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

I am currently a Walter-Benjamin-fellow at the University of Freiburg with my project 'Fundamentalgruppe und Divisorenklassengruppe: Endlichkeit und Zusammenspiel' funded by the DFG.

Before that, I was a postdoc at the University of Freiburg in the Arithmetic Geometry group of Prof. Annette Huber-Klawitter.

Even before that, 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.

I am interested in complex algebraic varieties with klt singularities. In particular, I am working on Mori Dream Spaces and Cox rings, questions surrounding the Minimal Model Program, varieties with group actions, and also on Invariant Theory.

You can find a copy of my CV here.
Also have a look at my private homepage!

Research

Preprints

Reductive quotients of klt singularities, with D. Greb, K. Langlois, J. Moraga.
Iteration of Cox rings of klt singularities, with J. Moraga; submitted.

Publications / accepted for publication

The Jordan property for local fundamental groups, with S. Filipazzi, J. Moraga, and R. Svaldi; Geometry and Topology 26 (2022), no. 1, 283-319.
Gorensteinness and iteration of Cox rings for Fano type varieties; Mathematische Zeitschrift 301 (2022), 1047–1061.
The local fundamental group of a Kawamata log terminal singularity is finite; Inventiones Mathematicae 226 (2021), no. 3, 845–896.
Invariant rings of sums of fundamental representations of SLn and colored hypergraphs, Advances in Mathematics 389 (2021), 107929; 34 pp.
Completing the classification of representations of SLn with complete intersection invariant ring, Transformation Groups 26 (2021), no. 1, 115-144.
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.

Upcoming Talks

08/2022: "TBA" at the Simons conference "Stability and Moduli", Simons Centre at Stony Brook

Past Talks

06/2022: "Reductive quotients of klt varieties" at the Oberseminar Algebraische Geometrie, Universität des Saarlandes
06/2022: "Reductive quotients of klt varieties" at the Birational Geometry Conference, EPFL Lausanne
06/2022: "Reductive quotients of klt varieties" at Universität Bayreuth
05/2022: "Reductive quotients of klt varieties" at the seminar Algèbre et Géométries at Institut Fourier/Université Grenoble-Alpes
03/2022: "Finiteness of local fundamental groups" at the MMP Learning Seminar, Princeton University
02/2022: "Kähler metrics, orbifold structures, and fundamental groups on resolutions of klt spaces" at the Conference on Subvarieties and Foliations of Complex Projective Varieties, Osaka City University.
06/2021: "Local Cox rings for klt singularities" at Politecnico/Università degli studi di Milano
06/2021: "Local Cox rings for klt singularities" at the Oberseminar Algebra, Zahlentheorie und algebraische Geometrie, Universität Freiburg
06/2021: "Local Cox rings for klt singularities" at the Oberseminar Algebraische Geometrie und Arithmetik, Universität Duisburg-Essen
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