johannes flake * math * bonn

Research I am interested in algebra, representation theory, and tensor categories, or more specifically: int Deligne's interpolation categories and their relatives cob cobordism categories and TQFTs, Frobenius algebras, Frobenius monoidal functors tcp tensor categories in positive characteristics, incompressible tensor categories rep algebraic (super)groups, Lie (super)algebras, and their representations cent monoidal centers / Drinfeld centers pbw PBW deformations, various kinds of Hecke and Cherednik algebras dirac algebraic Dirac operators, Dirac cohomology, cohomology functors diag "easy quantum groups", diagram algebras pgrp p-groups comp computer algebra (see also below under "misc")

- cent,rep,int,cob Frobenius monoidal functors from ambiadjunctions and their lifts to Drinfeld centers [arxiv 2024](arxiv:2410.08702) with Robert Laugwitz and Sebastian Posur - tcp,rep,pgrp Towards higher Frobenius functors for symmetric tensor categories [arxiv 2024](arxiv:2405.19506) with Kevin Coulembier - cent,rep,int Projection formulas and induced functors on centers of monoidal categories [arxiv 2024](arxiv:2402.10094) with Robert Laugwitz and Sebastian Posur - pbw,int,rep Interpolating PBW Deformations for the Orthosymplectic Groups [arxiv 2022](arxiv:2206.08226) with Verity Mackscheidt - cob,int Indecomposable objects in Khovanov--Sazdanovic's generalizations of Deligne's interpolation categories [Adv. Math. 2023](https://www.sciencedirect.com/science/article/abs/pii/S000187082300035X) [arxiv](arxiv:2106.05798) with Robert Laugwitz and Sebastian Posur - int,cent The indecomposable objects in the center of Deligne's category Rep(S_t) [Proc. London Math. Soc. 2023](https://londmathsoc.onlinelibrary.wiley.com/doi/full/10.1112/plms.12509) [arxiv](arxiv:2105.10492) with Nate Harman and Robert Laugwitz - pgrp Strata of p-origamis [Math. Nachr. 2023](https://onlinelibrary.wiley.com/doi/full/10.1002/mana.202100290) (arxiv:2003.13297) with Andrea Thevis - rep,comp Gröbner bases for fusion products [Algebr. Represent. Theory 2022](https://link.springer.com/article/10.1007/s10468-022-10179-6) (arxiv:2003.05639) with Ghislain Fourier and Viktor Levandovskyy - pgrp Groups G satisfying a functional equation f(xk)=xf(x) for some k in G [J. Group Theory 2022](https://www.degruyter.com/document/doi/10.1515/jgth-2021-0158) (arxiv:2105.09117) with Dominik Bernhardt, Tim Boykett, Alice Devillers, Stephen Glasby - pbw,dirac,rep Hopf--Hecke algebras, infinitesimal Cherednik algebras, and Dirac cohomology [Pure Appl. Math. Q. 2021](https://www.intlpress.com/site/pub/pages/journals/items/pamq/content/vols/0017/0004/a009)(arxiv:1608.07504) with Siddhartha Sahi - int,diag Semisimplicity and indecomposable objects in interpolating partition categories [Int. Math. Res. Not. IMRN 2021](https://academic.oup.com/imrn/advance-article-abstract/doi/10.1093/imrn/rnab217/6352819)(arxiv:2003.13798) with Laura Maaßen - int,cent On the monoidal center of Deligne's category Rep(S_t) [J. London Math. Soc. 2020](https://londmathsoc.onlinelibrary.wiley.com/doi/full/10.1112/jlms.12403)(arxiv:1901.08657) with Robert Laugwitz - pbw,dirac Barbasch--Sahi algebras and Dirac cohomology [Trans. Amer. Math. Soc. 2019](https://www.ams.org/journals/tran/2019-371-10/S0002-9947-2019-07446-9/home.html)(arxiv:1608.07509) - pbw,dirac,rep [PhD thesis 2018](https://rucore.libraries.rutgers.edu/rutgers-lib/59087/) Dirac cohomology for Hopf--Hecke algebras

Teaching Uni Bonn (as a postdoc) - Fall 2024: Foundations in Representation Theory with Catharina Stroppel [course page](rep24/index.html) - Fall 2024: Seminar Computer-assisted Representation Theory with Catharina Stroppel [seminar page](crep24/index.html) - Spring 2024: Graduate Seminar: Oligomorphic groups and tensor categories - Fall 2023: Graduate Seminar: Higher Segal Spaces - Spring 2023: Tensor categories in representation theory with Catharina Stroppel [course page](tc23/index.html) RWTH (2018 -- 2022, as a postdoc) - Spring 2022: Tensor Categories - Spring 2021: Algebraic Geometry - Spring 2019: Lecture in Pairs on filtered-graded transfer and PBW deformations with Viktor Levandovskyy - Spring 2019: Begleitpraktikum 2 - Fall 2018: Begleitpraktikum Rutgers (2015 -- 2018, as a TA / TA-at-large) - Math 351 -- Introduction to Abstract Algebra I - Math 451 -- Abstract Algebra I - Math 311 -- Introduction to Real Analysis I - Math 354 -- Linear Optimization - Math 421 -- Advanced Calculus for Engineering - Math 251 -- Multivariable Calculus - Math 152 -- Calculus II for the Mathematical and Physical Sciences

Misc [johannesflake/oscar](https://github.com/johannesflake/oscar-docker/), my personal unofficial [OSCAR] docker image [pbwdeformations.jl](https://gitlab.com/johannesflake/pbwdeformations.jl), a Julia package for PBW deformations of smash products using [OSCAR] and [GAP] (under development; [example](https://nbviewer.org/urls/gitlab.com/johannesflake/pbwdeformations.jl/-/raw/master/examples/PBWDeformationsNotebook.ipynb)) [polybases.jl](https://gitlab.com/johannesflake/polybases.jl), a Julia package for monomial bases using [OSCAR] and [polymake] (under development; [example](https://nbviewer.jupyter.org/github/johannesflake/polybases-examples/blob/master/polybases-example-1.ipynb)) [KnopCategoriesForGap](https://github.com/homalg-project/KnopCategoriesForCAP), a [GAP]/[CAP] package for Knop's tensor envelopes [slides](pdf/schur_weyl_links.pdf) on quantum Schur--Weyl duality and link invariants [slides](pdf/deligne_category_rep_st.pdf) on Deligne's category Rep(S_t) [slides](pdf/voa_constructions.pdf) on some constructions of vertex operator algebras and their modules [slides](pdf/quantum_groups.pdf) on quantum groups and tensor categories [3d rendering](./misc/3d/index.html) of affine surfaces [visualization](./misc/tsp25/index.html) of my implementation of a 2.5-opt algorithm approximately solving a random traveling salesman problem live in your browser, slowed down for visualization purposes. Which traveling salesman[?](https://www.quantamagazine.org/computer-scientists-find-new-shortcuts-to-traveling-salesman-problem-20130129/) [pictures](./misc/UDG/index.html) of some hexagonally symmetric unit-distance graphs in the plane with 745 vertices and chromatic number 5 that I discovered with a SAT solver. So what[?](https://www.quantamagazine.org/decades-old-graph-problem-yields-to-amateur-mathematician-20180417/) [pictures & video](./misc/mandelbrot/index.html) of the Mandelbrot set that I made with Julia, the language. What are we looking at[?](https://youtu.be/NGMRB4O922I) [pictures](./misc/RepSt/RepSt.html) of computations in the category Rep(S_t) and of objects in its monoidal center made with my own implementation of that category in Julia. This is related to some of my papers above.