Oberseminar "Algebra und Algebraische Geometrie"
| 15.04.2026 | Mingyu Ni (Paderborn) |
| Titel: | Weighted Cohomology, Hodge Theory and Intersection Cohomology of Shimura Varieties |
| Abstract: | We prove that the intersection cohomology of the Baily-Borel compactification of a complex Shimura variety is identified with the top weight quotient of the mixed Hodge structure on the reductive Borel-Serre compactification. This yields canonical cup products and functorial pullbacks on the intersection cohomology |
| 22.04.2026 | Daniel Perniok (Paderborn) |
| Titel: | Exceptional objects in the category of coherent sheaves of a tubular exceptional curve I |
| Abstract: | We give a complete description of the classes in the Grothendieck group of a tubular exceptional curve that correspond to exceptional objects in the associated category of coherent sheaves. |
| 29.04.2026 | Daniel Perniok (Paderborn) |
| Titel: | Exceptional objects in the category of coherent sheaves of a tubular exceptional curve II |
| Abstract: | This talk is a continuation of the talk on April 22, 2026. |
| 06.05.2026 | Lukas Klawuhn (Paderborn) |
| Title: | Applications of representation theory in combinatorics using association schemes |
| Abstract: | It is well-known that the permutation character of a group action carries valuable information about the action. We investigate the permutation characters of wreath products and show that knowledge about their decomposition gives rise to a characterisation of designs in an association scheme. These designs have a nice geometric interpretation using regular polytopes. Furthermore, we use our characterisation to obtain generalisations of the Livingstone-Wagner theorem. We also apply similar ideas to perfect matchings. Even though the underlying association scheme does not come from a group, it comes from a Gelfand pair. Its zonal spherical functions can be used to mimick the representation theoretic computations from the group case, allowing us to derive similar results. |
| 13.05.2026 | N.N. |
| Titel: | tba |
| Abstract: | tba |
| 20.05.2026 | Raschid Abedin (Hamburg) |
| Titel: | Double Lie algebras and the R-matrix method |
| Abstract: | The R-matrix method plays a central role in the theory of classical integrable systems and naturally leads to a generalization of the classical Yang–Baxter equation, a fundamental condition also appearing in the theory of quantum groups. A key tool in the study of solutions to the classical Yang–Baxter equation is the double Lie algebra constructed from the corresponding Lie bialgebra. In this talk, I will present a framework for constructing double Lie algebras associated with this generalized classical Yang–Baxter equation and discuss their relevance to classical integrability. |
| 27.05.2026 | Esther Banaian (Paderborn) |
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| 03.06.2026 | Mikhael Gekhtman (Notre Dame) |
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| 10.06.2026 | N.N. |
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| 17.06.2026 | Alexander Minets (MPIM Bonn) |
| Titel: | tba |
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| 24.06.2026 | N.N. |
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| 01.07.2026 | N.N. |
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| 08.07.2026 | N.N. |
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| 15.07.2026 | Oleksandr Tsymbaliuk (MPIM Bonn) |
| Title: | tba |
| Abstract: | tba |