Localizing the Fukaya category of a Stein manifold

Speaker: 

Sheel Ganatra

Institution: 

USC

Time: 

Tuesday, November 28, 2017 - 4:00pm

Location: 

RH 306

We introduce a new class of non-compact symplectic manifolds called
Liouville sectors and show they have well-behaved, covariantly functorial
Fukaya categories.  Stein manifolds frequently admit coverings by Liouville
sectors, which can be used to understand the Fukaya category of the total
space (we will study this geometry in examples). Our first main result in
this setup is a local-to-global criterion for generating Fukaya categories.
Our eventual goal is to obtain a combinatorial presentation of the Fukaya
category of any Stein manifold. This is joint work (in progress) with John
Pardon and Vivek Shende.

The realization problem of prism manifolds

Speaker: 

Yi Ni

Institution: 

Caltech

Time: 

Monday, October 9, 2017 - 4:00pm

Location: 

RH 340P

Prism manifolds are spherical 3-manifolds with D-type finite fundamental
groups. They can be parametrized by a pair of relatively prime integers p>1
and q. The realization problem of prism manifolds asks which prism manifolds
can be obtained by positive Dehn surgery on a knot in S^3. This problem has
been solved in the cases q<0 and q>p. We will discuss the basic idea of the
proof. This talk is based on joint work with Ballinger, Hsu, Mackey, Ochse
and Vafaee, and with Ballinger, Ochse and Vafaee.

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