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 |

**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 H_{1}(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
C^{1} 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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