|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|
Benson Farb. Title: Problems and progress in understanding the
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 Cr topology on the space of Cr diffeomorphisms Diffr(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.
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