Jens Niklas Eberhardt

I am a second year PhD student in mathematics. My advisor is Prof. Dr. Wolfgang Soergel and I am a member of the Graduiertenkolleg "Cohomological Methods in Geometry" at the Albert-Ludwigs-University Freiburg. The advisor for my master thesis was Prof. Dr. Wilhelm Plesken at RWTH Aachen.

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

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

Graded parabolic induction and stratified mixed Tate motives , Jens Niklas Eberhardt, arXiv Preprint, 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 and poster motivating and stating some of the results of my PhD thesis in an informal fashion. They were made for the investigation of our Graduiertenkolleg in June 2016 and also partly used in talks I gave in Regensburg (July 2016) and Bonn (August 2016).

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

Winter 2016/17 (Freiburg)	GRK Seminar on "$\operatorname{SL}_2$"
Summer 2015 (Freiburg)	GRK Seminar on "Sheaf cohomology"

Contact

Mathematisches Institut
Albert-Ludwigs-Universität Freiburg
Eckerstraße 1
D-79104 Freiburg

firstname.lastname@math.uni-freiburg.de