Apply for a PhD position! (deadline 2 April 2024)

RESEARCH INTEREST

I work on Lie theoretic representation theory. I am mainly interested in representation theory of algebraic groups in positive characteristic,  category O, higher(categorical) representation theory, and related topics like Coxeter groups and their Hecke algebras, Soergel bimodules, quantum groups, R-matrices and K-matrices, polynomial functors and functor cohomology, category theory and homological algebra. 

PAST POSITIONS

I came to Uppsala in 2019 and was a postdoc for the first two years.

I was a postdoc in Bonn for 2016-2019, partly at the Max Planck Institute for Mathematics and partly at the Mathematisches Institut (University Bonn). 

From 2012 to 2016, I was a graduate student at the University of Virginia. My PhD advisors were Brian Parshall (official) and Len Scott.

PAPERS (all are on arXiv)

On reduced expressions for core double cosets (with Ben Elias, Nicolas Libedinsky, Leonardo Patimo),  arXiv:2402.08673

Singular Light Leaves  (with Ben Elias, Nicolas Libedinsky, Leonardo Patimo), arXiv:2401.03053 (submitted)

An atomic Coxeter presentation, arXiv:2312.16666 (submitted),  slides (handout version) based on an FD seminar

Subexpressions and the Bruhat order for double cosets  (with Ben Elias, Nicolas Libedinsky, Leonardo Patimo), arXiv:2307.15726 (submitted)

Demazure operators for double cosets (with Ben Elias, Nicolas Libedinsky, Leonardo Patimo), arXiv:2307.15021 (submitted)

Graded extensions of Verma modules  (with Volodymyr Mazorchuk), arXiv.2210.15312 (submitted)

On first extensions in S-subcategories of O (with Volodymyr Mazorchuk), In: Dobrev, V. (eds) Lie Theory and Its Applications in Physics. LT 2021. Springer Proceedings in Mathematics & Statistics, vol 396. 

Join operation for the Bruhat order and Verma modules (with Volodymyr Mazorchuk and Rafael Mrđen), arXiv:2109.01067 (accepted)

Alternating sing matrices and Verma modules, Proceedings of the AMS, Volume 151, Number 3, March 2023, Pages 949–959 https://doi.org/10.1090/proc/16151

A singular Coxeter presentation (with Ben Elias), Proc. London Math. Soc. (2023) https://doi.org/10.1112/plms.12503 

Some homological properties of category O, VI (with Volodymyr Mazorchuk and Rafael Mrđen), Doc. Math. 26, 1237-1269 (2021) DOI: 10.25537/dm.2021v26.1237-1269

Bigrassmannian permutations and Verma modules (with Volodymyr Mazorchuk and Rafael Mrđen), Sel. Math. New Ser. 27, 55 (2021). https://doi.org/10.1007/s00029-021-00672-z 

Some homological properties of category O, V (with Volodymyr Mazorchuk and Rafael Mrđen), International Mathematics Research Notices (2021), DOI: 10.1093/imrn/rnab330 

Adjunction in the absence of identity (with Volodymyr Mazorchuk and Xiaoting Zhang),  Appl Categor Struct (2021). https://doi.org/10.1007/s10485-021-09652-y

Polynomial functors and and two-parameter quantum symmetric pairs (with Valentin Buciumas), Transformation Groups (2022). https://doi.org/10.1007/s00031-022-09716-w

2-representations of small quotients of Soergel bimodules in infinite types (with Volodymyr Mazorchuk), Proceedings of the AMS https://doi.org/10.1090/proc/14584

Quantum polynomial functors from $e$-Hecke pairs (with Valentin Buciumas), Math. Z. (2018) https://doi.org/10.1007/s00209-018-2106-1

Graded zero part of forced graded algebra, Sci. China Math. (2018) 61: 269. https://doi.org/10.1007/s11425-017-9163-0

On modules arising from quantum groups at $p^r$-th roots of unity, J. Algebra 520C (2019). https://doi.org/10.1016/j.jalgebra.2018.10.041

Cohomology in singular blocks for a quantum group at a root of unity, Algebr Represent Theor (2018). https://doi.org/10.1007/s10468-018-9814-4

EVENTS 

``Triangles and reflection groups; or, Plato and Coxeter'' (a public talk) at the fall meeting of Matematiska föreningen i Uppsala, December 2022

``Bruhat orders and Verma modules'' at the Nordic Congress of Mathematicians, Aalto University, August 2022 slides

A lecture series on highest weight categories in QSMS workshop on representation theory, July 2022

``Bruhat orders and Verma modules'' at the Conference on algebraic representation theory, November 2021 slides

A talk on singular Coxeter presentation at the  National University of Singapore, October 2021

 ``Bruhat orders and Verma modules''  at the OIST Representation Theory Seminar, September 2021. video and slides

A talk on singular Coxeter presentation at the Algebra and Geomretyr seminar Sydney Mathematical Research Institute, August 2021. video

A talk on Kostant's problem at the RepNet Virtual Seminar, June 2021 (video will be published)

A talk on Kostant's problem at the AMS Spring 2021 Western Sectional Meeting, May 2021

``Kostant's problem and actions of the Hecke category'', Algebra seminar at the University of Virginia, April 2021

``A Singular presentation of Coxeter systems'', Colloquium at the University of Virginia, April 2021 slides

``Polynomial functors and quantum symmetric pairs'' in Newcastle, November 2020 slides

and older events

TEACHING in UPPSALA

Algebraiska strukturer (Algebraic structures), HT2020-2023

Linjär algebra II, VT2022

Modules and homological algebra HT2022 

Lie groups VT2023

Grundläggande topologi VT2023

Elementär talteori (Elementary number theory), VT2022

LOCAL INFORMATION

The algebra group in Uppsala runs Algebra Seminar and has a YouTube channel.

The mathematics department regularly hires PhD students and postdocs/researchers.