Jun. Prof. Simon Brandhorst

Email: lastname [at] math.uni-sb.de
 
Phone: +49-681-302-2480
 
Address: Mathematik und Informatik
Gebäude E.2.4 - Raum: 222
Universität des Saarlandes
66123 Saarbrücken (Germany)
Office hour: By appointment.
 
Research interests:
  • algebraic surfaces, especially K3 and Enriques surfaces
  • irreducible holomorphic symplectic varieties
  • automorphisms and dynamics of surfaces
  • quadratic and hermitian forms and their applications to algebraic geometry
  • computer algebra
Preprints
  • Simon Brandhorst, Matthias Zach, An explicit Enriques surface with an automorphism of minimum entropy, arXiv.
  • Simon Brandhorst, Víctor González-Alonso, 527 elliptic fibrations on Enriques surfaces, arXiv.
  • Simon Brandhorst, Grégoire Menet, Stevell Muller, Automorphisms of Nikulin-type orbifolds, arXiv.

Publications

  1. Simon Brandhorst, Matthias Zach, Elliptic Fibrations on Vinberg's Most Algebraic K3 Surface, in The Computer Algebra System OSCAR: Algorithms and Examples, 
    Algorithms and Computation in Mathematics, Springer, Decker, Eder, Fieker, Horn, Joswig, eds., (2025). arXiv.
  2. Simon Brandhorst, Serkan Sonel, Davide Cesare Veniani. Idoneal genera and the classification of K3 surfaces covering an Enriques surface, J. Pure and Applied Algebra Vol. 229 No. 6 (2025), arXiv.
  3. Simon Brandhorst, Giacomo Mezzedimi, Borcherds lattices and K3 surfaces of zero entropy, American J. of Math., to appear, arXiv.
  4. Simon Brandhorst, Davide Cesare Veniani. Hensel lifting algorithms for quadratic forms, Math. Comp. 93 (2024), 1963-1991, arXiv.
  5. Simon Brandhorst, Tommy Hofmann. Finite subgroups of automorphisms of K3 surfaces. Forum of Math., Sigma, 11, E54 (2023).  arxiv.
  6. Simon Brandhorst, Alberto Cattaneo. Prime order isometries of unimodular lattices and automorphisms of IHS manifolds, IMRN Vol. 2023, Issue 18, pp. 15584–15638 (2022), arXiv.
  7. Simon Brandhorst, Tommy Hofmann, Appendix by Sven Manthe, Generation of local unitary groups, J. Algebra Vol. 609 (2022), pp. 484-513, arXiv.
  8. Simon Brandhorst, Noam D. Elkies, Equations for a K3 Lehmer map, Journal of Algebraic Geometry 32 (2023), 641-675 ,  arXiv.
  9. Simon Brandhorst, Sławomir Rams, Ichiro Shimada. On characteristic polynomials of automorphisms of Enriques surfaces, PRIMS Vol 59, no 3 (2023) , arXiv.
  10. Simon Brandhorst, Ichiro Shimada, Automorphism groups of certain Enriques surfaces, Found. Comput. Math. 22, pp. 1463–1512 (2022), arXiv.
  11. Simon Brandhorst, Kenji Hashimoto. Extensions of maximal symplectic actions on K3 surfaces, Ann. H. Lebesgue, Vol. 4 (2021) , pp. 785-809.,  arXiv.
  12. Simon Brandhorst, Ichiro Shimada. Borcherds' method for Enriques surfaces, Michigan Math. J. 71(1): 3-18 (March 2022), arXiv. 
  13. Simon Brandhorst. On the stable dynamical spectrum of complex surfaces, Math. Ann. 377, 421-434 (2020), arXiv.
  14. Simon Brandhorst. The classification of purely non-symplectic automorphisms of high order on K3 surfaces. J. Algebra, 533:229--265, 2019, arXiv.
  15. Simon Brandhorst, Víctor González-Alonso. Automorphisms of minimal entropy on supersingular K3 surfaces, London Math. Soc., 97: 282-305 (2018), arXiv.
  16. Simon Brandhorst. Automorphisms of Salem degree 22 on supersingular K3 surfaces of higher Artin invariant, Math. Res. Let. Vol 25 (2018) No 4, pp. 1143-1150, arXiv.
  17. Simon Brandhorst. Dynamics on supersingular K3 surfaces and automorphisms of Salem degree 22, Nagoya Math. J. Vol 227 (2017), pp. 1-15 , arXiv.
  18. Simon Brandhorst, Marcel Erné. Tychonoff-like product theorems for local topological properties, Topology Proc. 45 (2015), 121-138, arXiv.

Papers in a Research Magazine

1. Simon Brandhorst, Anne Frübis-Krüger, Matthias Zach. Schemes in OSCAR, Computeralgebra Rundbrief  No. 73 (2023)