Research Interests
 Derived algebraic geometry
 Logarithmic geometry
 Cluster algebras and their categorifications
 Representation theory of finitedimensional algebras
 Quiver Varieties
Working group
Postdocs: David Fernandez and Nina Morishige.
Phd student: Thilo Baumann joint with Pieter Belmans
Publications and preprints
 CalabiYau structures on (quasi)bisymplectic algebras
This is joint with Tristan Bozec and Damien Calaque.
 CalabiYau structures for multiplicative preprojective algebras
J. Noncommut. Geom. This is joint with Tristan Bozec and Damien Calaque.
 Derived Parabolic induction
Bulletin of the London Mathematical Society, Volume 54, Issue 1 (2022), 264274. This is joint with Peter Schneider.
 Relative critical loci and quiver moduli
To appear in Annales de l'ENS. This is joint with Tristan Bozec and Damien Calaque.
 The categorified GrothendieckRiemannRoch theorem
Compositio Mathematica, Volume 157, Issue 1 (2021) 154214. This is joint with Marc Hoyois, Pavel Safronov and Nicolo Sibilla.
 On the profinite homotopy type of log schemes
with David Carchedi, Nicolo Sibilla and Mattia Talpo
 Gluing semiorthogonal decompositions
Journal of Algebra 559 (2020) 132. This is joint with Nicolo Sibilla and Mattia Talpo.
 Parabolic semiorthogonal decompositions and Kummer flat invariants of log schemes
Doc. Math. 25, 9551009 (2020). This is joint with Nicolo Sibilla and Mattia Talpo.
 On a logarithmic version of the derived McKay correspondence
Compositio Mathematica, 154(12), 25342585. This is joint with Nicolo Sibilla and Mattia Talpo.
 Higher traces, noncommutative motives, and the categorified Chern character
Advances in Mathematics
309 (2017), 97154. This is joint with Marc Hoyois and Nicolo Sibilla.
 KatoNakayama spaces, infinite root stacks, and the profinite homotopy type of log schemes
Geometry and Topology 21 (2017) 30933158. This is joint with David Carchedi, Nicolo Sibilla and Mattia Talpo.
 Quiver varieties and Hall algebras
London Math. Soc. (2016) 112 (6), 10021018. This is joint with Nicolo Sibilla.
 Derived loop stacks and categorification of orbifold products
J. Noncommut. Geom. 13 (2019), 963–983.
This is joint with Nicolo Sibilla.
 Desingularisation of quiver Grassmannians via Nakajima categories
Algebras and Representation Theory 20, 231243(2017)
 Component Cluster for acyclic quiver
Colloquium Mathematicum 144 (2016), 245264.
 Generalized quiver varieties and triangulated categories
Mathematische Zeitschriften (2019), Vol.292,14531478
 The nonequivariant coherentconstructible correspondence and tilting
Selecta Mathematica (NS) (2016), Vol.22, Issue 1,38416. This is joint with Nicolo Sibilla.
 Desingularizations of quiver Grassmannians via graded quiver varieties
Advances in Mathematics 256 (2014) 318347. This is joint with Bernhard Keller.
 Graded quiver varieties and derived categories
J. reine angew. Math.(Crelles Journal) 2016 (713). This is joint with Bernhard Keller.
 Linear recurrence relations for cluster variables of affine quivers
Advances in Mathematics 228 (2011) 18421862.
This is joint with Bernhard Keller.
 The integral Cluster Category
Int Math Res Notices Vol. 2012, No.12, 28672887.
This is joint with Bernhard Keller.
 Rank Varieties for Hopf Algebras
Journal of Pure Applied Algebra 215 (2011), no.5, 829 to 838.
This is joint with Matthew Towers.
 Finite and bounded AuslanderReiten Components in the Derived Category
Journal of Pure Applied Algebra 215 (2011), no.3, 232241.
 Euclidean components for a class of selfinjective algebras
Colloquium Mathematicum 115 (2009), no. 2, 219 to 245.
 Classification of pointed rank one Hopf algebras
Journal of Algebra 319 (2008) 2889 to 2912.
 Formulas for primitive Idempotents in Frobenius Algebras and an Application to Decomposition maps
Representation Theory 12 (2008), 170 to 185.
This is joint with Max Neunhöffer.
 Euclidean AuslanderReiten components in the bounded derived Category
