Seminare und Vorträge im SS 2025
| Date | Lecturer | Seminar | Theme | Time | Location |
|---|---|---|---|---|---|
| 22 Apr 2025 | Kyungmin Rho (Universität Paderborn) | Representation Theory | Cohen-Macaulay modules from Fukaya category of surfaces Abstract: Burban-Drozd (2017) introduced the category of triples to classify all indecomposable Cohen-Macaulay modules over certain non-isolated surface singularities. They showed that this category is representation-tame, with indecomposable objects of either band or string type. Via homological mirror symmetry, these modules correspond to loops and arcs in the Fukaya category of the mirror symplectic surface. In this talk, we explicitly describe this correspondence using the localized mirror functor developed by Cho–Hong–Lau (2017), and present its applications for algebraic operations such as the Auslander–Reiten translation. We also examine its connection with the derived category of gentle algebras associated to the same surface. This is based on joint work with Cho–Jeong–Kim–Rho (2022) and Cho–Rho (2024). | Tuesday 4:00 pm (CET) | in person |
| 29 Apr 2025 | Callum Page (University of Plymouth) | Representation Theory | Thick subcategories of derived categories of gentle algebras Abstract: In this talk, I will present a classification of the thick subcategories generated by string objects in the derived category of a gentle algebra. Such a thick subcategory is generated by a set of objects corresponding to a collection of arcs on the derived category’s geometric model. I will use properties of the geometric model to show that any thick subcategory generated by string objects has a generating set corresponding to a non-crossing collection of arcs. I will then discuss the poset structure of the set of non-crossing collections of arcs and how this induces a poset structure on the thick subcategories generated by string objects. This talk is based on the preprint arxiv:2502.12023. | Tuesday 4:00 pm (CET) | in person |
| 30 Apr 2025 | Michael Wemyss (University of Glasgow, UK) | Representation Theory | The classification of 3-fold flops via Jacobi algebras Abstract. The talk will give an overview of the analytic classification of smooth, simple, 3-fold flops. There are three main aspects: (1) reducing the problem to the classification of certain noncommutative finite dimensional algebras, (2) a full understanding of those algebras, then lastly (3) building the associated geometry for each algebra in that class. There are various bonus corollaries. The talk will be algebraic, and so will focus mostly on (1) and (2), where new techniques in A∞ algebras and in noncommutative standard bases will be explained. Perhaps the main point is that a new invariant of Jacobi algebras on the two-loop quiver called the "algebraic length" will be introduced, and I will speculate on how general this construction really is. Part (1) is joint with Joe Karmazyn and Emma Lepri, the rest is joint with Gavin Brown. | Wednesday 2-3 pm (CET) | online |
| 06 May 2025 | Yuming Liu (Beijing Normal University) | Representation Theory | TBA | Tuesday 2:00 pm (CET) | online |
| 06 May 2025 | Li Fan (Tsinghua University) | Representation Theory | TBA | Tuesday 4:00 pm (CET) | in person |
| 13 May 2025 | Kai Meng Tan (National University of Singapore) | Representation Theory | Cores and core blocks of Ariki-Koike algebras Abstract: This talk will consist of two parts. In the first part, we will see how certain results (such as the Nakayama 'Conjecture') for the symmetric groups and Iwahori-Hecke algebras of type A can be generalised to Ariki-Koike algebras using the map from the set of multipartitions to that of (single) partitions first defined by Uglov. In the second part, we look at Fayers's core blocks, and see how these blocks may be classified using the notion of moving vectors which was first introduced by Yanbo Li and Xiangyu Qi. If time allows, we will discuss Scopes equivalences between these blocks arising as a consequence of this classification. | Tuesday 4:00 pm (CET) | in person |
| 28 May 2025 | Nick Williams (University of Cambridge, UK) | Representation theory, geometry and mathematical physics | Steenrod operations via higher Bruhat orders Abstract. The cohomology of a topological space has a ring structure via the cup product. The cup product is defined at the level of cochains, where it is not commutative, but it becomes commutative at the cohomology level. At the cochain level, the lack of commutativity is resolved homotopically by an infinite tower of higher products, known as the Steenrod cup-i products. This additional structure provides more refined information which can be used to tell apart non-homotopy-equivalent spaces. In this talk, I will explain recent work with Guillaume Laplante-Anfossi, where we show how conceptual proofs of the key properties of Steenrod's cup-i products can be given using the higher Bruhat orders of Manin and Schechtman. | Wednesday 2-3 pm CET | online |
| 25 Jun 2025 | Travis Schedler (Imperial College London, UK) | Representation theory, geometry and mathematical physics | Wednesday 2-3 pm CET | online |