Jens Niklas Eberhardt
I am a junior professor at the University of Mainz. I am also Principal Investigator of the European Doctoral Network REMOLD on geometric representation theory and the Langlands program, and of the collaborative research center CRC 326 - GAUS (Geometry and Arithmetic of Uniformized Structures).
Previously, I held a research position funded by my research grant "Equivariant K-motives and Koszul Duality" from the German Research Foundation (DFG). Before that, I served as a substitute professor at the University of Bonn, and was a postdoc at the University of Wuppertal funded by the same DFG grant, as well as at the University of Bonn and Max Planck Institute for Mathematics in the workgroup of Catharina Stroppel.
I also served as an Assistant Adjunct Professor at UCLA in the work group of Raphaël Rouquier. My PhD was completed under the supervision of Wolfgang Soergel at the University of Freiburg.
My CV.
Interests
My research area is geometric representation theory and motivic homotopy theory where I am particulary interested in:
- algebraic groups and Lie algebras,
- Soergel bimodules and Koszul duality,
- motivic cohomology, K-theory and Grothendieck-Witt theory,
- categories of motivic sheaves,
- six functor formalisms.
In very broad strokes, the general philosophy behind this area could be described like this:
Representation theory is a branch of mathematics concerned with the study of symmetrical objects, ranging from wallpapers with a repeating floral pattern to hydrogen atoms and automorphic forms. A powerful technique is to turn representation theoretic problems into questions about the shape or geometry of some space; this makes them amenable to methods from other areas of mathematics, as topology, algebraic or differential geometry, and one speaks of geometric representation theory.
Publications
Preprints
The Parabolic K-motivic Hecke Category
Jens Niklas Eberhardt, Arnaud Eteve
arxiv.
K-motives, Springer Theory and the Local Langlands Correspondence
Jens Niklas Eberhardt
arxiv.
Standard Extension Algebras I: Perverse Sheaves and Fukaya Calculus
Jens Niklas Eberhardt, Catharina Stroppel
arxiv.
Logical Operators and Derived Automorphisms of Tile Codes
Nikolas P. Breuckmann, Shin Ho Choe, Jens Niklas Eberhardt, Francisco Revson Fernandes Pereira, Vincent Steffan
arxiv.
Cups and Gates I: Cohomology invariants and logical quantum operations
Nikolas P. Breuckmann, Margarita Davydova, Jens Niklas Eberhardt, Nathanan Tantivasadakarn
arxiv.
Graded and Geometric Parabolic Induction for Category $\smash{\scriptstyle{\mathcal{O}}}$
Jens Niklas Eberhardt
arxiv.
Published/Accepted
An Intersection Matrix for Affine Hyperplane Arrangements
Jens Niklas Eberhardt, Carl Mautner
Algebraic Combinatorics, 2025 (accepted)
arxiv.
Universal Koszul Duality for Kac-Moody Groups
Jens Niklas Eberhardt, Arnaud Eteve
Compositio Mathematica, 2025 (accepted)
arxiv.
Tile Codes: High-Efficiency Quantum Codes on a Lattice with Boundary
Vincent Steffan, Shin Ho Choe, Nikolas P. Breuckmann, Francisco Revson Fernandes Pereira, Jens Niklas Eberhardt
Physical Review Letters, 2025
published version, arxiv.
Planar quantum low-density parity-check codes with open boundaries
Zijian Liang, Jens Niklas Eberhardt, Yu-An Chen
PRX Quantum, 2025
published version, arxiv.
Two proofs of a Jantzen Conjecture for Whittaker Modules
Jens Niklas Eberhardt, Anna Romanov
Selecta Mathematica, 2025
published version, arxiv.
Logical Operators and Fold-Transversal Gates of Bivariate Bicycle Codes
Jens Niklas Eberhardt, Vincent Steffan
IEEE Transactions on Information Theory, 2025
published version, arxiv.
K-theory Soergel Bimodules
Jens Niklas Eberhardt
Bulletin of the London Mathematical Society, 2024
published version, arxiv.
Integral Motivic Sheaves And Geometric Representation Theory
Jens Niklas Eberhardt, Jakob Scholbach
Advances in Mathematics, 2023
published version, arxiv.
K-motives and Koszul Duality
Jens Niklas Eberhardt
Bulletin of the London Mathematical Society, 2022
published version, arxiv.
Motivic Springer Theory
Jens Niklas Eberhardt, Catharina Stroppel
Indagationes Mathematicae, 2022
published version, arxiv.
Group completion in the K-theory and Grothendieck-Witt theory of proto-exact categories
Jens Niklas Eberhardt, Oliver Lorscheid, Matthew B. Young
Journal of Pure and Applied Algebra, 2022
published version, arxiv.
Algebraic K-theory and Grothendieck-Witt theory of monoid schemes
Jens Niklas Eberhardt, Oliver Lorscheid, Matthew B. Young
Mathematische Zeitschrift, 2022
published version, arxiv.
Quantum Low-Density Parity-Check Codes
Nikolas P. Breuckmann, Jens Niklas Eberhardt
PRX Quantum, 2021
published version, arxiv.
Balanced Product Quantum Codes
Nikolas P. Breuckmann, Jens Niklas Eberhardt
IEEE Transactions on Information Theory, 2021
published version, arxiv.
Springer Motives
Jens Niklas Eberhardt
Proceedings of the American Mathematical Society, 2021
published version, arxiv.
Real Springer fibers and odd arc algebras
Jens Niklas Eberhardt, Grégoire Naisse, Arik Wilbert
Journal of the London Mathematical Society, 2020
published version, arxiv.
Mixed Motives and Geometric Representation Theory in Equal Characteristic
Jens Niklas Eberhardt and Shane Kelly
Selecta Mathematica New Series, 2019,
published version, arxiv.
Computing the Tutte Polynomial of a Matroid from its Lattice of Cyclic Flats
Jens Niklas Eberhardt
The Electronic Journal of Combinatorics, 2014
published version, arxiv.
Other Publications
Soergel and Springer: Motives and Correspondences
Jens Niklas Eberhardt
Oberwolfach Report, 23/2022
online version.
Perverse Sheaves on Flag Varieties
Jens Niklas Eberhardt
Oberwolfach Report, 18/2022
online version.
Pruning qLDPC codes: Towards bivariate bicycle codes with open boundary conditions
Jens Niklas Eberhardt, Francisco Revson F. Pereira, Vincent Steffan
arxiv.
Challenges and issues of SARS-CoV-2 pool testing
Jens Niklas Eberhardt, Nikolas P. Breuckmann, Christiane S. Eberhardt
The Lancet Infectious Diseases, 2020
online version.
Multi-Stage Group Testing Improves Efficiency of Large-Scale COVID-19 Screening
Jens Niklas Eberhardt, Nikolas P. Breuckmann, Christiane S. Eberhardt,
Journal of Clinical Virology, 2020,
online version.
Theses
Graded and Geometric Parabolic Induction
Jens Niklas Eberhardt
PhD Thesis, 2017
PDF
Slides and Notes
Slides for my talk on universal Koszul duality at TU Darmstadt (July 2025).
Slides for my talk on sheaves on stratified spaces at the ISTA (March 2024).
Slides for my talk on K-motives and the local Langlands correspondence at the University of Tokyo (February 2024).
Slides for my talk on motivic Springer theory at the workshop Interactions between Algebraic Geometry and Noncommutative Algebra in Oberwolfach (May 2022).
Slides for an expository talk on perverse sheaves at the Arbeitsgemeinschaft: Geometric Representation Theory in Oberwolfach (April 2022).
Video of my talk on motivic Springer theory at the conference Representation theory's hidden motives at the University of Münster and the University of Sydney (September 2021).
Video and Slides of my talk outlining a new K-theoretic perspective on Koszul duality at the Geometric and Modular Representation Theory Seminar at IAS Princeton (April 2021).
Slides for a my talk on K-motives and Koszul duality at the Geometric Representation Theory conference at the MPIM Bonn/Perimeter Institute (June 2020).
Notes for a talk giving an overview of different applications of motivic sheaves in geometric representation theory. They were used in talks in Oxford (September 2019), Kaiserslautern and Bochum (October 2019).
Slides motivating and sketching a category of mixed sheaves with coefficients in $\smash{\mathbb{F}_p}$ constructed in joint work with Shane Kelly (see Publications). They were made for a talk at the Erwin Schroedinger Institute in Vienna (2017).
Slides motivating and stating some of the results of my PhD thesis. They were made for the investigation of our Graduiertenkolleg in June 2016 and also partly used in talks I gave in Regensburg (July 2016), Bonn (August 2016), Clermont-Ferrand (2017) and in my PhD defense.
Handwritten notes (thanks to Konrad Voelkel) of a joint talk with Florian Beck, explaining the relation between Verdier duality, Borel–Moore homology and cosheaves.
Slides describing the content of my master thesis developing a new algorithm for the computation of the Tutte polynomial of a matroid.
Teaching
| In 2019, I was awarded the Distinguished Teaching Award of the UCLA math department. | 
My hardworking students!
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Current
| Winter 25/26 (Mainz) | Representation Theory of Algebraic Groups I |
Past
Contact
email: mail at jenseberhardt.com