Vorträge

Donnerstag, 12.11.2026: An overview of shape-morphing solutions and their application to evolutional neural networks

Prof. Mohammad Farazmand (North Carolina State University)

Shape-morphing solutions (SMS) refer to a class of approximate solutions of partial differential equations (PDEs) with the distinguishing feature that they depend nonlinearly on a set of time-dependent parameters. They generalize Galerkin truncations by allowing the basis (or trial functions) to evolve in time in order to adapt to the solution of the PDE. As such, SMS are particularly suitable for reduced-order modeling as well as high fidelity simulation of multiscale systems which exhibit localized time-dependent features, such as vortices, dispersive wave packets, and shocks. Furthermore, being mesh-free, SMS is scalable for solving PDEs in higher spatial dimensions. As a special case, SMS allows the approximation of the PDE’s solution by an evolutional neural network whose weights and biases depend on time. The evolution of SMS parameters is dictated by the SMS equation, a set of ordinary differential equations derived from the Dirac–Frenkel variational principle. Over the past five years, contributions to the theory and computation of SMS have been growing rapidly. In this talk, I will survey these developments, showcase some applications of SMS, and highlight important open problems for future research.

Montag, 16.11.2026: Vortrag in der Reihe "Mathematiker:innen im Beruf"

Dr. Lisa Hilken (AVAT Automation GmbH)

In der Vortragsreihe "Mathematiker:innen im Beruf", die sich vor allem an die Studierenden des Fachbereichs Mathematik richtet, berichten Mathematiker über ihren Werdegang, ihr jetziges Arbeitsfeld und wie ihnen ihr Mathematikstudium dabei zu gute kommt. --- Abstract: Blockheizkraftwerke und andere Energieanlagen werden heute über Software konfiguriert, überwacht und aus der Ferne gesteuert. Bei AVAT entwickeln wir solche Software: ein über viele Jahre gewachsenes Produkt, das vom Bedienpanel an der Anlage bis zum Desktop-Programm für Servicetechniker reicht. Ich möchte einen Einblick in die Arbeit in unserem Team geben und zeigen, wie ein neues Feature in das Produkt gelangt. Welche Schritte sind dafür zu tun? Wie organisieren wir uns? Und warum passt man als Mathematiker:in in die Softwareentwicklung?

Mittwoch, 18.11.2026: Degenerating Discriminants

Viktoriia Borovik (MPI Leipzig)

In this talk, I will discuss how discriminants behave under flat degenerations. The key object is the relative conormal space, whose special fiber controls the limit of conormal varieties and, after projection, the limit of dual varieties. For Gröbner degenerations, the relative conormal space is itself a Gröbner degeneration, with the opposite weight on the dual coordinates. Extra components in the limit arise from Whitney strata of the family lying in the special fiber, and their multiplicities can be computed from Euler obstructions and local Milnor fibers via Sabbah’s formula. I will illustrate the results with examples from singular hypersurfaces, generic complete intersections, reciprocal linear spaces, and mixed discriminants of polynomial systems. This is joint work with Clara Briand.

Donnerstag, 19.11.2026: A mean-field theory for the ground state of bosonic lattice systems

Dr. Denis Périce (Lyon 1, Frankreich)

The Bose–Hubbard model describes interacting bosons on a lattice, where competition between hopping and repulsive interactions leads to Mott insulating and superfluid phases. We will introduce its zero-temperature mean-field description, that has been derived from the Bose–Hubbard model for uniform graphs of large degrees [2, 3]. In a joint work with S. Farhat, M. Lemm, and S. Petrat we study the mean-field phase diagram presented in [1]. After presenting our main results, we will discuss the phenomenology of the phase transition through numerical illustrations and, if time permits, sketch the proofs. [1] M. P. A. Fisher, P. B. Weichman, G. Grinstein, and D. S. Fisher, Boson localization and the superfluid-insulator transition, Physical Review B (1989). [2] S. Farhat, D. Périce, and S. Petrat, Ground state energy of the Bose–Hubbard model with large coordination number with a polaron-type quantum de Finetti theorem, arXiv:2603.29562 (2026). [3] S. Farhat, D. Périce, and S. Petrat, Mean-Field Dynamics of the Bose-Hubbard Model in High Dimension, Annales Henri Poincaré (2026).

Donnerstag, 26.11.2026: TBA

Giacomo Gavelli (Tübingen)

Montag, 30.11.2026: Zwischenevaluation Felix Röhrle: The tropical approach to Prym varieties

Felix Röhrle (Tübingen)

[Vortrag beeinhaltet 20 minütige Lehrprobe zum Thema Zirkel und Lineal Konstruktion, gefolgt von 45 minütigem Forschungsvortrag.] Algebraic geometry models geometric objects as solution sets of polynomial equation systems. Over the past twenty years, tropical geometry has emerged as a combinatorial counterpart, redeveloping analogs of major theorems from algebraic geometry while using graphs instead of curves and bilinear forms instead of group varieties as the central players. The result is a much more accessible theory, which still recovers a surprising amount of structure from algebraic geometry and recently, the tropical viewpoint produced new insights into classical problems, for example the topology of moduli spaces. In this talk, I will focus on developments in tropical Prym varieties, which are the natural abelian varieties associated to double covers of curves. In joint work with Thomas Saillez we proved the tropical Donagi theorem and in joint work with Dmitry Zakharov we developed a matroidal perspective on the tropical Prym variety. These results motivate my current collaborations with Dmitry Zakharov on computing the degree of the tropical Prym--Torelli morphism in genus 6 as well as ongoing work with Margarida Melo and Kevin Kühn on expanding the matroidal perspective to harmonic double covers.

Donnerstag, 14.01.2027: TBA

Dr. Tim Möbus (Tübingen)

Donnerstag, 21.01.2027: TBA

Dr. Jérémy Faupin (Université de Lorraine)

Donnerstag, 04.02.2027: TBA

Sergii Solomakha (University of Washington)

Donnerstag, 18.02.2027: TBA

Dr. Alvaro Alhambra (CSIC Madrid)