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]( Deligne categories and quantum groups (postponed due to COVID-19)
research I am interested in algebra and representation theory, more specifically: - tensor categories, Deligne's interpolation categories, 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 (2020) (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]( with Siddhartha Sahi: Hopf--Hecke algebras, infinitesimal Cherednik algebras, and Dirac cohomology. Pure Appl. Math. Q. (Kostant special edition, 2022) [article]( with Laura Maaßen: Semisimplicity and indecomposable objects in interpolating partition categories. Int. Math. Res. Not. IMRN (2021) [article]( with Robert Laugwitz: On the monoidal center of Deligne's category Rep(S_t). J. London Math. Soc. (2020) [article]( Barbasch--Sahi algebras and Dirac cohomology. Trans. Amer. Math. Soc. (2019) [PhD thesis]( Dirac cohomology for Hopf--Hecke algebras (Oct 2018)
teaching RWTH - Spring 2022: Tensor Categories [course page]( - 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 - Spring 2018: TA for Math 351 -- Introduction to Abstract Algebra I - Fall 2017: TA for Math 351 -- Introduction to Abstract Algebra I - Fall 2017: TA for Math 451 -- Abstract Algebra I - Spring 2017: TA for Math 311 -- Introduction to Real Analysis I - Spring 2017: TA-at-large for Math 354 -- Linear Optimization - Fall 2016: TA-at-large for Math 421 -- Advanced Calculus for Engineering - Spring 2016: TA for Math 251 -- Multivariable Calculus - Fall 2015: TA for Math 152 -- Calculus II for the Mathematical and Physical Sciences
misc [johannesflake/oscar](, my personal unofficial [OSCAR] docker image [pbwdeformations.jl](, a Julia package for PBW deformations of smash products using [OSCAR] and [GAP] (under development; [example]( [polybases.jl](, a Julia package for monomial bases using [OSCAR] and [polymake] (under development; [example]( [KnopCategoriesForGap](, 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[?]( [pictures](./misc/UDG/index.html) of some D6-symmetric unit-distance graphs in the plane with 745 vertices and chromatic number five that I discovered with a SAT solver. So what[?]( [pictures and video](./misc/mandelbrot/index.html) of the Mandelbrot set I made with Julia, the language. What are we looking at[?]( [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. It's related to some of my papers above.
maintained by me -- updated on Jun 24, 2022
Warming Stripes[*]( by Ed Hawkins[*](