Seminare und Vorträge im WS 2025/2026
| Date | Lecturer | Seminar | Theme | Time | Location |
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| 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 | Register here to obtain the Zoom link: https://sites.google.com/view/lagoonwebinar/home |
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| 03 Feb 2026 | Juan Omar Gómez Rodríguez (Universität Bielefeld) | Conservativity via purity in tensor triangulated categories Abstract: Given a family of coproduct-preserving tensor-triangulated (tt) functors between rigidly-compactly generated tt-categories, it is natural to ask when they are jointly conservative. Such joint conservativity is the minimal requirement for attempting to descend tt-geometric information along the family. In this talk, I will present a criterion for determining when a family of geometric functors is jointly conservative through the lens of purity in compactly generated triangulated categories, highlighting its homological flavor. We introduce the notion of pure descendability and we apply it to two particular situations involving sequential limits of ring spectra. The talk is based on joint work with Natalia Castellana. | Tuesday, 2pm (CEST) in person | Stefan-Cohn-Vossen-Raum Mathematik (Raum 313) |
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| 25 Feb 2026 | Tristan Bozec (Université Angers, France) | Abstract. One very nice feature of derived algebraic geometry, and specifically shifted symplectic geometry, is how convenient it is to tackle topological field theories. We will first review the recent history of this approach, through the fundamental use of mapping stacks and the Betti shape. We will illustrate our review with many very concrete examples and noncommutative applications, before explaining how the (recently proved) Moore–Tachikawa conjecture leads us to considering the Dolbeault shape in view of defining a new TFT associated to Higgs fields. This reports an ongoing collaboration with Damien Calaque, Julien Grivaux and Hugo Pourcelot. | Wednesday, 2pm–3pm Time Zone Berlin, Rome, Paris | Register here to obtain the Zoom link: https://sites.google.com/view/lagoonwebinar/home |
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| 25 Mar 2026 | Xiao-Wu Chen (University of Science and Technology of China, Hefei, China) | Frobenius quotients, inflation categories and weighted projective lines Abstract. By the work of Kussin, Lenzing and Meltzer, the category of vector bundles on a certain weighted projective line is closely related to the graded submodule problem, studied by Ringel-Schmidmeier. However, the connection is quite mysterious. We construct an explicit functor, which yields Kussin-Lenzing-Meltzer’s stable equivalence. Inspired by Demonet-Iyama's work, we introduce a general notion of Frobenius quotients. We use multifold matrix factorizations in the proof. This is joint with Qiang Dong and Shiquan Ruan. | Wednesday 2pm–3pm Time Zone Berlin, Rome, Paris | Register here to obtain the Zoom link: https://sites.google.com/view/lagoonwebinar/home |
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