# 2023-06-30: Tübingen-Stuttgart Seminar (TüS\S)

June 30, 2023 / Rebekka Lutz

Our next Tübingen-Stuttgart Seminar takes place on 30.06.2023 from 13:15-17:15 pm in Stuttgart!
University of Stuttgart, Pfaffenwaldring 57, Department of Mathematics, room: 8.122

**Speaker: 13:15-14:15: Prof. Dr. Irene Bouw, University Ulm**

**Title: „Reduction of curves and Galois representations“**

Abstact: In this talk we discuss arithmetic aspects of curves defined over the rational numbers. We focus on superelliptic curves, which may be described by an algebraic equation of the form y^m=f(x), where f(x) is a

polynomial. We explain how reduction to positive characteristic can be used to determine the (local) Galois representation of a curve.

**14:45-15:45: Prof. Dr. Stefan**

**Wewers, University Ulm**

**Title: „An**

**analytic**

**approach**

**to**

**the**

**computation**

**of**

**semistable**

**reduction**

**of**

**curves**

**“**

Abstract: Let Y be a smooth projective curve over p-adic number field K. The semistable reduction theorem says that there exists a finite extension L/K and a semistable model of Y over the ring of integers of L. In my talk I will discuss methods for explicitly computing such a model. These method have a very convenient formulation in the language of analytic geometry a la Berkovich.

**16:15-17:15: Prof. Dr. Jeroen**

**Sijsling, University Ulm**

Title: „Determining endomorphism rings of Jacobians“

Abstract: Given an algebraic curve, we can construct its Jacobian. This is both an algebraic and an analytic object. We discuss how these different ways of considering the Jacobian allow us to algorithmically determine an important invariant associated to it, namely its endomorphism ring, and we briefly discuss the applications of these algorithms, for example in the context of modularity. This uses joint work with Edgar Costa, Nicolas Mascot, and John Voight.

Title: „Determining endomorphism rings of Jacobians“