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

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.

- The Jordan property for local fundamental groups (with S. Filipazzi, J. Moraga, and R. Svaldi), preprint
- The local fundamental group of a Kawamata log terminal singularity is finite, preprint
- Gorensteinness and iteration of Cox rings for Fano type varieties, preprint
- Invariant rings of sums of fundamental representations of SLn and colored hypergraphs, preprint
- Completing the classification of representations of SLn with complete intersection invariant ring,
*Transformation Groups*, to appear. - 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 SL
_{4}(C) and incidence geometry of P_{3}(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, 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