# Jens Niklas Eberhardt

 Currently, I work at the University of Wuppertal funded by my research grant of the German Research Foundation (DFG). Previously, I was a postdoc at the University of Bonn and Max Planck Institute for Mathematics in the workgroup of Catharina Stroppel. Before that, I was an Assistant Adjunct Professor at the UCLA Department of Mathematics in the work group of Raphaël Rouquier. My PhD advisor was Wolfgang Soergel at Mathematisches Institut der Albert-Ludwigs-Universität 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 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.

## Publications

#### Preprints

K-theory Soergel Bimodules,
Jens Niklas Eberhardt,
arxiv.

Graded and Geometric Parabolic Induction for Category $\smash{\scriptstyle{\mathcal{O}}}$,
Jens Niklas Eberhardt,
arxiv.

#### Published/Accepted

Integral Motivic Sheaves And Geometric Representation Theory,
Jens Niklas Eberhardt, Jakob Scholbach,
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) 25: 30,
published version, arxiv.

Computing the Tutte Polynomial of a Matroid from its Lattice of Cyclic Flats,
Jens Niklas Eberhardt,
The Electronic Journal of Combinatorics, Volume 21, Issue 3, 2014,
published version, arxiv.

#### Other Publications

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

Jens Niklas Eberhardt,
PhD Thesis, 2017
PDF

## Slides and Notes

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!

### Past

 Summer 21 (Bonn) S4A2 - Graduate Seminar - Geometric Representation Theory of Weyl Groups Winter 20/21 (Bonn) S4A2 - Graduate Seminar on Real Reductive Groups and D-Modules Winter 19/20 (Bonn) Seminar on Advanced Algebra: Quiver Algebras Spring 19 (UCLA) Math 131A: Real Analysis Winter 19 (UCLA) Math 31A: Differential and Integral Calculus Winter 19 (UCLA) Math 115AH: Linear Algebra Honors Fall 18 (UCLA) Math 31B: Integration and Infinite Series Fall 18 (UCLA) Math 115AH: Linear Algebra Honors Spring 18 (UCLA) Math 31A: Differential and Integral Calculus Spring 18 (UCLA) Math 115A: Linear Algebra Winter 17 (UCLA) Math 61: Introduction to Discrete Structures Fall 17 (UCLA) Math 31A: Differential and Integral Calculus Fall 17 (UCLA) Math 115A: Linear Algebra Winter 16/17 (Freiburg) GRK Seminar on "$\smash{\operatorname{SL}_2}$" Summer 15 (Freiburg) GRK Seminar on "Sheaf cohomology"

## Contact

email: mail at jenseberhardt.com

University of Wuppertal
Gaußstr. 20
Wuppertal
Germany