# Jens Niklas Eberhardt

 I am a post-doctoral fellow in Bonn at the Max Planck Institute for Mathematics Bonn in the workgroup of Catharina Stroppel. Previously, 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

Balanced Product Quantum codes,
Jens Niklas Eberhardt, Nikolas P. Breuckmann
arxiv.

Algebraic K-theory and Grothendieck-Witt theory of monoid schemes,
Jens Niklas Eberhardt, Oliver Lorscheid, Matthew B. Young,
arxiv.

Group completion in the K-theory and Grothendieck-Witt theory of proto-exact categories,
Jens Niklas Eberhardt, Oliver Lorscheid, Matthew B. Young,
arxiv.

K-motives and Koszul Duality,
Jens Niklas Eberhardt,
arxiv.

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

#### Accepted

Springer Motives,
Jens Niklas Eberhardt,
Proceedings of the American Mathematical Society, 2020,
arxiv.

#### Published

Real Springer fibers and odd arc algebras,
Jens Niklas Eberhardt, Grégoire Naisse, Arik Wilbert,
Journal of the London Mathematical Society, 2020,
published version, 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.

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.

#### Theses

Jens Niklas Eberhardt,
PhD Thesis, 2017
PDF

## Slides and Notes

Slides which outline a new K-theoretic perspective on Koszul duality and giving a potential definition for K-theoretic intersection cohomology complexes. They were used for a talk 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!

### Current

 Winter 20/21 (Bonn) S4A2 - Graduate Seminar on Real Reductive Groups and D-Modules

### Past

 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

Max Planck Institute for Mathematics
Vivatsgasse 7
53111 Bonn
Germany