PhD from Rutgers University with Siddhartha Sahi
Mathematical Institute
Endenicher Allee 60, 53115 Bonn, Germany
office: 1.002
email: second name at math dot uni minus bonn dot de
# Research 🔬
I am interested in representation theory, tensor categories, and related areas.
Things I have worked on include:
int Deligne's interpolation categories and their relatives
cob cobordism categories, TQFTs, Frobenius algebras, Frobenius monoidal functors
tcp tensor categories in positive characteristics, incompressible tensor categories
rep algebraic (super)groups, Lie (super)algebras, and their representations
cent monoidal centers, Drinfeld centers
pbw PBW deformations, various kinds of Hecke and Cherednik algebras
dirac algebraic Dirac operators, Dirac cohomology, cohomology functors
diag "easy quantum groups", diagram algebras
pgrp p-groups
comp computer algebra (see also below under "misc")
(arxiv:2412.15056) cob, cent, rep Frobenius monoidal functors induced by Frobenius extensions of Hopf algebras, with Robert Laugwitz, Sebastian Posur
(arxiv:2405.19506) tcp, rep, pgrp Towards higher Frobenius functors for symmetric tensor categories, with Kevin Coulembier
(arxiv:2402.10094) cent, rep, int Projection formulas and induced functors on centers of monoidal categories, with Robert Laugwitz, Sebastian Posur
(arxiv:2206.08226) pbw, int, rep Interpolating PBW Deformations for the Orthosymplectic Groups, with Verity Mackscheidt
(arxiv:2410.08702)[Adv. Math.](...) cob, cent, rep, int Frobenius monoidal functors from ambiadjunctions and their lifts to Drinfeld centers, with Robert Laugwitz, Sebastian Posur
(arxiv:2106.05798)[Adv. Math.](https://www.sciencedirect.com/science/article/abs/pii/S000187082300035X) cob, int Indecomposable objects in Khovanov--Sazdanovic's generalizations of Deligne's interpolation categories, with Robert Laugwitz, Sebastian Posur
(arxiv:2105.10492)[Proc. London Math. Soc.](https://londmathsoc.onlinelibrary.wiley.com/doi/full/10.1112/plms.12509) int, cent The indecomposable objects in the center of Deligne's category Rep(S_t), with Nate Harman, Robert Laugwitz
(arxiv:2105.09117)[J. Group Theory](https://www.degruyter.com/document/doi/10.1515/jgth-2021-0158) pgrp Groups G satisfying a functional equation f(xk)=xf(x) for some k in G, with Dominik Bernhardt, Tim Boykett, Alice Devillers, Stephen Glasby
(arxiv:2003.13798)[Int. Math. Res. Not. IMRN](https://academic.oup.com/imrn/advance-article-abstract/doi/10.1093/imrn/rnab217/6352819) int, diag Semisimplicity and indecomposable objects in interpolating partition categories, with Laura Maaßen
(arxiv:2003.13297)[Math. Nachr.](https://onlinelibrary.wiley.com/doi/full/10.1002/mana.202100290) pgrp Strata of p-origamis, with Andrea Thevis
(arxiv:2003.05639)[Algebr. Represent. Theory](https://link.springer.com/article/10.1007/s10468-022-10179-6) rep, comp Gröbner bases for fusion products, with Ghislain Fourier, Viktor Levandovskyy
(arxiv:1901.08657)[J. London Math. Soc.](https://londmathsoc.onlinelibrary.wiley.com/doi/full/10.1112/jlms.12403) int, cent On the monoidal center of Deligne's category Rep(S_t), with Robert Laugwitz
(arxiv:1608.07509)[Trans. Amer. Math. Soc.](https://www.ams.org/journals/tran/2019-371-10/S0002-9947-2019-07446-9/home.html) pbw, dirac Barbasch--Sahi algebras and Dirac cohomology
(arxiv:1608.07504)[Pure Appl. Math. Q.](https://www.intlpress.com/site/pub/pages/journals/items/pamq/content/vols/0017/0004/a009) pbw, dirac, rep Hopf--Hecke algebras, infinitesimal Cherednik algebras, and Dirac cohomology, with Siddhartha Sahi
[PhD thesis](https://rucore.libraries.rutgers.edu/rutgers-lib/59087/) pbw, dirac, rep Dirac cohomology for Hopf--Hecke algebras
# Teaching 🎓
Spring 2025, Uni Bonn
[seminar](crep25/index.html) Computer-Assisted Representation Theory II
[course](rep25/index.html)Representation Theory I by Catharina Stroppel
Uni Bonn
- Fall 2024: [seminar](crep24/index.html) Computer-Assisted Representation Theory
[course](rep24/index.html) Foundations in Representation Theory by Catharina Stroppel - Spring 2024: Graduate Seminar: Oligomorphic groups and tensor categories - Fall 2023: Graduate Seminar: Higher Segal Spaces - Spring 2023: [course](tc23/index.html) Tensor categories in representation theory, joint with Catharina Stroppel RWTH Aachen - 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
# Misc 🎉
[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 in Julia. This is related to some of my papers above.
[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/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/)
[visualization](./misc/tsp25/index.html) of my implementation of a 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/)
[3d rendering](./misc/3d/index.html) of affine surfaces
[course](rep24/index.html) Foundations in Representation Theory by Catharina Stroppel - Spring 2024: Graduate Seminar: Oligomorphic groups and tensor categories - Fall 2023: Graduate Seminar: Higher Segal Spaces - Spring 2023: [course](tc23/index.html) Tensor categories in representation theory, joint with Catharina Stroppel RWTH Aachen - 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
[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
[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))
> this webpage was written by me & updated in April 2025
> Warming Stripes by Ed Hawkins