##### Department of Mathematics,

University of California San Diego

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### Special Recruiting Colloquium

## Nathanael Berestycki

#### University of British Columbia

## Random walks, geometry and comparative genomics

##### Abstract:

We will see how a problem in genome rearrangement leads to describe a new kind of phase transition for random walks on graphs. This phase transition is related to the well-known Erdos-Renyi double jump phenomenon for random graphs. I will particularly try to describe the effect that the scale of mutations may have on the analysis of the problem, and will outline two possible approaches: one borrowing ideas from hyperbolic geometry and the other based on cheating and using branching random walks.

Host: Ruth Williams

### December 6, 2006

### 12:00 PM

### AP&M 6402

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