Interests
My research has two main directions: geometric representation theory and quantum error correction.
Geometric representation theory and motives
My work in pure mathematics is mainly in geometric representation theory and motivic homotopy theory.
I am particularly interested in:
- algebraic groups and Lie algebras,
- Soergel bimodules, Hecke categories and Koszul duality,
- motivic cohomology, K-theory and Grothendieck–Witt theory,
- categories of motivic sheaves,
- six-functor formalisms,
- the Langlands program.
In very broad strokes, the general philosophy behind this area could be described as follows:
Representation theory is a branch of mathematics concerned with the study of symmetrical objects, ranging from wallpapers with repeating floral patterns to hydrogen atoms and automorphic forms.
A powerful technique is to turn representation-theoretic problems into questions about the shape or geometry of a space.
This makes them amenable to methods from topology, algebraic geometry and differential geometry, and one speaks of geometric representation theory.
Quantum error correction
I work mainly on quantum low-density parity-check codes.
I approach quantum error correction using methods from pure mathematics, and I am particularly interested in bringing ideas from geometric representation theory into the subject.
With Nikolas Breuckmann, I introduced balanced-product quantum codes.
Balanced products led to quantum LDPC codes with asymptotically optimal parameters and were a key ingredient in the proof of the NLTS conjecture.
Quantum codes can be constructed from chain complexes, and some of the best constructions come from rather deep pure mathematics.
Number theory and representation theory enter through arithmetic quotients of Bruhat–Tits buildings and the Jacquet–Langlands correspondence, which underlie important constructions of expander graphs and complexes.
Hyperbolic Coxeter groups provide a different source of highly symmetric complexes.
Homology and cohomology describe logical operators, while cup products and other cohomology operations produce logical gates.
My current work concerns codes with open boundaries, nearest-neighbour syndrome extraction and fault-tolerant logical gates.
In the long run, I want to help build the first fault-tolerant universal quantum computer.
For an introduction to quantum LDPC codes, see Quantum Low-Density Parity-Check Codes.
Publications
Pure mathematics
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.
Graded and Geometric Parabolic Induction for Category \(\mathcal{O}\)
Jens Niklas Eberhardt
arXiv.
Published and accepted
An Intersection Matrix for Affine Hyperplane Arrangements
Jens Niklas Eberhardt, Carl Mautner
Algebraic Combinatorics 9 (2026), no. 2, 499–512
published version, arXiv.
Universal Koszul Duality for Kac–Moody Groups
Jens Niklas Eberhardt, Arnaud Eteve
Compositio Mathematica 162 (2026), no. 5, 1053–1092
published version, arXiv.
Two proofs of a Jantzen Conjecture for Whittaker Modules
Jens Niklas Eberhardt, Anna Romanov
Selecta Mathematica, 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.
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, Shane Kelly
Selecta Mathematica, 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.
Quantum error correction
Preprints
Nearest-neighbour gates are all you need: High-rate quantum low-density parity-check codes on a planar grid
Boren Gu, Tamas Noszko, Vincent Steffan, Jens Niklas Eberhardt, Joschka Roffe, Jens Eisert, Stergios Koutsioumpas
arXiv.
Pruning qLDPC codes: Towards bivariate bicycle codes with open boundary conditions
Jens Niklas Eberhardt, Francisco Revson F. Pereira, Vincent Steffan
arXiv.
Published and accepted
Logical Operators and Derived Automorphisms of Tile Codes
Nikolas P. Breuckmann, Shin Ho Choe, Jens Niklas Eberhardt, Francisco Revson Fernandes Pereira, Vincent Steffan
Communications in Mathematical Physics, 2026, accepted
arXiv.
Cups and Gates I: Cohomology invariants and logical quantum operations
Nikolas P. Breuckmann, Margarita Davydova, Jens Niklas Eberhardt, Nathanan Tantivasadakarn
Communications in Mathematical Physics 407 (2026), article 86
published version, 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. Contributed talk at QIP 2026
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.
Logical Operators and Fold-Transversal Gates of Bivariate Bicycle Codes
Jens Niklas Eberhardt, Vincent Steffan
IEEE Transactions on Information Theory, 2025. Contributed talk at QIP 2025
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. Plenary talk at QIP 2022
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.
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.
Talks, 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 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 for 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 my talk on K-motives and Koszul duality at the Geometric Representation Theory conference at the MPIM Bonn and the Perimeter Institute (June 2020).
Notes for a talk giving an overview of 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 \(\mathbb{F}_p\), constructed in joint work with Shane Kelly.
They were made for a talk at the Erwin Schrödinger Institute in Vienna (2017).
Slides motivating and stating some results from my PhD thesis.
They were made for the evaluation of our graduate school in June 2016 and were also partly used in talks in Regensburg (July 2016), Bonn (August 2016), Clermont-Ferrand (2017) and in my PhD defence.
Handwritten notes, thanks to Konrad Völkel, from a joint talk with Florian Beck explaining the relation between Verdier duality, Borel–Moore homology and cosheaves.
Slides describing my master's thesis, which developed a new algorithm for computing the Tutte polynomial of a matroid.
