##### Department of Mathematics,

University of California San Diego

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### Math 208: Seminar in Algebraic Geometry

## Dr. Gavril Farkas

#### Humboldt University

## The birational geometry of $M_g$ via tropical geometry and non-abelian Brill-Noether theory

##### Abstract:

I will discuss how novel ideas from non-abelian Brill-Noether theory coupled with tropical geometry can be used to prove that the moduli space of genus 16 is uniruled. This is the highest genus for which the moduli space is known not to be of general type. For the much studied question of determining the Kodaira dimension of $M_g$, this case has long been understood to be crucial in order to make further progress. This is joint work with Verra

Host: Elham Izadi

### April 2, 2024

### 9:00 AM

APM 7321

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