The seminar covers topics in algebra and representation theory and its interactions with other areas of mathematics. The seminar is organised by Gustavo Jasso and Sibylle Schroll, with assistance from Anna Rodriguez Rasmussen and Jan Thomm.
Depending on the occasion the talk will be held online or in person at the mathematical institute in Cologne. You can check the situation for each seperate talk below. In any case the seminar will be streamed in the following Zoom conference:
https://uni-koeln.zoom.us/j/93313763551?pwd=47Tvo8JbSd4IkEahahHM83rMxFu4G6.1
ID: 933 1376 3551, Password: algebra
The address for the seminar when held in presence is:
Universität zu Köln: Mathematisches Institut, Stefan Cohn-Vossen Raum (Nr. 313 on floor 3)
Weyertal 86-90, 50931 Köln
If you would like to be added to the mailing list please sign up under the following link https://lists.uni-koeln.de/mailman/listinfo/cologne-algebra-seminar.
17 Nov in person Jan Thomm (Universität zu Köln)
The many facets of the octahedral axiom
Abstract: In 2019, Nakaoka and Palu introduced extriangulated categories unifying both exact and triangulated categories under a common axiomatisation. Extriangulated categories thus explain the many similarities between the two theories. We discuss an alternative axiomatisation of extriangulated categories arising form the study of pushout and pullback squares. In particular, we examine the most elusive axiom of (ex)triangulated categories: The octahedral axiom. We give an equivalent reformulation inspired by pasting laws and unravel where the octahedral axiom is hidden in the axiomatics of an exact category. Moreover, this new perspective allows us to naturally rediscover many examples of (ex)triangulated categories such as the homotopy category of a stable infinity category.
13 Oct in person Johanne Haugland (Ruhr-Universität Bochum/NTNU)
A geometric model for the module category of a special biserial algebra
Abstract: In recent years, geometric models have emerged as an important tool in the study of the representation theory of algebras, and such models have highlighted important connections to other areas of mathematics. A geometric model for the module category of a gentle algebra, and more generally of a string algebra, has been developed by Baur and Coelho Simões. In this talk, we use this as a starting point for constructing a geometric model for the module category of a special biserial algebra. The talk is based on joint work in progress with Azzurra Ciliberti, Raquel Coelho Simões and Martin Herschend.
20 Oct no seminar
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27 Oct in person Robert Szafarczyk (Københavns Universitet)
A Curious Characterisation of Dedekind Domains
Abstract: We characterise Dedekind rings among not necessarily Noetherian domains by a simple property of their module homomorphisms. Even the case of Z is non-trivial. Our proof relies on a homological algebra argument. We will try to present its main ideas and illustrate with several examples.
03 Nov in person Lior Silberberg (IMJ-PRG)
Folding of cluster algebras and quantum toroidal algebras
Abstract: I will present a relationship between the representation theory of the infinite rank quantum affine algebra Uq(sl_∞,aff) and that of the quantum toroidal algebra Uq(sl_2n,tor). In particular, we will discuss folding techniques for cluster algebras arising from infinite quivers, and show that the monoidal categorifications associated to these quantum algebras (due to Hernandez-Leclerc and Nakajima) are related by folding.
10 Nov no seminar
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17 Nov in person Jan Thomm (Universität zu Köln)
The many facets of the octahedral axiom
Abstract: In 2019, Nakaoka and Palu introduced extriangulated categories unifying both exact and triangulated categories under a common axiomatisation. Extriangulated categories thus explain the many similarities between the two theories. We discuss an alternative axiomatisation of extriangulated categories arising form the study of pushout and pullback squares. In particular, we examine the most elusive axiom of (ex)triangulated categories: The octahedral axiom. We give an equivalent reformulation inspired by pasting laws and unravel where the octahedral axiom is hidden in the axiomatics of an exact category. Moreover, this new perspective allows us to naturally rediscover many examples of (ex)triangulated categories such as the homotopy category of a stable infinity category.
24 Nov in person Francesca Fedele (Ruhr-Universität Bochum)
TBA
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01 Dec in person Esha Gupta (MPIM Bonn)
TBA
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08 Dec in person Edoardo Tacchetti (Università degli Studi di Verona)
TBA
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15 Dec in person Tudor Pădurariu (Universität Bonn)
TBA
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12 Jan in person Carlo Klapproth (Universität Stuttgart)
TBA
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19 Jan no seminar
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26 Jan Tiago Cruz (Universität Stuttgart)
TBA
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02 Feb TBD
TBA
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