Goethe-Universität — Frankfurter Seminar - Kolloquium des Instituts für Mathematik

Ginkgo Seminar

Vorkolloquium für Doktoranden, Post-Docs und interessierte Studierende

An den jeweiligen Veranstaltungstagen wird mit dem Ginkgo-Seminar (Gingko - Grundlagen, Intuition, Neugier für und auf das Kolloquium) gestartet, einer exklusiven Veranstaltung von Doktoranden für Doktoranden, Post-Docs und interessierte Studierende.

Ziel ist es, die Vorträge "aus der anderen Ecke des Instituts" für alle Interessierten zugänglicher zu machen.

Das Vorkolloquium findet immer ab 15.00 (c.t.) in Raum 711 groß vor dem jeweiligen Vortrag statt.

Frankfurter Seminar

Jan 28 2026

16:45

Irem Portakal: Algebraic methods for Nash equilibrium

MPI Leipzig

Abstract: The set of Nash equilibria of a finite game admits a natural description as a semi-algebraic set, that is, defined by a finite system of polynomial equalities and inequalities whose variables correspond to the mixed strategies of the players. This algebraic viewpoint oﬀers both conceptual and computational insights into the study of equilibrium.

The talk will begin with a brief introduction to the basic setup of finite games and the definiton of Nash equilibrium, emphasizing the underlying polynomial structure.

We will then discuss how this description enables the application of tools from real algebraic geometry to game theory. In particular, we will highlight classical and recent results concerning the maximal number of Nash equilibria in generic games and explore how these bounds reflect the geometry of the corresponding solution sets.

Ginkgo-Seminar

Jan 28 2026

15:15

Robert-Mayer-Straße 10 | Raum 711

Arne Riester: Some background on game theory

Frankfurter Seminar

Jan 14 2026

16:45

Stefan Schreieder: Matroids and the integral Hodge conjecture for abelian varieties

(Leibniz Universität Hannover)

Abstract: Hodge originally formulated his conjecture — one of the seven Millennium Prize Problems — with integral coefficients.

Atiyah and Hirzebruch showed in 1962 that it fails for torsion classes, and later Kollár produced non-torsion counterexamples. Since then, the conjecture has been understood with rational coefficients, while its integral form is regarded as a property of individual varieties rather than a universal statement. A central and longstanding open case concerned the integral Hodge conjecture for abelian varieties.

In this talk, I will explain how ideas from the combinatorial theory of regular matroids allow us to prove that it fails for large classes of abelian varieties. As a consequence, building on work of Voisin, we show that very general cubic threefolds are not stably rational, strengthening the classical result of Clemens and Griffiths (1972) that smooth cubic threefolds are not rational.

This is joint work with Philip Engel and Olivier de Gaay Fortman.

Ginkgo-Seminar

Jan 14 2026

15:15

Robert-Mayer-Straße 10 | Raum 711

Nicole Müller: Abelian varieties and Theta divisors

Frankfurter Seminar

Nov 26 2025

16:45

Johannes Ruf: The Numeraire E-Variable and Reverse Information Projection

London School of Economics

A recent approach to statistical inference is based on the concept of an e-variable: a nonnegative sample statistic whose expected value is at most one if a given null hypothesis is true. This approach has been found to produce strong statistical error bounds and high statistical power and is easily extendible to sequential, or online, settings. E-variables admit a natural interpretation as the payoff of a financial bet.

In this talk I will discuss how classical ideas from mathematical finance, in particular the numeraire portfolio, enables an optimality theory for e-variables that significantly generalizes earlier results. Our results also lead to a duality theory which yields the so-called reverse information projection in complete generality.

Our work showcases the power of financial methods in a setting where information-theoretic tools have traditionally been preferred.

(Joint work with Martin Larsson and Aaditya Ramdas.)