Johannes Flake
member of the SFB-TRR 195
Postdoc at RWTH Aachen with Ghislain Fourier
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 and, more specifically, things like:
- 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
preprint with Laura Maaßen: *Semisimplicity and Indecomposable Objects in Interpolating Partition Categories* (2020)
preprint with Andrea Thevis: *Strata of p-Origamis* (2020)
preprint with Ghislain Fourier and Viktor Levandovskyy: *Gröbner bases for fusion products* (2020)
preprint with Siddhartha Sahi: *Hopf-Hecke algebras, infinitesimal Cherednik algebras and Dirac cohomology.* Pure Appl. Math. Q., Kostant edition (in press).
articlepreprint with Robert Laugwitz: *On the Monoidal Center of Deligne's Category Rep(S_t).* J. London Math. Soc. (2020).
articlepreprint *Barbasch-Sahi algebras and Dirac cohomology.* Trans. Amer. Math. Soc. 371.10 (2019): 6883-6902.
PhD thesis Dirac cohomology for Hopf-Hecke algebras, September 2018.

Teaching
RWTH
- **Spring 2021: Algebraic Geometry** course page
- 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
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 on quantum Schur-Weyl duality and link invariants
slides on Deligne's category Rep(S_t)
slides on some constructions of vertex operator algebras and their modules
slides on quantum groups and tensor categories
3d rendering of affine surfaces
visualization 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 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?

Maintained by me. Last update on Jan 24, 2021.