# 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 representation categories of Lie algebras, finite-dimensional algebras, or dg algebras. I'm also trying to apply ideas from silting theory to Nichols algebras.

## Publications and Preprints

*Orthogonality between weight and t-structures: 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 study orthogonality of weight structures and t-structures in terms of silting collections and simple-minded collections, and formulate this relation using derived projective covers. 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

## News

Bonn mathematics performs excellently again in QS ranking

Stefan Schwede is invited speaker at the ECM 2024 in Sevilla

Jessica Fintzen wins Cole Prize

Regula Krapf receives university teaching award

Catharina Stroppel joined the North Rhine-Westphalia Academy for Sciences and Arts

Daniel Huybrechts receives the Compositio Prize for the periode 2017-2019

Catharina Stroppel receives Gottfried Wilhelm Leibniz Prize 2023

Grants for Mathematics students from Ukraine

Jessica Fintzen is awarded a Whitehead Prize of the London Mathematical Society

Peter Scholze elected as Foreign Member of the Royal Society