Dr. Lukas Braun
Office: Ernst-Zermelo-Str. 1, 79104 Freiburg i. Br., Room 433
Office hours: Di, 8-10
Phone: 0761 / 203 5550
About me and my research
I am currently working at the University of Freiburg in the Arithmetic Geometry group of Prof. Annette Huber-Klawitter. On November 08th, 2019, I defended my PhD thesis entitled "Quotient presentations of Mori Dream Spaces" with summa cum laude under the supervision of Prof. Jürgen Hausen.
At the moment, I am interested in the Chow and homotopy groups of complex algebraic varieties with klt singularities. Just recently, I proved that the local fundamental group of a klt singularity is finite. Apart from that, I am working on Mori Dream Spaces, questions surrounding the Minimal Model Program, varieties with group actions, and Invariant Theory.
Publications / accepted for publication
- The Jordan property for local fundamental groups, with S. Filipazzi, J. Moraga, and R. Svaldi; accepted for publication in Geometry and Topology.
- Completing the classification of representations of SLn with complete intersection invariant ring, Transformation Groups (2020). https://doi.org/10.1007/s00031-020-09605-0.
- Canonical threefold singularities with a torus action of complexity one and k-empty polytopes, with D. Hättig; Rocky Mountain Journal of Mathematics 50 (2020), no. 3, 881-939.
- Hilbert series of the Grassmannian and k-Narayana numbers, Communications in Mathematics 27 (2019), no. 1, 27-41.
- Covariants of SL4(C) and incidence geometry of P3(C), J. Phys.: Conf. Ser. 1194 (2019), 012015.
- Log terminal singularities, platonic tuples and iteration of Cox rings, with I. Arzhantsev, J. Hausen, and M. Wrobel; European Journal of Mathematics 4 (2018), no. 1, 242-312.
- 08/2020: "Finiteness and klt singularities" at the Oberwolfach Workshop "Komplexe Analysis - Algebraicity and Transcendence"
- 06/2020: "Some finiteness results on klt singularities in
characteristic zero" at the Groups, Arithmetic & Algebraic Geometry Seminar,
- 04/2020: "Fundamental groups of smooth loci of klt spaces" at the Yale Algebraic Geometry online seminar
- 06/2019: "Gorensteinness and iteration of Cox rings" at the Basel-Dijon-EPFL joint conference, Universität Basel
- 05/2019: "Gorensteinness and iteration of Cox rings" at the Oberseminar Algebra, Zahlentheorie und algebraische Geometrie, Universität Freiburg
- 05/2019: "Gorensteinness and iteration of Cox rings" at the Oberseminar Zahlentheorie und Arithmetische Geometrie, Leibniz Universität Hannover
- 08/2018: "Invariants of fundamental representations of SLn and colored hypergraphs" , Short Communication at the ICM 2018 in Rio de Janeiro
- 07/2018: "Invariants of fundamental representations of SLn and colored hypergraphs" at the GROUP32 Conference at Technical University of Prague
- 04/2018: "Can the Big Bang be embedded somewhere and is it a quotient?" at the Doctoral club seminar series, Forum Scientiarum, Universität Tübingen
- 08/2017: "Classification of compound du Val and canonical threefold singularities with torus action of complexity one" at the workshop Experimental Classification of Fano varieties, Universität Tübingen