PD Dr. Markus Kirschmer Address   Fakultät für Mathematik Universität Bielefeld Universitätsstraße 25 33501 Bielefeld Germany Office   Room UHG V5-121 Phone   +49 -(0)521 -106 -4790 Email

Current Teaching

Vorlesung Computeralgebra

Vorlesung Diskrete Mathematik

Publications

• (with C. Ling and A. Sadreddin) Cryptanalysis of Definite and Indefinite Lattice Isomorphism Problems with applications to DEFI,
  In: Heninger, N., Rosulek, M. (eds) Advances in Cryptology -- CRYPTO 2026. Lecture Notes in Computer Science, vol 16802. Springer, 295-326.   DOI Link   preprint
• (with S. Brandhorst) Appendix to Simon Brandhorst and Giacomo Mezzedimi, Virtually abelian symmetry groups of hyperbolic lattices,   arXiv
• (with Jürgen Klüners) Enumerating orders in number fields   arXiv
• (with Jürgen Klüners) Chow groups of one-dimensional noetherian domains, Research in Number Theory 10 (2024) no. 89.   DOI Link   arXiv
• Appendix to Klaus Hulek and Michael Lönne, Moduli of elliptic K3 surfaces: monodromy and Shimada root lattice strata, Algebraic Geometry 9 (2022) no. 2, 159--213.   DOI Link   arXiv
• (with Fabien Narbonne, Christophe Ritzenthaler and Damien Robert) Spanning the isogeny class of a power of an elliptic curve, Mathematics of Computation 91 (2022), 401--449.   DOI Link   arXiv
• (with Gabriele Nebe) Binary hermitian lattices over number fields, Exp. Math. 31 (2022) no. 1, 280--301.   DOI Link   preprint
• Determinant groups of hermitian lattices over local fields, Archiv der Mathematik, 113 (2019), no. 4, 337--347.   DOI Link   preprint
• Automorphisms of even unimodular lattices over number fields, Journal of Number Theory, 197 (2019), 121--134.   DOI Link   preprint
• (with Gabriele Nebe) Quaternary quadratic lattices over number fields, International Journal of Number Theory, 15 (2019), 309--325.   DOI Link   preprint
• One class genera of exceptional groups over number fields, J. Théorie Nombres Bordeaux, 30 (2018), no. 3, 847--857.   DOI Link  preprint
• (with Gabriele Nebe) One class genera of lattice chains over number fields. In Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory, eds. G. Böckle, W. Decker and G. Malle, Springer, 2018, 503--532. DOI Link   preprint
• (with Marion Rüther) The constructive membership problem for discrete two-generator subgroups of SL(2,R), J. Algebra 480 (2017), 519--548.   DOI Link   preprint
• (with David Lorch) Ternary quadratic forms over number fields with small class number, Journal of Number Theory 161 (2016), 343--361.   DOI Link   preprint
  A list of all quaternion orders of type or class number at most two is available here.
• One-class genera of maximal integral quadratic forms. Journal of Number Theory 136C (2014), 375--393. DOI Link   preprint
  A list of these genera is available here.
• (with Bettina Eick and Charles R. Leedham-Green) The constructive membership problem for discrete free subgroups of rank 2 of SL(2,R), LMS J. Comput. Math. 17 (2014), no. 1, 345--359.   DOI Link   preprint   Magma code
• (with Charles R. Leedham-Green) Computing with subgroups of the modular group, Glasgow Mathematical Journal 57 (2014), no. 1, 173--180.   DOI Link   preprint   Magma code
• (with David Lorch) Single-class genera of positive integral lattices, LMS J. Comput. Math. 16 (2013), 172--186.   DOI Link
• (with Michael H. Mertens) On an Analogue to the Lucas-Lehmer-Riesel test using Elliptic Curves, INTEGERS 13 (2013), A15. Link
• A normal form for definite quadratic forms over F_q[t]. Math. Comp. 81 (2012), 1619--1634.   DOI Link   preprint
• Finite symplectic matrix groups. Exp. Math. 20 (2011) no. 2, 217--228.   DOI Link
• (with John Voight) Algorithmic enumeration of ideal classes for quaternion orders. SIAM J. Comput. (SICOMP) 39 (2010), no. 5, 1714--1747.   DOI Link   corrected

Theses

• Definite quadratic and hermitian forms with small class number. Habilitationsschrift. RWTH Aachen University, 2016   pdf
  The lattices of class number one and two are available here
• Finite symplectic matrix groups. Dissertation. RWTH Aachen University, 2009   pdf
  The invariant forms given in the appendix are available here.
• Konstruktive Idealtheorie in Quaternionenalgebren. Diplomarbeit. Universität Ulm, 2005   pdf

Magma Code

• Quadratic and hermitian lattices over number fields
• Quaternion orders with type number one
• Two-generator subgroups of (P)SL(2,R)
• Algorithms for the modular group
• Magma code for Moduli of elliptic K3 surfaces: monodromy and root lattice strata

Tables

• List of squarefree reflective Lorentzian lattices