The N+3rd Southern California Topology Conference

(also Ko Honda's 100th birthday^*)

Saturday January 20th, 2007

Map of campus is available here

Parking:

There is free parking in the Caltech lots on weekends. A complete map of the lots can be found here. There is also parking on the street, mainly on California or on Arden.

Lodging:

If you need a hotel, the Saga is close and cheap.

Getting to Pasadena by air:

We encourage people from outside Southern California to attend, especially graduate students. The most convenient airport is Burbank, but LAX has more flights. For Northern California folks, Southwest has frequent service from Oakland, San Jose, and Sacramento to Burbank. Ontario and Long Beach airports are also reasonable choices, but ground transit from them to Pasadena is more expensive. For all airports, you can use SuperShuttle to get to Pasadena (about $20 one-way for Burbank, $30 for LAX and $50 + for the other two).

Support:

Some travel and accomodation support is available for graduate students (especially those coming from Northern California). Please contact Danny Calegari by email (I'm sure you can track down my address somehow . . .)

Coffee and donuts available outside 151 Sloan, 10-10:30 am

Schedule of talks:

Speaker	Time	Room	Title
Benson Farb, U Chicago	10:30-11:30 am	151 Sloan	Problems and progress in understanding the Torelli group
Ko Honda, USC	1:30-2:30 pm	151 Sloan	Reeb vector fields and open book decompositions
Henry Segerman, Stanford	2:45-3:45 pm	151 Sloan	Incompressible Surfaces in Punctured Torus Bundles, and the Ideal Points They Come From
Amie Wilkinson, Northwestern	4-5 pm	151 Sloan	Asymmetrical diffeomorphisms

Abstracts of talks:

Benson Farb. Title: Problems and progress in understanding the Torelli group
Abstract: The Torelli group T(S) of a surface S is defined to be the subgroup of the mapping class group of S consisting of the elements acting trivially on H₁(S,Z). The study of T(S) connects to 3-manifold theory, symplectic representation theory, combinatorial group theory, and algebraic geometry. In this talk I will explain some of the main themes in this beautiful topic. I will describe some recent progress in this area, as well as some of the basic open problems.

Ko Honda. Title: Reeb vector fields and open book decompositions
Abstract: According to a theorem of Giroux, there is a 1-1 correspondence between isotopy classes of contact structures and equivalence classes of open book decompositions. We give partial results towards calculating the contact homology of a contact structure (M,&xi) (in dimension 3) which is supported by an open book with pseudo-Anosov monodromy. This is joint work with Vincent Colin.

Henry Segerman. Title: Incompressible Surfaces in Punctured Torus Bundles, and the Ideal Points They Come From
Abstract: Culler and Shalen give us a way to produce incompressible surfaces in a 3-manifold from ideal points of its character variety. However, not much is known about the reverse direction: given an incompressible surface, does it come from an ideal point? I will talk about this question in the context of punctured torus bundles, for which the answer is always "Yes".

Amie Wilkinson. Title: Asymmetrical diffeomorphisms
Abstract: Abstract: Which diffeomorphisms of a compact manifold M commute with no other diffeomorphisms (except their own powers)? Smale asked if such highly asymmetrical diffeomorphisms are typical, in that they are dense in the C^r topology on the space of C^r diffeomorphisms Diff^r(M). In this talk I will explain the recent (positive) solution to Smale's question for C¹ symplectomorphisms and volume-preserving diffeomorphisms. I will also discuss progress on the general case. This is joint work with Christian Bonatti and Sylvain Crovisier.

Recreational activities:

Dinner at some fine local Pasadena restaurant.