Dr. Max Horn AG Algebra und Diskrete Mathematik Institut Computational Mathematics Fachbereich Mathematik und Informatik Technische Universität Braunschweig Pockelsstraße 14 38106 Braunschweig Office: F 613 Phone: +49 (531) 391-7526 Fax: +49 (531) 391-7414 Email: mhorn [at] tu-bs.de

Current

• Lecture "Computeralgebra" (WS 2011/2012), Exercises

Research Interests

• Geometry: Tits buildings, automorphisms, involutions, flips
• Groups: Algebraic groups, amalgams, Kac-Moody groups, groups of lie type
• Computer algebra

Past projects

• Master's thesis: Amalgams of unitary groups in Sp(2n,q).
  TU Darmstadt (submitted version)
  Supervised by Ralf Gramlich and Werner Nickel.
• PhD Thesis: Involutions of Kac-Moody groups.
  TU Darmstadt
  Supervised by Ralf Gramlich.

Publications

• Ralf Gramlich, Max Horn, Werner Nickel
  The complete Phan-type theorem for Sp(2n,q)
  J. Group Theory 9 (2006)
  603-626
• Ralf Gramlich, Max Horn, Werner Nickel
  Odd-dimensional orthogonal groups as amalgams of unitary groups. Part 2: machine computations
  J. Algebra 316 (2007)
  591 - 607
  source code available
• Max Horn
  On the Phan system of the Schur cover of $\SU(4,3^2)$
  Designs, Codes and Cryptography 47 (2008)
  243 - 247
• Ralf Gramlich, Max Horn, Antonio Pasini, Hendrik Van Maldeghem
  Intransitive geometries and fused amalgams
  J. Group Theory 11 (2008)
  443 - 464
  arXiv version
  source code available
• Tom De Medts, Ralf Gramlich, Max Horn
  Iwasawa decompositions of split Kac-Moody groups
  J. Lie Theory 19 (2009)
  311 - 337
  arXiv-Version
  
• Ralf Gramlich, Max Horn, Bernhard Mühlherr
  Abstract involutions of algebraic groups and of Kac-Moody groups
  J. Group Theory 14 (2011)
  213 - 249
  arXiv-Version
  
• Hans Cuypers, Max Horn, Jos in 't panhuis, Sergey Shpectorov
  Lie algebras and 3-transpositions
  arXiv-Version -- source code available
  submitted
• Bettina Eick, Max Horn, Seiran Zandi
  Schur multipliers and the Lazard correspondence
  submitted

Conference proceedings

• Bettina Eick, Max Horn
  Computing polycyclic quotients of finitely (L-)presented groups via Groebner bases
  ICMS'10 Proceedings of the Third international congress conference on Mathematical software

Conference talks

• December 11, 2004
  "Computations with geometric amalgams"
  Nikolaus Conference 2004 (RWTH Aachen, Germany)
• June 16, 2005
  "Computations with amalgams of unitary groups"
  2nd Joint Meeting of AMS, DMV, OeMG (Uni Mainz, Germany)
• September 14, 2006
  "Phan amalgams"
  Finite Geometries, Second Irsee Conference (Kloster Irsee, Germany)
• October 10, 2006
  "Flips of algebraic groups"
  Buildings 2006 (Uni Münster, Germany)
• October 11, 2007
  "Non-standard geometric covering theory"
  Buildings 2007 (Uni Münster, Germany)
• July 19, 2008
  "Involutionen von algebraischen und Kac-Moody Gruppen"
  Norddeutsches Gruppentheoriekolloquium 2008 (Uni Kiel, Germany)
• September 30, 2008
  "Involutions of algebraic and Kac-Moody groups"
  Buildings 2008 (Uni Münster, Germany)
• November 16, 2008
  "Involutions of algebraic and Kac-Moody groups"
  Mini-Workshop: Symmetric Varieties and Involutions of Algebraic Groups (Oberwolfach, Germany)
• July 19, 2009
  "The geometry of involutions of algebraic groups and of Kac-Moody groups"
  International Workshop on Algebraic Groups, Quantum Groups and Related Topics (Peking University, Beijing, China)
• December 12, 2009
  "Fischer Spaces and Lie Algebras"
  Nikolaus Conference 2009 (RWTH Aachen, Germany)
• June 26, 2010
  "Computing polycyclic quotients of finitely (L-)presented groups"
  ACA 2010 (University of Vlora, Albania)
• September 16, 2010
  "Computing polycyclic quotients of finitely (L-)presented groups via Gröbner bases"
  ICMS 2010 (Kobe University, Japan)
• October 6, 2010
  "From Fischer spaces to (Lie) algebras"
  Buildings 2010 (Uni Münster, Germany)
• August 2, 2011
  "Polycyclic quotients and non-commutative Gröbner bases"
  Conference on Group Theory (Harlaxton College, England)
• September 19, 2011
  "Polyzyklische Quotienten und nicht-kommutative Gröbnerbasen"
  DMV Tagung 2011, Minisymposium "Algorithmische Algebra" (Uni Köln, Germany)
• April 12, 2012
  "Double coset decompositions of Kac-Moody groups"
  Mini-Workshop: Generalizations of Symmetric Spaces (Oberwolfach, Germany)
• May 10, 2012
  "Computing Schur multipliers of p-groups and Lie rings"
  Tagung der Fachgruppe Computeralgebra (Uni Kassel, Germany)

Talks at other universities

• Mai 4, 2005
  "Amalgame"
  Uni Braunschweig, Germany
• February 10, 2009
  "Involutions of Kac-Moody groups"
  Cornell University, USA
• February 17, 2009
  "Involutions of Kac-Moody groups"
  Martin-Luther-Universität Halle-Wittenberg, Germany
• February 20, 2009
  "Unitary forms of Kac-Moody groups"
  Cornell University, USA
• March 12, 2009
  "Unitary forms of Kac-Moody groups"
  Binghamton University, USA
• July 1, 2009
  "The geometry of involutions of algebraic groups and of Kac-Moody groups"
  TU Eindhoven, Netherlands
• January 14, 2010
  "Fischer Spaces, 3-transposition groups and Lie Algebras"
  Leibniz Universität Hannover, Germany
• December 21, 2010
  "Polyzyklische Quotienten und nicht-kommutative Gröbnerbasen"
  Friedrich-Schiller-Universität Jena, Germany
• January 19, 2011
  "Connectedness of flip-flop systems"
  Universiteit Gent, Belgium

Non-mathematical talks

• August 31, 2011
  "Benefits of open source development and open tools"
  SICSA2011 Summer school "Advanced techniques in computer algebra systems development" (University of St Andrews, Scotland)

Teaching

• Seminar "Commutative Algebra and Algebraic Geometry" (SS 2006)
• MCS Introductory Course WS 2006/2007
• Seminar "Number Theory and Cryptography" (SS 2007)
• Seminar "Tits Buildings" (WS 2007/2008)
• Lecture "Gruppentheorie" (WS 2009/2010)
• Lecture "Algorithmische Gruppentheorie" (SS 2010)
• Lecture "Darstellungstheorie" (WS 2010/2011)
• Lecture "Computeralgebra" (WS 2011/2012), Exercises

Some links

Bettina Eick - Ralf Köhl (born Gramlich) - Hendrik Van Maldeghem