Seminar Geometric Methods in Mathematics
Link: https://bbb.tu-dresden.de/b/ulr-ha4-xul-uoo
This is the website of the research seminar of Uli (Prof. Dr. Ulrich Krähmer) and his group. The talks usually cover topics such as homological algebra and category theory, noncommutative algebra and geometry, or Hopf algebras and their generalisations. The target audience consists of PhD and MSc students who write their thesis in one of these areas. Of course everyone is welcome, please contact us to be added to the email list if you want to join.
There will be a blend of external and internal speakers giving formal and informal talks, or we just read and discuss as a group, sometimes focussing for a few weeks on one topic. The only rule is that we meet each week in term time.
Unless otherwise indicated, the seminar takes place every Monday at 3:00 PM (CEST/CET). It is streamed on BigBlueButton: https://bbb.tu-dresden.de/b/ulr-ha4-xul-uoo. We will try to stream even the offline talks, so that people outside of Dresden will not miss out on anything.
In person talks will most likely happen in the room Z21/250.
Please register for the Mailing-List via: https://mailman.zih.tu-dresden.de/groups/listinfo/math-geometric-method
The speakers for the summer term 2023/24 are:
Monday |
Christian Lomp, University of Porto |
Monday 15.04.2024 online |
Ayelet Lindenstrauss, Indiana University |
Monday 22.04.2024 |
Zbigniew Wojciechowski, TU Dresden Diagrammatics for representations of the smallest quantum symmetric pair Representations are good, but diagrams are better. I explain how to do diagrammatics for type I and II representations of Uq(sl2) and how to extend that diagrammatics to module category diagrammatics for the coideal subalgebra Uq'(gl1), which forms with Uq(sl2) the smallest quantum symmetric pair. If time allows I explain some combinatorial applications of our diagrammatics, involving counting dimensions of Hom spaces. |
Monday |
Boris Shoikhet, Euler International Mathematical Institute A generalisation of the Davydov-Yetter complex and deformations of monoidal categories We introduce a new complex associated with the following data. Let k be a field, and let C,D be k-linear (dg) bicategories (k a field), F,G: C-->D be strong functors, \eta,\theta: F-->G be strong natural transformations. Then our complex A(C,D)(F,G)(\eta,\theta) can be thought of as the complex of derived modifications (that is, it is a derived version of classical 3-morphisms in the 3-category Bicat, known as modifications). (It is the n=2 version of the well-known complex associated with 1-dg-categories C,D, and dg functors F,G: C-->D, equal to the Hochschild cochain complex Hoch(C, M_{F,G}), where the C-bimodule M_{F,G}=D(F(-),G(=)), which plays the role od derived natural transformations). This complex A(C,D)(F,G)(\eta,\theta) is a totalisation of a functor \Theta_2-->(complexes). For the case of monoidal category C (a bicategory with 1 object), it is shown that H^3 of our complex A(C,C) for F=G=id, \eta=\theta=id is equal to the classes of infinitesimal deformations of C. Some higher structures on these complexes are constructed. It is expected that there is a e_3-algebra structure on A(C,C) for any k-linear bicategory C. (Joint work with P. Panero). |
Monday 06.05.2024 |
Adam Rennie, University of Wollongong |
Monday
27.05.2024 |
Andre Henriques, Oxford University
Bicommutant categories |
Monday |
Niels Kowalzig, University of Rome Tor Vergata |
Monday 10.06.2024 |
Liao Wang, University of Bonn Annular webs and K-matrices We define a diagrammatic category which captures the structure of a braided module category generated by a braided vector space and a solution of the reflection equation or boundary Yang-Baxter equation. Our diagrammatic category often behaves like a monoidal category, which is explained via a realization as annular webs. As an example, this category admits a functor to the category of representations of various quantum symmetric pair coideal subalgebras. Quantum symmetric pairs are introduced in the 1990s by Gail Letzter as generalizations of Drinfeld-Jimbo quantum groups. Balagovic-Kolb constructed a universal K-matrices which act on representations of the coideal subalgebra and solves the reflection equation. We explicitly compute the K-matrices associated to type AIII quantum symmetric pairs and extend the theory to type II representations of quantum gl Γ. We expect the annular web category controls this representation category, which we will explore in future works. |
Monday 17.06.2024 |
Jean-Simon Pacaud Lemay, Macquarie University This is joint work with Masahito Hasegawa, and is based on our paper [2], available at: https://compositionality-journal.org/papers/compositionality-5-10/. |
Monday 24.06.2024, 5pm online |
Justin Barthite, University of Colorado Boulder |
Monday 01.07.2024 online |
Sean Sanford, Ohio State University Invertible Fusion Categories A tensor category $\mathcal C$ over a field $\mathbb K$ is said to be invertible if there is a tensor category $\mathcal D$ such that $\mathcal C\boxtimes\mathcal D$ is Morita equivalent to $\mathrm{Vec}_{\mathbb K}$. When $\mathbb K$ is algebraically closed, it is well-known that the only invertible fusion category is $\mathrm{Vec}_{\mathbb K}$, and any invertible multi-fusion category is Morita equivalent to $\mathrm{Vec}_{\mathbb K}$. In contrast, we show that for general $\mathbb K$, the invertible multi-fusion categories over $\mathbb K$ are classified (up to Morita equivalence) by $H^3(\mathbb K;\mathbb G_m)$, the third Galois cohomology of the absolute Galois group of $\mathbb K$. This group of invertible fusion categories is a higher-dimensional analogue of the Brauer group of (which is isomorphic to $H^2(\mathbb K;\mathbb G_m)$). As an application, we show that the Morita classification of fusion categories by their Drinfel’d centers breaks when $H^3(\mathbb K;\mathbb G_m)$ is nontrivial. |
Monday 08.07.2024 |
Mateusz Stroinski, Uppsala University Lax module functors, bialgebras and tensor categories In this talk, I will explain how one can extend the reconstruction theory for module categories over tensor categories to the non-rigid case, with particular focus on categories associated to (non-Hopf!) bialgebras. The crucial tool towards that end is lax module functors, which I will describe explicitly in the bialgebraic case. I will then show the additional applications of this formalism in the rigid setting of tensor categories, extending the Etingof–Ostrik reconstruction theory and answering a conjecture of Etingof–Ostrik, regarding a generalization of Skryabin's theorem on projectivity for comodule algebras. Time permitting, I will show how the Hausser–Nill theorem and the Bruguières–Lack–Virelizier generalization of Sweedler's theorem on Hopf modules can be reinterpreted, reproven and, in the first case, also generalized, using our methods. These results are joint work in progress with Tony Zorman. |
Monday 16.07.2024 |
Ken Brown, University of Glasgow Twisted unipotent groups I will review the twisting procedure of Drinfeld as applied in particular to the Hopf algebra O(G) of regular functions on a unipotent algebraic group G. This uses a Hopf 2-cocycle J to produce a new Hopf algebra which we denote by J_O(G)_J, with the same coalgebra structure as O(G) but a different multiplication. I'll discuss the structure and representation theory of J_O(G)_J, illustrated by a specific example. All necessary terminology will de defined in the talk. This is joint work with Shlomo Gelaki. |
The speakers for the winter term 2023/24 are:
Monday |
Benjamin Haïoun, Paul Sabatier University (Toulouse III) |
Wednesday 18.10.2023 |
John Boiquaye, University of Ghana PhD Defense |
Monday 06.11.2023 |
Oliver Sander, TU Dresden |
Monday 13.11.2023 |
Pedro Tamaroff, Humboldt University of Berlin |
Monday 20.11.2023 online |
Marco De Renzi, University of Montpellier |
Monday |
Cole Comfort, University of Lorraine |
Monday |
Ehud Meir, University of Aberdeen |
Monday |
Adriana Balan, University Politehnica of Bucharest On 2-categorical aspects of (quasi)bialgebras Over the past decades, a plethora of results have been obtained concerning the structure of various categories of (co)algebras, bialgebras and Hopf algebras. These include among others, completeness and cocompleteness, local presentability, whether the respective category is abelian, monoidal, Tannaka reconstruction theory, and so on. In this talk we shall bring forward some 2-categorical aspects of the above-mentioned structures, starting from Day and Street’s observation that (dual) quasi-bialgebras are the pseudomonoids in the monoidal 2-category of coalgebras, and (dual) quasi-Hopf algebras are instances of autonomous pseudomonoids in the monoidal bicategory of coalgebras and bicomodules. |
Monday 15.01.2024 |
Daniel Gromada, Czech Technical University in Prague |
Monday |
Anna Rodriguez Rasmussen, Uppsala University |
Monday |
Manuel Bodirsky, TU Dresden |
The speakers for the summer term 2023 were:
Date | Speaker |
31.08.2023 |
Josefin Bernhard |
10.07.2023 |
Mateusz Stroinski |
03.07.2023 |
Daniel Graves |
26.06.2023 |
Anna-Katharina Hirmer |
19.06.2023 |
Eamon Quinlan-Gallego |
12.06.2023 |
Ján Pulmann |
05.06.2023 |
Nima Rasekh |
15.05.2023 | Estanislao Herscovich |
08.05.2023 |
Ben Elias |
24.04.2023 |
Andrew Baker |
17.04.2023 | Friedrich Wagemann |
The speakers for the winter term 2022/23 were:
Date | Speaker |
17.10.2022 |
Daniel Tubbenhauer |
24.10.2022 |
Richard Garner |
07.11.2022 |
John Bourke |
14.11.2022 | Julian Holstein |
15.11.2022 |
Chris Heunen |
21.11.2022 |
Misha Feigin |
28.11.2022 | Joanna Meinel |
05.12.2022 |
Andrea Gagna |
12.12.2022 | Vanessa Miemietz |
19.12.2022 |
George Balla |
16.01.2023 |
Tony Zorman |
23.01.2023 |
Zbigniew Wojciechowski |
30.01.2023 | Ulrich Krähmer |
The speakers for the summer term 2022 were:
Date |
Speaker |
04.04.2022 11.04.2022 25.04.2022 02.05.2022 09.05.2022 16.05.2022 23.05.2022 30.05.2022 02.06.2022 13.06.2022 20.06.2022 27.06.2022 04.07.2022 11.07.2022 08.08.2022 22.08.2022 |
Robert Laugwitz Gregory Ginot Janez Mrcun Catherine Meussburger Ben Ward Michael Batanin Muriel Livernet Pierre-Louis Curien Ivan Bartulović Bojana Femic Natalia Iyudu Ralph Kaufmann Fosco Loregian Ieke Moerdijk Noemi Combe Hans-Christian Herbig |
The speakers for the winter term 2021/22 were:
Date |
Speaker |
04.10.2021 11.10.2021 18.10.2021 25.10.2021 01.11.2021 08.11.2021 15.11.2021 22.11.2021 29.11.2021 06.12.2021 13.12.2021 20.12.2021 10.01.2022 24.01.2022 31.01.2022 |
Martin Markl Lukas Woike Sebastian Halbig Myriam Mahaman Aryan Ghobadi Laiachi El-Kaoutit Jeff Giansiracusa Jens Kaad Bruce Bartlett Chelsea Walton Michael Cuntz Shahn Majid Tony Zorman Stephanie Feilitzsch (Viva) Myriam Mahaman |
The speakers for the summer term 2021 were:
Date |
Speaker |
19.04.2021 26.04.2021 03.05.2021 10.05.2021 17.05.2021 31.05.2021 07.06.2021 14.06.2021 21.06.2021 28.06.2021 05.07.2021 12.07.2021 26.07.2021 |
Christian Korff Cigdem Yirtici internal presentations Manuel Martins Nicolas Garrel Ingo Runkel Azat Gainutdinov Yorck Sommerhäuser Claudia Scheimbauer Paolo Saracco Tom Leinster Martin Hyland Tony Zorman |
The speakers for the winter term 2020/21 were:
Date |
Speaker |
26.10.2020 02.11.2020 09.11.2020 16.11.2020 23.11.2020 30.11.2020 07.12.2020 14.12.2020 11.01.2021 18.01.2021 25.01.2021 01.02.2021 08.02.2021 15.02.2021 |
Atabey Kaygun Lucia Rotheray Sebastian Halbig Matthias Valvekens Friedrich Wagemann Stephanie Feilitzsch David Jordan Tomasz Brzezinski Anna Kula Ilya Shaprio Yuri Berest Blessing Oni John Boiquaye Ivan Angiono |