Seminare und Vorträge im SS 2025
| Date | Lecturer | Seminar | Theme | Time | Location |
|---|---|---|---|---|---|
| 17 Jun 2025 | Azzurra Ciliberti (Bochum), Wassilij Gnedin (Paderborn) Mikhail Gorsky (Hamburg | Cologne Representation Theory Day | 2-6pm | in person | |
| 25 Jun 2025 | Travis Schedler (Imperial College London, UK) | Representation theory, geometry and mathematical physics | Creating quantum projective spaces by deforming q-symmetric algebras Abstract. I will explain how to construct new "quantum projective spaces", in the form of Koszul, Calabi–Yau algebras with the Hilbert series of a polynomial ring. To do so we deform the relations of toric ones — q-symmetric algebras — using a diagrammatic calculus. Such deformations are unobstructed under suitable nondegeneracy conditions, which also guarantee that the algebras are Kontsevich's canonical quantizations of corresponding quadratic Poisson structures. This produces the first broad class of quadratic Poisson structures for which his quantization can be computed and shown to converge, as he conjectured in 2001. On the other hand, we also give examples of purely noncommutative deformations, which cannot be obtained by quantizing Poisson structures. This is joint work with Mykola Matviichuk and Brent Pym. | Wednesday 2-3 pm CET | online |
| 01 Jul 2025 | Gustavo Jasso (Universität zu Köln) | Q-shaped derived categories as derived categories of differential graded bimodules Abstract: We prove that, under mild assumptions, the Q-shaped derived categories introduced by Holm and Jørgensen are equivalent to derived categories of differential graded bimodules over differential graded categories. This yields new derived invariance results for Q-shaped derived categories that allow us to extend known descriptions of such categories as derived categories of differential graded bimodules over (possibly graded) algebras. | Tuesday 2:00 pm (CET) | in person | |
| 15 Jul 2025 | Martin Kalck (Universität Graz) | Representation Theory | Paths into transcendence Abstract: Algebraic numbers $\overline{\mathbb{Q}} \subset \mathbb{C}$ are complex numbers that are roots of polynomials with rational coefficients. All other complex numbers are called transcendental. It is typically a hard question to decide whether a given complex number is transcendental. A more general, classical question in ‘transcendental number theory’ (cf. e.g. works of Lindemann and Weierstraß, Gelfond and Schneider, Baker, Wüstholz) is the following: determine the dimension of the $\overline{\mathbb{Q}}$-vectorspace generated by a (finite) set of complex numbers. For example, the $\overline{\mathbb{Q}}$-vectorspace 〈1, π〉is two-dimensional since π is transcendental by Lindemann’s Theorem. For certain complex numbers called periods, we will try to explain how this transcendence question can (sometimes) be translated into determining dimensions of certain finite dimensional algebras – in other words, into counting (equivalence classes of) paths in ‘modulated’ quivers (with ‘multiplicities’). The dimension formulas obtained in this way improve and clarify earlier resultsof Huber & Wüstholz and recover a dimension estimate of Deligne & Goncharov. This is based on joint work with Annette Huber (Freiburg). | Tuesday 2:00 pm (CET) | in person |
| 24 Sep 2025 | Jon Pridham (Hodge Institute, University of Edinburgh, UK) |