RESEARCH INTERESTS
My research is in noncommutative algebraic geometry and related topics in deformation theory, homological algebra and representation theory. More specifically, I like to think about Hochschild-type invariants for enhanced triangulated categories, and am also particularly interested in smoothness and properness for such categories, in relation to the existence of geometric realizations. As a byproduct, I also study Fourier-Mukai transforms and their deformations (often associated to moduli spaces of some kind, such as Hilbert schemes), and am doing a lot of explicit computations involving noncommutative motives, Koszul duality and representations of finite dimensional algebras.
PUBLICATIONS & PREPRINTS
My research is in noncommutative algebraic geometry and related topics in deformation theory, homological algebra and representation theory. More specifically, I like to think about Hochschild-type invariants for enhanced triangulated categories, and am also particularly interested in smoothness and properness for such categories, in relation to the existence of geometric realizations. As a byproduct, I also study Fourier-Mukai transforms and their deformations (often associated to moduli spaces of some kind, such as Hilbert schemes), and am doing a lot of explicit computations involving noncommutative motives, Koszul duality and representations of finite dimensional algebras.
PUBLICATIONS & PREPRINTS
- Derived categories of flips and cubic hypersurfaces
with Pieter Belmans and Lie Fu
arXiv - Proper connective differential graded algebras and their geometric realizations
with Greg Stevenson
arXiv - New examples of non-Fourier-Mukai functors
with Alice Rizzardo and Michel Van den Bergh
arXiv - Hochschild cohomology and deformations of \(\mathbb{P}\)-functors
with Ciaran Meachan
arXiv - On solvability of the first Hochschild cohomology of a finite-dimensional algebra
with Florian Eisele
to appear in Transactions of the American Mathematical Society (2019)
arXiv - The Frobenius morphism in invariant theory II
with Špela Špenko and Michel Van den Bergh
arXiv - Hilbert squares: derived categories and deformations
with Pieter Belmans and Lie Fu
Selecta Mathematica New Series 25, no. 3, 25:37 (2019)
Journal | arXiv - The Tannaka-Krein formalism and (re)presentations of universal quantum groups
with Michel Van den Bergh
Chapter in: Quantum Groups and Noncommutative Geometry , by Yuri I. Manin, Second Edition, CRM Short Courses, Springer (2018)
Book | arXiv
- The Frobenius morphism in invariant theory
with Špela Špenko and Michel Van den Bergh
Advances in Mathematics 348, 183-254 (2019)
Journal | arXiv
- Non-split Severi-Brauer varieties do not admit full exceptional collections
not intended for publication (2016)
arXiv - Derived categories of noncommutative quadrics and Hilbert squares
with Pieter Belmans
published online ahead of print in International Mathematics Research Notices (2018)
Journal | arXiv - A reduction theorem for tau-rigid modules
with Florian Eisele and Geoffrey Janssens
Mathematische Zeitschrift 290 (3-4), 1377-1413 (2018)
Journal | arXiv - The representation theory of noncommutative \(\mathcal{O}(\mathrm{GL}_2)\)
with Michel Van den Bergh
Journal of Noncommutative Geometry 11 (3), 845-886 (2017)
Journal | arXiv - The Manin Hopf algebra of a Koszul Artin-Schelter regular algebra is quasi-hereditary
with Michel Van den Bergh
Advances in Mathematics 305, 601-660 (2017)
Journal | arXiv - Embeddings of algebras in derived categories of surfaces
with Pieter Belmans
Proceedings of the American Mathematical Society 145 (7), 2757-2770 (2017)
Journal | arXiv
My arXiv profile is here and my Google Scholar profile is here.