Jens Niklas Eberhardt

I am a postdoc at the UCLA Department of Mathematics with 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:

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

Mixed Motives and Geometric Representation Theory in Equal Characteristic, Jens Niklas Eberhardt and Shane Kelly, arXiv Preprint, 2016 (PDF)

Graded and geometric parabolic induction, Jens Niklas Eberhardt, PhD Thesis, 2016 (PDF)

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. (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

Fall 17 (UCLA) Math 31A: Differential and Integral Calculus
Fall 17 (UCLA) Math 115A: Linear Algebra

Past

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