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 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.)

Ginkgo-Seminar

Nov 26 2025

15:15 - 16:00

Robert-Mayer-Straße 10 | Raum 711

Alexander Dimitrov: Hypothesis Testing: From Binary Testing to E-Variables

Frankfurter Seminar

Okt 29 2025

16:45

Xavier Ros-Oton: Regularity theory for PDE and free boundary problems

Universitat de Barcelona

Abstract: One of the most basic and important questions in PDE is that of regularity: to decide whether all solutions to a given PDE are smooth or not.

A classical example is Hilbert's 19th problem, solved in 1956 by De Giorgi and Nash. The regularity theory for elliptic and parabolic PDE experienced a huge development during the second half of the 20th century, and nowadays there are still several problems of crucial importance that remain open.

The aim of this talk is to give an overview of this topic and present some recent results in this direction.