Rudolf Scharlau


Number theory, discrete geometry, algebraic methods:

  • Arithmetic theory of quadratic forms, relations with modular forms
  • Geometry of numbers: lattices, sphere packings and codes
  • Regular tilings, mathematical crystallography, geometry of lattices
  • Tits buildings, Coxeter groups, hyperbolic reflection groups
  • Algorithms for quadratic forms and lattices


  • Journals, refereed proceedings, books complete list
  • Recent Preprints
  • Proceedings, Manuscripts, Tables
    • Classifying lattices using modular forms, joint with Boris B. Venkov; in: M. Ozeki, E. Bannai, M. Harada (eds.): Codes, Lattices, Modular Forms and Vertex Operator Algebras, Conference Yamagata University, October 2 - 4, 2000 (Proceedings 2001)
    • On the classification of arithmetic reflection groups on hyperbolic 3-space, 26 pages, Bielefeld 1989, scan as pdf
  • Seminar and Lecture Notes

Talks (since 2005)

  • Existenz und Nichtexistenz von extremalen Gittern, TU Darmstadt, 21.06.2011, Folien als pdf
  • Similar Sublattices of Higher-Dimensional Lattices, Erwin Schrödinger Institute, Vienna, 08.06 2011
  • Existence and Non-Existence of Extremal Lattices, TU Wien, Institut für Diskrete Mathematik und Geometrie, 07.06.2011, slides as pdf
  • Existenz und Nichtexistenz von extremalen Gittern, Universität Rostock, Kolloquium, 13.04.2011
  • Classification of p-Elementary and Extremal Lattices, Workshop on the Arithmetic of Quadratic Forms and Integral Lattices, Futrono, Lago Ranco, Chile, 14.12.2010, slides as pdf
  • On the explicit construction of arithmetic hyperbolic reflection groups, Conference "Lie algebras, vertex algebras and automorphic forms", ICMS Edinburgh, 31.08.2009, slides as pdf
  • Martin Kneser's Work on Quadratic Forms and Algebraic Groups, International Conference on the Arithmetic and Algebraic Theory of Quadratic Forms, Llanquihue, Chile, 19.12.2007 slides as pdf
  • Arithmetik, Algebra und Geometrie quadratischer Formen, Gedenkkolloquium für Martin Kneser, Göttingen, 13.01.2005

Conferences (since 2013)

  • International Conference on the Algebraic and Arithmetic Theory of Quadratic Forms Official site
  • ICM 2014 Satellite Conference on Integral Quadratic Forms and Related Topics Official site

Tables and Data