NoGAGS 2026 - Third RTG Colloquium

The Northern German Algebraic Geometry Seminar is a regular joint seminar of the algebraic geometry groups in Berlin, Bielefeld, Hamburg, Hannover, Leipzig and Oldenburg. Information on the previous meetings can be found here.

This year's edition will take place in the Humbold University Berlin, and will be combined with the final MATH+ Colloquium, given by Alexei Skorobogatov.

Thursday 29. 

• 13:00-14:00: Ben Heuer

• Coffee Break

• 14:30-15:30: Kathlen Kohn

• 16:00-17:00: Salvatore Floccari

• 19:00-: Social dinner (time to be determined).

Friday 30. 

• 10:00-11:00: Lukas Kühne

• Coffee Break

• 11:30-12:30: Stefan Kebekus

• Lunch break

• 14:15-15:30 Kolloquium MATH+ Alexei Skorobogatov, RUD 26, 0'119

The  talks will take place in the following rooms:

• Thursday: room 0'311 in the Erwin Schrödinger-Zentrum, Rudower Chaussee 26, 12489 Berlin-Adlershof.

• Friday morning: room 1.013 of the Institut für Mathematik, Rudower Chaussee 25, 12489 Berlin-Adlershof.

• Friday afternoon: room 0'119 in the Erwin Schrödinger-Zentrum, Rudower Chaussee 26, 12489 Berlin-Adlershof.

Thursday

• 13:00-14:00 Ben Heuer: p-adic non-abelian Hodge theory for non-p-adic geometers

This talk will give an introduction to the p-adic Simpson correspondence without assuming any background in p-adic geometry: In analogy to classical Hodge theory, p-adic Hodge theory aims to compare different cohomology theories for varieties over p-adic fields. The idea of p-adic non-abelian Hodge theory is to extend this to a comparison of different categories of coefficients for these cohomology theories, such as local systems and Higgs bundles. The focus will be on explaining analogies to the complex theory, especially regarding the role of moduli spaces.

• 14:30-15:30 Kathlen Kohn: Algebraic Neural Network Theory

The space of functions parametrized by a fixed neural network architecture is known as its "neuromanifold", a term coined by Amari. Training the network means to solve an optimization problem over the neuromanifold. Thus, a complete understanding of its intricate geometry would shed light on the mysteries of deep learning. This talk explores the approach to approximate neural networks by algebraic ones that have semialgebraic neuromanifolds. In this setting, we can interpret training the network as   finding a "closest" point on the neuromanifold to some data point in the ambient space. In particular, this perspective enables us to see that the singularities (and boundary points) of the neuromanifold can cause a tradeoff between efficient optimization and good generalization to unseen data. We discuss several conjectures on singularities and hidden parameter symmetries (i.e., fibers) of neuromanifolds. This talk will focus on 3 popular architectures: multilayer perceptrons, convolutional networks, and self-attention networks that are the key ingredient of large language models like ChatGPT. The results presented in this talk are based on several joint works with Paul Breiding, Erin Connelly, Nathan Henry, Giovanni Marchetti, Stefano Mereta, Vahid Shahverdi, and  Matthew Trager.

• 16:00-17:00 Salvatore Floccari: Weil fourfolds with discriminant 1 and singular OG6-varieties

Markman and O'Grady uncovered a deep relation between abelian fourfolds of Weil type with discriminant 1 and hyper-Kähler varieties of generalized Kummer type, at the level of Hodge theory and period domains. Markman was able to use this to prove the Hodge conjecture for these fourfolds; he later found a different proof which works for Weil fourfolds with arbitrary discriminant and implies the Hodge conjecture for all abelian varieties of dimension 4.

In my talk I will explain how Weil fourfolds with discriminant 1 are also closely related to certain hyper-Kähler varieties of OG6-type in a direct and geometric way. As a consequence, we obtain yet another proof of the Hodge conjecture for Weil fourfolds with discriminant 1, as well as for many families of hyper-Kähler varieties of OG6-type which form loci of codimension 1 in their moduli spaces. The results that I will discuss are joint work with Lie Fu.

Friday:

• 10:00-11:00 Lukas Kühne: Matroids, Incidence Theorems, and Tilings

A matroid is a fundamental and actively studied object in combinatorics. Matroids generalize linear independence in vector spaces as well as many aspects of graph theory. After a gentle introduction to matroids, I will present parts of a new OSCAR module for matroids through several examples. I will focus on computing the moduli space of a matroid, which is the space of all arrangements of hyperplanes with that matroid as their intersection lattice.

Fomin and Pylyavskyy describe how to obtain incidence theorems from tilings of an orientable surface; they call this result the "master theorem". Since most classically known incidence theorems, such as Pappus's and Desargues's theorems, are instances of the master theorem, they ask whether this holds for all incidence theorems. As an application of the presented OSCAR module, we provide an explicit example of an incidence theorem involving 13 points, based on a matroid with an exotic moduli space, that is not an instance of the master theorem. Based on joint work with Matt Larson.

• 11:30-12:30 Stefan Kebekus: Hyperbolicity in C-pairs

Almost twenty years ago, Campana introduced C-pairs to complex geometry. Interpolating between compact and non-compact geometry, C-pairs capture the notion of “fractional positivity” in the “fractional logarithmic tangent bundle”. Today, they are an indispensible tool in the study of hyperbolicity, complex geometry and several branches of arithmetic geometry. This talk reports on joint work with Erwan Rousseau. We clarify the notion of a “morphism of C-pairs”, define (and prove the existence of) a “C-Albanese variety”, generalize the classic Bloch-Ochiai theorem, and discuss the beginnings of a Nevanlinna theory for “orbifold entire curves”.

• 14:15-15:15 Alexei Skorobogatov (Math+ Colloquium): Rational points on surfaces 

Rational points are solutions of Diophantine equations in rational numbers and other fields of interest for number theory. The talk will survey the local-to-global principle for rational points, also known as the Hasse principle, with focus on surfaces. The story starts with Legendre who gave a necessary and sufficient condition for solubility of conics in integers, an early precursor of the Hasse-Minkowski theorem. After describing the state of the art for conic bundle surfaces (families of conics over a curve) and emphasizing the role played by the Brauer group and the Brauer-Manin obstruction, Skorobogatov will talk about more recent results that go beyond conic bundles. Alexei Skorobogatov is Professor of Pure Mathematics at the Imperial College London. He received his PhD in Moscow in 1987 under the supervision of Yuri Manin. He is a recipient of the Whitehead Prize of the London Mathematical Society and a Fellow of the American Mathematical Society. He works in arithmetic geometry, mostly on rational points and Brauer groups.

In order to get an idea of the number of participants, a free registration is requested.

We also plan to organise a social dinner on Thursday evening at the restaurant Zwölf Apostel in Savigny Platz. Unfortunately we cannot cover the costs.

Please write a short E-Mail to Ms. Kati Blaudzun (kati.blaudzun@hu-berlin.de) by January 26, indicating also if you would like to join the dinner.