johannesflake.de
Johannes Flake member of the [SFB-TRR 195] Postdoc at RWTH Aachen PhD from Rutgers University (2018) with Siddhartha Sahi Algebra and Representation Theory RWTH Aachen University Pontdriesch 10--16, 52062 Aachen, Germany Office: room 402, building no. 1952 Email: second name at art dot rwth minus aachen 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: - Deligne's interpolation categories and their relatives, monoidal centers - algebraic Dirac operators, Dirac cohomology, cohomology functors - PBW deformations, various kinds of Hecke and Cherednik algebras - "easy quantum groups", diagram algebras - p-groups - computer algebra (arxiv:2206.08226) with Verity Mackscheidt: Interpolating PBW Deformations for the Orthosymplectic Groups (2022) (arxiv:2106.05798) with Robert Laugwitz and Sebastian Posur: Indecomposable objects in Khovanov--Sazdanovic's generalizations of Deligne's interpolation categories (2021) (arxiv:2105.10492) with Nate Harman and Robert Laugwitz: The indecomposable objects in the center of Deligne's category Rep(S_t) (2021) (arxiv:2003.05639) with Ghislain Fourier and Viktor Levandovskyy: Gröbner bases for fusion products. Algebr. Represent. Theory (in press) (arxiv:2105.09117) with Dominik Bernhardt, Tim Boykett, Alice Devillers, Stephen Glasby: Groups G satisfying a functional equation f(xk)=xf(x) for some k in G. J. Group Theory (in press) (arxiv:2003.13297) with Andrea Thevis: Strata of p-origamis. Math. Nachr. (in press) [article](https://www.intlpress.com/site/pub/pages/journals/items/pamq/content/vols/0017/0004/a009)(arxiv:1608.07504) with Siddhartha Sahi: Hopf--Hecke algebras, infinitesimal Cherednik algebras, and Dirac cohomology. Pure Appl. Math. Q. (Kostant special edition, 2022) [article](https://academic.oup.com/imrn/advance-article-abstract/doi/10.1093/imrn/rnab217/6352819)(arxiv:2003.13798) with Laura Maaßen: Semisimplicity and indecomposable objects in interpolating partition categories. Int. Math. Res. Not. IMRN (2021) [article](https://londmathsoc.onlinelibrary.wiley.com/doi/full/10.1112/jlms.12403)(arxiv:1901.08657) with Robert Laugwitz: On the monoidal center of Deligne's category Rep(S_t). J. London Math. Soc. (2020) [article](https://www.ams.org/journals/tran/2019-371-10/S0002-9947-2019-07446-9/home.html)(arxiv:1608.07509): Barbasch--Sahi algebras and Dirac cohomology. Trans. Amer. Math. Soc. (2019) [PhD thesis](https://rucore.libraries.rutgers.edu/rutgers-lib/59087/) Dirac cohomology for Hopf--Hecke algebras (Oct 2018)
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 Sep 30, 2022
 
Warming Stripes[*](https://showyourstripes.info/s/globe) by Ed Hawkins[*](http://www.met.reading.ac.uk/~ed/home/index.php)