johannesflake.de
Johannes Flake Postdoc at MPIM Bonn PhD from Rutgers University (2018) with Siddhartha Sahi Max Planck Institute for Mathematics Vivatsgasse 7, 53111 Bonn, Germany office: 309 email: second name at mpim minus bonn dot mpg dot de [workshop](http://deligne-categories-quantum-groups.rwth-aachen.de/) Deligne categories and quantum groups (postponed due to COVID-19)
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 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") - Interpolating PBW Deformations for the Orthosymplectic Groups 1,2,4 [arxiv 2022](arxiv:2206.08226) with Verity Mackscheidt - Indecomposable objects in Khovanov--Sazdanovic's generalizations of Deligne's interpolation categories 1 [arxiv 2021](arxiv:2106.05798) with Robert Laugwitz and Sebastian Posur - The indecomposable objects in the center of Deligne's category Rep(S_t) 1,3 [arxiv 2021](arxiv:2105.10492) with Nate Harman and Robert Laugwitz - Strata of p-origamis 7 [Math. Nachr. (in press)](...) (arxiv:2003.13297) with Andrea Thevis - Gröbner bases for fusion products 2,8 [Algebr. Represent. Theory 2022](https://link.springer.com/article/10.1007/s10468-022-10179-6) (arxiv:2003.05639) with Ghislain Fourier and Viktor Levandovskyy - Groups G satisfying a functional equation f(xk)=xf(x) for some k in G 7 [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 - Hopf--Hecke algebras, infinitesimal Cherednik algebras, and Dirac cohomology 2,4,5 [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 - Semisimplicity and indecomposable objects in interpolating partition categories 1,6 [IMRN 2021](https://academic.oup.com/imrn/advance-article-abstract/doi/10.1093/imrn/rnab217/6352819)(arxiv:2003.13798) with Laura Maaßen - On the monoidal center of Deligne's category Rep(S_t) 1,3 [J. London Math. Soc. 2020](https://londmathsoc.onlinelibrary.wiley.com/doi/full/10.1112/jlms.12403)(arxiv:1901.08657) with Robert Laugwitz - Barbasch--Sahi algebras and Dirac cohomology 4,5 [Trans. Amer. Math. Soc. 2019](https://www.ams.org/journals/tran/2019-371-10/S0002-9947-2019-07446-9/home.html)(arxiv:1608.07509) [PhD thesis 2018](https://rucore.libraries.rutgers.edu/rutgers-lib/59087/) 2,4,5 Dirac cohomology for Hopf--Hecke algebras
teaching RWTH - Spring 2022: Tensor Categories [course page](https://www.art.rwth-aachen.de/go/id/tswgv) - 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 (Fall 2015 -- Spring 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.
this webpage was written by me & updated on Oct 31, 2022
 
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