Fachbereich Mathematik

Lukas Braun

I moved to the University of Freiburg. This website is not updated any more. You can find my new website here.

Research interests

Group actions on algebraic varieties, Invariant theory,

Singularities, Singular Calabi-Yau and Fano type varieties,

Mori Dream Spaces and Cox Rings.

Publications and preprints

  1. Gorensteinness and iteration of Cox rings for Fano type varieties, preprint
  2. Completing the classification of representations of SLn with complete intersection invariant ring, preprint
  3. Invariant rings of sums of fundamental representations of SLn and colored hypergraphs, preprint
  4. Canonical threefold singularities with a torus action of complexity one and k-empty polytopes (with D. Hättig), Rocky Mountain Journal of Mathematics, to appear.
  5. Hilbert series of the Grassmannian and k-Narayana numbers, Communications in Mathematics 27 (2019), no. 1, 27-41.
  6. Covariants of SL4(C) and incidence geometry of P3(C), J. Phys.: Conf. Ser. 1194 (2019), 012015.
  7. 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.

Talks

  1. 06/2019: "Gorensteinness and iteration of Cox rings" at the Basel-Dijon-EPFL joint conference, Universität Basel
  2. 05/2019: "Gorensteinness and iteration of Cox rings" at the Oberseminar Algebra, Zahlentheorie und algebraische Geometrie, Universität Freiburg
  3. 05/2019: "Gorensteinness and iteration of Cox rings" at the Oberseminar Zahlentheorie und Arithmetische Geometrie, Leibniz Universität Hannover
  4. 08/2018: "Invariants of fundamental representations of SLn and colored hypergraphs" , Short Communication at the ICM 2018 in Rio de Janeiro
  5. 07/2018: "Invariants of fundamental representations of SLn and colored hypergraphs" at the GROUP32 Conference at Technical University of Prague
  6. 04/2018: "Can the Big Bang be embedded somewhere and is it a quotient?" at the Doctoral club seminar series, Forum Scientiarum, Universität Tübingen
  7. 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