Johannes Flake * math * MPIM Bonn

Research I am interested in algebra, representation theory, and tensor categories; more specifically: 1 Deligne's interpolation categories and their relatives 2 algebraic (super)groups, Lie (super)algebras, and their representations 3 monoidal centers / Drinfeld centers 4 PBW deformations, various kinds of Hecke and Cherednik algebras 5 algebraic Dirac operators, Dirac cohomology, cohomology functors 6 "easy quantum groups", diagram algebras 7 p-groups 8 computer algebra (see also below under "misc")

- 1,2,4 Interpolating PBW Deformations for the Orthosymplectic Groups [arxiv 2022](arxiv:2206.08226) with Verity Mackscheidt - 1 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 - 1,3 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 - 7 Strata of p-origamis [Math. Nachr. 2023](https://onlinelibrary.wiley.com/doi/full/10.1002/mana.202100290) (arxiv:2003.13297) with Andrea Thevis - 2,8 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 - 7 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 - 2,4,5 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 - 1,6 Semisimplicity and indecomposable objects in interpolating partition categories [IMRN 2021](https://academic.oup.com/imrn/advance-article-abstract/doi/10.1093/imrn/rnab217/6352819)(arxiv:2003.13798) with Laura Maaßen - 1,3 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 - 4,5 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) - 2,4,5 [PhD thesis 2018](https://rucore.libraries.rutgers.edu/rutgers-lib/59087/) Dirac cohomology for Hopf--Hecke algebras

Teaching Uni Bonn (as a postdoc at MPIM) - 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 implementaton of an 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.