Lukas Bonfert
I'm a PhD student of Catharina Stroppel, funded by the Max Planck Institute for Mathematics.
Contact
Email: bonfert[symbol in every email address]mpim-bonn.mpg.de
Research Interests
I am interested in representation theory, particularly that of Lie (super)algebras and related topics such as perverse sheaves or Koszul duality. My PhD project is (mostly) about silting theory, which means that I study the relation between weight structures (aka co-$t$-structures) and $t$-structures on triangulated categories such as derived categories of finite-dimensional algebras or dg algebras. I'm also thinking about perverse $t$-structures on flag varieties, which have deep connections to the representation theory of Lie algebras. Furthermore, I spent some time thinking about combinatorial ways to understand the structure of Lie superalgebras.
Publications and Preprints
- Serre functor and $\mathbb{P}$-objects for perverse sheaves on $\mathbb{P}^n$ (joint with Alessio Cipriani). Preprint. arXiv:2506.06051
- Derived projective covers and Koszul duality of simple-minded and silting collections. Preprint, submitted. arXiv:2309.00554
- The Weyl Groupoids of $\mathfrak{sl}(m|n)$ and $\mathfrak{osp}(r|2n)$ (joint with Jonas Nehme). Journal of Algebra 641 (2024), pp. 795–822. arXiv:2305.04751
Abstract
We show that the inverse Serre functor for the constructible derived category $\mathbf{D}^\mathrm{b}_\mathrm{c}(\mathbb{P}^n)$ is given by the $\mathbb{P}$-twist at the simple perverse sheaf corresponding to the open stratum. Moreover, we show that all indecomposable perverse sheaves on $\mathbb{P}^n$ are $\mathbb{P}$-like objects, and explicitly construct morphisms spanning their total endomorphism spaces.
Abstract
We introduce derived projective covers and explain how they are related to the notion of enough derived projectives. This provides an if-and-only if criterion for when derived projective covers form a silting collection. We prove moreover a Koszul duality result for silting and simple-minded collections.
Abstract
We provide a convenient formulation of the definition of Cartan graphs and Weyl groupoids introduced by Heckenberger and Schneider, and construct Cartan graphs for regular symmetrizable contragredient Lie superalgebras. For $\mathfrak{sl}(m|n)$, $\mathfrak{osp}(2m+1|2n)$ and $\mathfrak{osp}(2m|2n)$ we explicitly describe the Cartan graph in terms of partitions and determine the relations between the generators of their Weyl groupoids.
Teaching
Previous- Tutor for Foundations of Representation Theory, lecture course by Prof. Schröer, summer term 2023
- Tutor for Representation Theory II: Representation Theory, Geometry and Combinatorics, lecture course by Prof. Stroppel, winter term 2022/23
- Tutor for Algebra I, lecture course by Prof. Blomer, summer term 2022
- Tutor for Einführung in die Algebra, lecture course by Prof. Blomer, winter term 2021/22
- Tutor for Representation Theory II: Auslander–Reiten Theory, lecture course by Prof. Schröer, summer term 2021
- Tutor for Advanced Algebra I: Lie Algebras and their Representations, lecture course by Dr. Heidersdorf, winter term 2020/21
- Tutor for Algebra II: Modular Forms, lecture course by Prof. Blomer, winter term 2019/20
- Tutor for Einführung in die komplexe Analysis, lecture course by Prof. Bödigheimer, summer term 2019
- Tutor for Lineare Algebra I, lecture course by Prof. Huybrechts, winter term 2018/19
- Tutor for Analysis II, lecture course by Prof. Koch, summer term 2018
- Tutor for the Programmierkurs C++, preparatory course by Dr. Brenner, 09/2018
- Tutor for the Programmierkurs C, preparatory course by Johannes Holke and Clelia Albrecht, 09/2017
Aktuelles
Das Mathematische Institut trauert um Günter Harder
Floris van Doorn und Koautoren erhalten den Skolem Award
Förderung des Hausdorff Centers for Mathematics für weitere 7 Jahre verlängert
Markus Hausmann erhält die Minkowski-Medaille der Deutschen Mathematiker-Vereinigung
Rajula Srivastava erhält den Maryam Mirzakhani New Frontiers Prize
Dennis Gaitsgory erhält den Breakthrough Prize in Mathematics 2025
Daniel Huybrechts zum Mitglied der Leopoldina gewählt
Catharina Stroppel erhält Ehrendoktorwürde der Universität Uppsala
Angkana Rüland erhält Gottfried Wilhelm Leibniz-Preis 2025
Wolfgang Lück erhält den von Staudt-Preis
Gerd Faltings in den Orden pour le mérite aufgenommen
Geordie Williamson erhält den Max-Planck-Humboldt Forschungspreis 2024