##### Department of Mathematics,

University of California San Diego

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### Algebraic Geometry Seminar

## Zhiyu Tian

#### Caltech

## On the symplectic Graber-Harris-Starr theorems

##### Abstract:

There is a close relation between some aspects of algebraic geometry (in particular, birational geometry) and symplectic geometry via Gromov-Witten theory. For example, Kollar made some conjectures about the symplectic topology of rationally connected varieties, and Ruan speculated the existence of the so-called symplectic birational geometry. A theorem of Graber-Harris-Starr states that sections of rationally connected fibrations over a curve always exist, which has many important consequences in the theory of uniruled and rationally connected varieties. In this talk I will discuss the symplectic analogues of their result and how these results might be used to understand the conjectures of Kollar and Ruan.

Host: Dragos Oprea

### February 15, 2012

### 3:00 PM

### AP&M 6402

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