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 are:
Thursday 31.08.2023 |
Josefin Bernhard, TU Dresden (Master's thesis defence)
Hopf algebra actions on coordinate rings |
Monday 10.07.2023 |
Mateusz Stroinski, Uppsala University
In my recent work, I show that one can remove the assumption that C is closed by replacing PC with TC, the category of Tambara modules over C. Tambara modules can be thought of as profunctors of module categories; they were first introduced by Tambara in 2006, but have been studied in greater detail only in the last couple of years. In this talk, I will give a more detailed account of the above results, including the definitions and constructions involved. |
Monday 03.07.2023 |
Daniel Graves, University of Leeds Categorifying equivariant monoids PROPs are "product and permutation categories". They encode structure borne by objects in a symmetric monoidal category. In this talk I will discuss how the PROP that indexes the structure of a monoid in a symmetric monoidal category is closely related to the theory of crossed simplicial groups. I will then report on recent work which generalizes this in two ways. I'll talk about how we can obtain PROPs encoding the structure of monoids with a group action. I will also talk about how we can obtain analogous indexing categories in the setting of braided monoidal categories. |
Monday 26.06.2023 |
Anna-Katharina Hirmer, Friedrich-Alexander-Universität Erlangen-Nürnberg Generalised Kitaev models from Hopf monoids: topological invariance and examples Quantum double models were introduced by Kitaev to obtain a realistic model for a topological quantum computer. They are based on a directed ribbon graph and a finite-dimensional semisimple Hopf algebra. The ground state of these models is a topological invariant of a surface, i.e. only depends on the homeomorphism class of the oriented surface but not the ribbon graph. Meusburger and Voß generalised part of the construction from Hopf algebras to pivotal Hopf monoids in symmetric monoidal categories. We explain the construction of the ground state for involutive Hopf monoids and show that it is topological invariant. We explicitly describe this construction for Hopf monoids in Set, Top, Cat and SSet. |
Monday 19.06.2023 ON ZOOM Passcode: 177540 |
Eamon Quinlan-Gallego, University of Utah Finiteness properties of local cohomology If R is a commutative noetherian ring and J is an ideal of R, the local cohomology modules of R with support in J tend to have surprising finiteness properties despite being not finitely generated. In this talk I will survey some results in this direction and, if time permits, I will talk about some recent work. |
Monday 12.06.2023 online |
Ján Pulmann, University of Edinburgh |
Monday |
Nima Rasekh, Max Planck Institute for Mathematics Bonn Formalizing (Double-)Categories In recent years mathematical formalization has experienced a meteoric growth with applications ranging from computing stable homotopy groups of spheres to condensed mathematics. In this talk we will focus on the formalization of the concept of a category and in particular surprising mathematical challenges that one encounters in this setting. If time permits I will also discuss ongoing joint work with Benedikt Ahrens, Paige North and Niels van der Weide aimed at generalizing this formalization to double categories. |
Monday 15.05.2023 online |
Estanislao Herscovich, Université Grenoble Alpes Double quasi-Poisson algebras are pre-Calabi–Yau |
Monday |
Ben Elias, University of Oregon Categorial Diagonalization |
Monday 24.04.2023 online |
Andrew Baker, University of Glasgow |
Monday 17.04.2023 |
Friedrich Wagemann, University of Nantes Crossed modules of algebras over an operad This is joint work with Salim Rivière and Johan Leray. Equivalence classes of crossed modules of Lie algebras or associative algebras are well-known to be in bijection with cohomology classes in degree 3 for Chevalley-Eilenberg resp. Hochschild cohomology. We generalize this correspondence to algebras over an operad (with a fixed resolution, for example, a Koszul operad). We show that the Homotopy Transfer Theorem can be interpreted as associating to a crossed module a cocycle, and the Rectification Theorem as associating to a cocycle a crossed module. |
The speakers for the winter term 2022/23 were:
Monday |
Daniel Tubbenhauer, University of Sydney |
Monday |
Richard Garner, Macquarie University
Cofree cocommutative coalgebras and abstract differentiation |
Monday |
John Bourke, Masaryk University A skew approach to enrichment for Gray-categories |
Monday 14.11.2022 |
Julian Holstein, Universität Hamburg Koszul duality and dg categories as coalgebras |
Tuesday 15.11.2022 online |
Chris Heunen, University of Edinburgh
Sheaf representation of monoidal categories |
Monday |
Misha Feigin, University of Glasgow On Dunkl angular momenta algebra |
Monday 28.11.2022 |
Joanna Meinel, Universität Bonn How to find highest weight vectors in tensor powers |
Monday 05.12.2022 |
Andrea Gagna, The Czech Academy of Sciences
A rough overview on the Geometric Langlands correspondence
In this talk I will give a rather naive overview of the statement of the Geometric Langlands correspondence, as presented by Arinkin and Gaitsgory, touching on all the three points above to help give a solid intuition of the problem at hand. |
Monday 12.12.2022 online |
Vanessa Miemietz, University of East Anglia Hopf algebras and symmetric bimodules |
Monday 19.12.2022 |
George Balla, RWTH Aachen Symplectic PBW degenerate flag varieties |
Monday 16.01.2023 |
Tony Zorman, TU Dresden Duality in Monoidal Categories There are at least three categorical gadgets that capture various notions of mathematical duality: closed monoidal, *-autonomous, and rigid monoidal categories. These concepts are all interlinked—rigid monoidal categories are always *-autonomous, and they in turn are necessarily closed monoidal. In fact, the resulting internal-hom is very well-behaved. We will explore connections in the other direction: does the shape of the internal-hom of a closed monoidal category already characterise rigidity or *-autonomy? This talk is based on joint work with Sebastian Halbig. |
Monday 23.01.2023 |
Zbigniew Wojciechowski, TU Dresden Tensor product decompositions over a coideal subalgebra of U_q(gl2) and Type D Jones-Wenzl Projectors A classical problem is the decomposition of tensor powers of the natural representation k^n viewed as module over GL_n or its lie algebra counterpart gl_n. Answering this problem gives rise to beautiful diagrammatics and combinatorics via Schur-Weyl duality of S_n and GL_n, which can be quantized and categorified. In the talk I will discuss a non-trivial analogue of the story, where we replace S_n by the type B/D Weyl group (resp. their Hecke algebras) and GL_n by a certain coideal subalgebra of U_q(gl_2n). Moreover we will discuss idempotents in a Temperley-Lieb quotient of the Hecke algebra and an approximation theorem for those via the type D full twist. |
Monday 30.01.2023 |
Ulrich Krähmer, TU Dresden Incidence Hopf Algebras |
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 |