E-mail: clemens@koppensteiner.site

My main area of work is broadly within algebraic geometry, taking inspiration from representation theory. As such, my work takes ideas and insights that arise in (geometric) representation theory and puts them into a wider geometric context. Conversely this wider context can than be used to increase our understanding of representation theoretic questions.

My main focus is on different types of derived categories of sheaves. These are gadgets associated to a geometric or topological space which can be viewed as a kind of linearization. Thus they are often more tractable to algebraic study, while still retaining information about the underlying space. Simultaneously, such categories can be used to encode questions from other fields of mathematics, most notably representation theory. This allows for the use of geometric methods in the study of such questions.

The concrete topics I am working on include t-structures on categories of coherent sheaves, categorical algebra actions, D-modules in logarithmic geometry and Riemann–Hilbert correspondences, and Hochschild cohomology and support theory for D-modules on stacks.

*The Heisenberg category of a category*, with Ádám Gyenge and Timothy Logvinenko

Preprint [arXiv]*Traces, Schubert calculus, and Hochschild cohomology of category O*

Preprint [arXiv]*Exotic t-structures and actions of quantum affine algebras*, with Sabin Cautis.

Journal of the European Mathematical Society 22, 10 (2020) [DOI] [arXiv]*The de Rham functor for logarithmic D-modules.*

Selecta Mathematica 26, 49 (2020). [DOI] [arXiv]*Graded topological spaces.*

Proceedings of the American Mathematical Society 148 (2020). [DOI] [arXiv]*Holonomic and perverse logarithmic D-modules*, with Mattia Talpo.

Advances in Mathematics 346 (2019). [DOI] [arXiv]*Hochschild cohomology of torus-equivariant D-modules.*

International Mathematics Research Notices 2020, 19 (2018). [Advance Access] [DOI] [arXiv]*Exact functors on perverse coherent sheaves.*

Compositio Mathematica 151 (2015), no. 9. [DOI] [arXiv]

*Logarithmic Riemann-Hilbert correspondences*, Institute for Advanced Study, September 2018 [PDF] [video]*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]

- Algebraic D-modules (Oxford, 2020)
- Derived categories of coherent sheaves (Oxford, 2019)
- Algebraic Geometry I (UBC, 2016)