SCTC2013

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+7^th Southern California Topology Colloquium (SCTC), to be held on Saturday, March 30^th, 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 1^st, 2013.

Speaker	Time	Title and Abstract
Coffee and snacks	9:30
Francis Bonahon University of Southern California	10:30-11:30	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.
lunch	11:30-1:30
Ciprian Manolescu University of California, Los Angeles	1:30-2:30	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 Fr�yshov�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	2:45-3:45	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	4:00-5:00	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	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.