Seminare und Vorträge im WS 2025/2026
| Date | Lecturer | Seminar | Theme | Time | Location |
|---|---|---|---|---|---|
| 13 Jan 2026 | Merlin Christ (Universität Bonn) | Oberseminar Cologne Algebra Seminar | Rigid extensions for derived preprojective algebras Abstract: A well known construction associates with every reduced positive braid word a rigid module over a preprojective algebra of type A. More generally, one can associate rigid dg modules over the derived preprojective algebra of type A with non-reduced positive braid words. In this talk we will consider iterated extensions between such rigid dg modules arising from a family of increasing braid words decorated with positive numbers. Using a geometric model based on curves in the plane, we will give a criterion for the existence of a unique rigid extension. As an application, we will show that the rigid extension is invariant under braid moves. Based on ongoing joint work with Roger Casals. | Tuesday, 2pm (CEST) in person | Stefan-Cohn-Vossen-Raum Mathematik (Raum 313) |
| 20 Jan 2026 | Joseph Winspeare (Université Grenoble Alpes) | Oberseminar Cologne Algebra Seminar | The 1-periodic derived category of a gentle algebra Abstract: Combining results from Keller and Buchweitz, we describe the 1-periodic derived category of a finite dimensional algebra of finite global dimension as the stable category of maximal Cohen-Macaulay modules over some Gorenstein algebra. In the case of gentle algebras, using the geometric model introduced by Opper, Plamondon and Schroll, we describe indecomposable objects in this category using homotopy classes of curves on a surface. In particular, we associate a family of indecompoable objects to each primitive closed curve. I will then discuss the dependence of this category on the marked graded surface associated to A. | Tuesday, 3pm (CEST) in person | Stefan-Cohn-Vossen-Raum Mathematik (Raum 313) |
| 27 Jan 2026 | Ricardo Canesin (Université Paris Cité) | Oberseminar Cologne Algebra Seminar | Graded quiver varieties and categories of split filtrations Abstract: Nakajima quiver varieties can be used to give geometric realizations of modules over quantum affine algebras. In the graded case, Keller and Scherotzke gave an algebraic description of these varieties in terms of modules over the singular Nakajima category S and showed that their stratification is governed by the derived category of a Dynkin quiver. In this talk, we explain how this picture extends to Nakajima’s n-fold tensor product varieties, which allow one to geometrically realize n-fold tensor products of standard modules. We do this by introducing a category of filtrations of S-modules with a splitting, whose objects are parametrized by the tensor product varieties. We show that this category is equivalent to the module category of another category S^n, and we describe the category of Gorenstein projective S^n-modules via derived categories. | Tuesday, 2pm (CEST) in person | Stefan-Cohn-Vossen-Raum Mathematik (Raum 313) |
| 28 Jan 2026 | Álvaro Sánchez (Universidad de Murcia, Spain) | Abstract representation theory of quivers and spectral Picard groups Abstract. While the (derived) representation theory of quivers over a field is by now well-understood, much less is known when moving to coefficients in the integers or an arbitrary commutative ring. In this talk, we take a rather radical but well-founded approach: it has recently been observed that certain well-known symmetries of categories of representations (tilting results) are actually mere consequences of the stability of the coefficients involved, and so they exist in a much broader generality, often for the corresponding representations in any stable homotopy theory — this includes arbitrary rings, schemes, dg algebras, or ring spectra. For a finite acyclic quiver Q, we present here a method for producing universal autoequivalences of representations C^Q in any stable ∞-category C, which are the elements of the spectral Picard group of Q. This is based on an abstract equivalence of C^Q with a certain mesh ∞-category of representations of the Auslander–Reiten quiver Γ_Q. Then our universal equivalences arise from symmetries of Γ_Q, and thus yield abstract versions of key functors in classical representation theory — e.g. the Auslander-Reiten translation, the Serre functor, etc. Moreover, for representations of trees this allows us to realize the whole derived Picard group over a field as a factor of the spectral Picard group. | Wednesday, 2pm–3pm Time Zone Berlin, Rome, Paris | ||
| 25 Feb 2026 | Tristan Bozec (Université Angers, France) | Wednesday, 2pm–3pm Time Zone Berlin, Rome, Paris |