 
polynomials, and physics work of Aganagic, Vafa, Gukov, and others. I 
will give a brief overview of knot contact homology and discuss these 
recent developments. This is partly joint work with Mina Aganagic, 
Tobias Ekholm, and Cumrun Vafa.

Ian Agol

University of California, Berkeley


Virtually special cube complexes


We'll discuss the resolution of a conjecture of Dani Wise, that compact cube complexes with hyperbolic fundamental group are virtually special. In particular, we'll discuss a technical result of Wise, the Malnormal Special Quotient Theorem, which is a key input to the proof of Wise's conjecture via a hyperbolic Dehn filling result which is joint work with Daniel Groves and Jason Manning. The consequences of Wise's conjecture, in particular the virtual Haken conjecture, will be discussed in the Alaoglu lecture.

Party at Francis and Erica's

spouses and children are welcome






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