Seminare und Vorträge im SS 2025
| Date | Lecturer | Seminar | Theme | Time | Location |
|---|---|---|---|---|---|
| 06 May 2025 | Yuming Liu (Beijing Normal University) | Representation Theory | Fractional Brauer configuration algebras and their covering theory Abstract: Brauer configuration algebras were introduced by Green and Schroll in 2017, which are generalizations of Brauer graph algebras. Each Brauer configuration algebra is defined by a combinational data called Brauer configuration. In this talk we introduce a further generalization of Brauer configuration called fractional Brauer configuration, and define the associated fractional Brauer configuration algebra (category). We also introduce various types of fractional Brauer configurations, and study the properties of associated fractional Brauer configuration algebras (categories). Then we establish a covering theory for fractional Brauer configurations, and give a connection between the covering of fractional Brauer configurations and the covering of associated fractional Brauer configuration algebras (categories). We also define Brauer $G$-sets and study their covering theory. Finally, we apply our covering theory to study the representation theory of some fractional Brauer configuration algebras. This talk is based on joint work with Nengqun Li. | Tuesday 2:00 pm (CET) | online |
| 06 May 2025 | Li Fan (Tsinghua University) | Representation Theory | Categorical realization of collapsing subsurfaces via perverse schobers Abstract: Categorical realization of collapsing subsurfaces via perverse schobers Abstract: In Barbieri-Moller-Qiu-So's work, they studied the verdier quotient of three-Calabi-Yau categories from (decorated) marked surfaces with collapsing its subsurface. We give a quotient perverse schober of the collapsed surface to describe the Verdier quotient category. Generally, if the collapsed surface has quadratic differential with arbitrary order zeros and poles, we show the isomorphism between the principal part of two exchange graphs, where one is obtained by tilting hearts in the quotient categories and the other is by flipping mixed angulations on the collapsed surface. | 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 |
| 20 May 2025 | Henning Krause (Universität Bielefeld) | Representation Theory | Derived Morita theory and completions Abstract: The derived category of any ring admits various triangulated subcategories which determine the ring up to derived Morita equivalence. This follows from seminal work of Rickard and has been revisited in recent work of Neeman, using the concept of metric completion for triangulated categories. The talk aims to explain these concepts and ideas, without going into the technicalities. | Tuesday 2:00 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 |
| 03 Jun 2025 | Iacopo Nonis (University of Leeds) | Representation Theory | tau-exceptional sequences for representations of quivers over local algebras Abstract: Exceptional sequences were first introduced in triangulated categories by the Moscow school of algebraic geometry. Later, Crawley-Boevey and Ringel considered exceptional sequences in the module categories of hereditary finite-dimensional algebras. Motivated by tau-tilting theory introduced by Adachi, Iyama, and Reiten, Jasso’s reduction for tau-tilting modules, and signed exceptional sequences introduced by Igusa and Todorov, Buan and Marsh developed the theory of (signed) tau-exceptional sequences – a natural generalization of (signed) exceptional sequences that behave well over arbitrary finite-dimensional algebras. In this talk, we will study (signed) tau-exceptional sequences over the algebra Λ=RQ, where R is a finite-dimensional local commutative algebra over an algebraically closed field, and Q is an acyclic quiver. I will explain how (signed) tau-exceptional sequences over Λ can be fully understood in terms of (signed) exceptional sequences over kQ. | Tuesday 2:00 pm (CET) | in person |
| 25 Jun 2025 | Travis Schedler (Imperial College London, UK) | Representation theory, geometry and mathematical physics | Wednesday 2-3 pm CET | online | |
| 24 Sep 2025 | Jon Pridham (Hodge Institute, University of Edinburgh, UK) |