Termine

We introduce command-line assistants as LLM-based systems that can do real work through tools, permissions, and sandboxed execution environments. We explain how these assistants differ from plain chatbots, opening new possibilities but also introducing challenges and risks.

The main focus is on existing and possible applications in our department.

Benjamin Brück and Michael Wiemeler will talk about their Habilitation. Margarete will give a Departure Talk.

via zoom If you are interested please contact Prof. Dr. Anna Siffert (asiffert@uni-muenster.de)

Generalizing work of Poizat in the stable case, motivated by the definability status of important spaces of definable types in algebraically closed valued fields, Cubides Kovacsics, Ye and I introduced and studied beautiful pairs for unstable theories, as a more semantic way to approach such definability questions. As one of the main applications, we could establish the strict pro-definability of all definable types of various kinds. In the talk, I will explain the main ideas behind this approach, and I will then report on some ongoing project, joint with Hrushovski, Ye and Zou, on versions of the results where a non-standard Frobenius automorphism is added to the structure. We obtain in particular surprisingly simple axioms for the resulting pairs, as these turn out to be beautiful as well. I will focus on the situation without valuation, which corresponds to the theory of proper pairs of existentially closed difference fields, where the small one is transformally algebraically closed in the large one.

A line field on a manifold is a smooth and continuous assignment of a tangent line to each point on the manifold. The projective span of a smooth manifold is the maximal number of linearly independent line fields. After motivating the study of this fascinating numerical invariant, I will not only give a necessary condition for the existence of linearly independent line fields on (almost) complex manifolds, but I will also explain that this condition is additionally sufficient in certain cases. Finally, we will apply these necessary and sufficient conditions to obtain a refinement of the Schwarzenberger condition that dictates which cohomology classes can be the Chern classes of a complex vector bundle (with prescribed line bundle splitting properties) over complex projective space. This is joint work with Nikola Sadovek (Dresden) based on [arXiv:2411.14161] (recently accepted for publication in Mathematische Annalen).

Abstract: Calabi-Yau manifolds form an important class of complex manifolds which admit Ricci-flat Kähler metrics thanks to Yau's solution of Calabi's conjecture. As such, in terms of the Berger classification, Calabi-Yau manifolds constitute building blocks of Riemannian manifolds with special holonomy included in SU(n). These play an important role in string theories compactifications. Calabi-Yau manifolds are also the objects of the mirror symmetry conjecture. In this talk, we describe a gluing constructions for families of Ricci-flat Kähler metrics on crepant resolutions and on polarized smoothings of Calabi-Yau manifolds with isolated conical singularities as obtained by Hein-Sun and we obtain asymptotic expansions in terms of the parameters of degeneration.