##### Department of Mathematics,

University of California San Diego

****************************

### Special Colloquium

## Mathew Hedden

#### Massachusetts Institute of Technology

## Symplectic geometry and invariants for low-dimensional topology

##### Abstract:

Over the past few years, ideas from symplectic geometry have had a major impact on low-dimensional topology. Some of the most impressive results stem from a set of invariants developed by Ozsvath and Szabo. Though defined using symplectic geometry, they turn out to be surprisingly powerful invariants of low-dimensional objects e.g. knots, and three- and four-manifolds. In this talk, I will survey these invariants and discuss how I have used them to prove results related to knot theory, complex curves, surgery theory in dimension three, and the theory of foliations and contact structures on three-manifolds.

Host: Jim Lin

### January 11, 2008

### 1:00 PM

### AP&M 6402

****************************