##### Department of Mathematics,

University of California San Diego

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### Food For Thought Seminar

## Dan Budreau

#### UCSD

## Basics of Mirror Symmetry

##### Abstract:

String theory suggests that the universe works in a 10 dimensional construct: 4-dimensional spacetime and a 6-dimensional compact object called a Calabi-Yau space. Physics suggests that it might be possible for two different Calabi-Yaus to give identical physics. These are called mirror pairs. What is the geometric relation between these two objects? One incredible suggestion is that counting curves in one Calabi-Yau is tied to the coefficients of an integral on the mirror. Up to this point geometers had enough trouble counting degree 2 or 3 curves in a Calabi-Yau and it usually involved esoteric machinery. Now it could be calculated by just an integral on a different space and looking at the coefficients. I will outline some of conjectures and implications then try to do an example on a particular three-fold.

### November 6, 2008

### 10:00 AM

### AP&M B412

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