Dr. Lukas Braun

Contact information

Office: Ernst-Zermelo-Str. 1, 79104 Freiburg i. Br., Room 433

Office hours: Di, 8-10

E-Mail: lukas.braun@math.uni-freiburg.de

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.

Preprints

Iteration of Cox rings of klt singularities, with J. Moraga; submitted.
The local fundamental group of a Kawamata log terminal singularity is finite, submitted.
Gorensteinness and iteration of Cox rings for Fano type varieties, submitted.
Invariant rings of sums of fundamental representations of SLn and colored hypergraphs, submitted.

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.

Other writings

Finiteness and klt singularities, Oberwolfach Report 24/2020, Komplexe Analysis - Algebraicity and Transcendence (2020), 18-23.

Talks

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, EPFL Lausanne
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