Lukas Bonfert

I'm a PhD student of Catharina Stroppel, funded by the Max Planck Institute for Mathematics.


Email: bonfert[symbol in every email address]

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

  1. Orthogonality between weight and t-structures: simple-minded and silting collections. Preprint, submitted. arXiv:2309.00554
  2. 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.

  3. 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
  4. 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.