Jens Niklas Eberhardt

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 quantum-mechanical systems 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.

Preprints

Cups and Gates I: Cohomology invariants and logical quantum operations,
Nikolas P. Breuckmann, Margarita Davydova, Jens Niklas Eberhardt, Nathanan Tantivasadakarn,
arxiv.

Universal Koszul Duality for Kac-Moody Groups,
Jens Niklas Eberhardt, Arnaud Eteve,
arxiv.

Two proofs of a Jantzen Conjecture for Whittaker Modules,
Jens Niklas Eberhardt, Anna Romanov,
arxiv.

An Intersection Matrix for Affine Hyperplane Arrangements,
Jens Niklas Eberhardt, Carl Mautner,
arxiv.

Logical Operators and Fold-Transversal Gates of Bivariate Bicycle Codes,
Jens Niklas Eberhardt, Vincent Steffan,
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 $\smash{\scriptstyle{\mathcal{O}}}$,
Jens Niklas Eberhardt,
arxiv.

Published

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.

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 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.

In 2019, I was awarded the Distinguished Teaching Award of the UCLA math department.

My hardworking students!

Current

Past