# Clemens Koppensteiner

I am a Member of the Institute for Advanced Study's School of Mathematics.
Before then, I was a Postdoctoral Research Fellow at the University of British Columbia's Department of Mathematics.
E-mail: clemens@ias.edu

Office: A-104

CV

## Teaching

Previous terms.

## Research

I am interested in algebraic geometry and geometric representation theory, focusing on new approaches to understanding
categories of coherent sheaves and D-modules. In particular, my current projects include:

- giving new characterizations of perverse coherent and exotic sheaves, with regards to their microlocal nature and interactions with geometric Lie algebra actions;
- exploiting the new characterizations to generalize these theories;
- computations of Hochschild cohomology of categories of D-modules;
- understanding cohomological support of D-modules on stacks of representation theoretic interest;
- D-modules in log geometry and their application to representation theory.

### Publications & Preprints

*Holonomic and perverse logarithmic D-modules*, with Mattia Talpo [arXiv]
*Exotic t-structures and actions of quantum affine algebras*, with Sabin Cautis [arXiv]
*Hochschild cohomology of torus-equivariant D-modules.* [arXiv]
*Exact functors on perverse coherent sheaves.* Compositio Mathematica 151 (2015), no. 9 [DOI] [arXiv]

My thesis, *Some microlocal aspects of perverse coherent sheaves and equivariant D-modules*.
### Downloadable presentations

*Exotic sheaves and actions of quantum affine algebras*, Hausdorff Institute for Mathematics, November 2017 [Poster PDF] [Talk PDF]
*Categorical actions in geometry and representation theory*, Institute for Advanced Study, September 2017 [PDF]
*Exotic sheaves and actions of quantum affine algebras*, Poster at Interactions between Representation Theory and Algebraic Geometry, Chicago, August 2017 [PDF]