##### Department of Mathematics,

University of California San Diego

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### Group Actions Seminar

## Anthony Sanchez- Graduate student

#### University of Washington

## Gaps of saddle connection directions for some branched covers of tori

##### Abstract:

Holonomy vectors of translation surfaces provide a geometric generalization for higher genus surfaces of (primitive) integer lattice points. The counting and distribution properties of holonomy vectors on translation surfaces have been studied extensively. A natural question to ask is: How random are the holonomy vectors of a translation surface? We motivate the gap distribution of slopes of holonomy vectors as a measure of randomness and compute the gap distribution for the class of translation surfaces given by gluing two identical tori along a slit. No prior background on translation surfaces or gap distributions will be assumed.

Host: Nattalie Tamam

### October 20, 2020

### 10:00 AM

### Zoom Meeting ID 967 4109 3409 (email Nattalie Tamam or Brandon Seward for the password)

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