# Jens Niklas Eberhardt

 I am 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.

## Research

My research area is geometric representation theory, where I am particulary interested in:

• semisimple algebraic groups and Lie algebras,
• Soergel modules and Koszul duality,
• categories of sheaves and motives,
• 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

#### Submitted

Springer Motives, Jens Niklas Eberhardt, submitted, (PDF).

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

#### Published

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

Graded and Geometric Parabolic Induction, Jens Niklas Eberhardt, PhD Thesis, 2016 PDF

### Slides, Notes and Posters

Slides motivating and sketching a category of mixed sheaves with coefficients in $\mathbb{F}_p$ 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

### Current

 Spring 19 (UCLA) Math 131A: Real Analysis

### Past

 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 "$\operatorname{SL}_2$" Summer 15 (Freiburg) GRK Seminar on "Sheaf cohomology"

## Contact

email: firstname@math.ucla.edu

Math Sciences Building, Room 6304
520 Portola Plaza
Los Angeles, CA 90095

Office hours: TBA