##### Department of Mathematics,

University of California San Diego

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### Differential Geometry Seminar

## Diego Matessi

#### Universita degli Studi del Piemonte Orientale

## Conifold transitions via tropical geometry

##### Abstract:

The process of degenerating a complex variety $X$ to a singular variety $X_0$ and then resolving to obtain $X'$ is called a geometric transition. The case where the singularities are just double points is called a conifold transition. There are known obstructions to either resolving a set of nodes or smoothing them, depending on whether we want to preserve respectively the symplectic or complex structure. Moreover mirror symmetry is thought to reverse this process, i.e. the mirror of a smoothing is expected to be a resolution and vice versa. I will explain an interpretation of these facts in terms of ``tropical geometry", which encodes information of both symplectic and complex geometry in terms of discrete data.

Host: Mark Gross

### December 1, 2010

### 3:00 PM

### AP&M 5829

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