##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory

## Vlad Matei

#### University of Wisconsin

## Counting low degree covers of the projective line over finite fields

##### Abstract:

In joint work with Daniel Hast and Joseph we count degree 3 and 4 covers of the projective line over finite fields. This is a geometric analogue of the number field side of counting cubic and quartic fields. We take a geometric approach, by using a vector bundle parametrization of these curves which is different from the recent work of Manjul Bhargava, Arul Shankar, Xiaoheng Wang "Geometry of numbers methods over global fields: Prehomogeneous vector spaces" in which the authors extend the geometry of numbers methods to global fields. Our count is just for $S_3$ and $S_4$ covers, and we put the rest of the curves in our error term.

Host: Kiran Kedlaya

### December 1, 2016

### 1:00 PM

### AP&M 7321

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