Prof. Dr. Max Horn

AG Algebra, Geometrie und Computeralgebra (AGAG)
Department of Mathematics
TU Kaiserslautern
Gottlieb-Daimler-Straße 48
67663 Kaiserslautern

Building 48, room 430
Phone: +49 (631) 205-2730
Email: LASTNAME [at] mathematik.uni-kl.de



Current



Research Interests

Research statement



Past projects



Publications

  1. Ralf Gramlich, Max Horn, Werner Nickel
    The complete Phan-type theorem for $Sp(2n,q)$
    J. Group Theory 9 (2006), no. 5, 603–626
    PDFDOI
  2. Ralf Gramlich, Max Horn, Werner Nickel
    Odd-dimensional orthogonal groups as amalgams of unitary groups. Part 2: machine computations
    J. Algebra 316 (2007), no. 2, 591–607
  3. Max Horn
    On the Phan system of the Schur cover of $SU(4,3^2)$
    Designs, Codes and Cryptography 47 (2008), 243–247
    PDFDOI
  4. Ralf Gramlich, Max Horn, Antonio Pasini, Hendrik Van Maldeghem
    Intransitive geometries and fused amalgams
    J. Group Theory 11 (2008), 443–464
  5. Tom De Medts, Ralf Gramlich, Max Horn
    Iwasawa decompositions of split Kac-Moody groups
    J. Lie Theory 19 (2009), no. 2, 311–337
  6. Ralf Gramlich, Max Horn, Bernhard Mühlherr
    Abstract involutions of algebraic groups and of Kac-Moody groups
    J. Group Theory 14 (2011), 213–249
  7. Hans Cuypers, Max Horn, Jos in 't panhuis, Sergey Shpectorov
    Lie algebras and 3-transpositions
    J. Algebra 368 (2012), 21–39
  8. Bettina Eick, Max Horn, Seiran Zandi
    Schur multipliers and the Lazard correspondence
    Archiv der Mathematik 99 (2012), no. 3, 217–226
  9. Bettina Eick, Max Horn
    The construction of finite solvable groups revisited
    J. Algebra 408 (2014), 166–182
  10. Max Horn, Seiran Zandi
    Second cohomology of Lie rings and the Schur multiplier
    Intl. J. Group Theory 3 (2014), no. 2, 9–20
  11. Max Horn, Ralf Köhl
    Cartan-Bott periodicity for the real $E_n$ series (appendix to "Generalized spin representations" by Guntram Hainke, Ralf Köhl, and Paul Levy)
    Münster J. of Math 8 (2015), 181–210
    arXivDOIURL
  12. Max Horn, Reed Nessler, Hendrik Van Maldeghem
    Simple Connectivity in Polar Spaces
    Forum Mathematicum 28 (2015), no. 3, 491–505
  13. Amir Farahmand Parsa, Max Horn, Ralf Köhl
    Isomorphisms and rigidity of arithmetic Kac-Moody groups
    J. Lie Theory 26 (2016), no. 2, 1079–1105
  14. Matthias Grüninger, Max Horn, Bernhard Mühlherr
    Moufang twin trees of prime order
    Adv. Math. 302 (2016), 1–24
  15. David Ghatei, Max Horn, Ralf Köhl, Sebastian Weiß
    Spin covers of maximal compact subgroups of Kac-Moody groups, and Spin-extended Weyl groups
    J. Group Theory 20 (2017), no. 3, 401–504
  16. Bettina Eick, Max Horn, Alexander Hulpke
    Constructing groups of ‘small’ order: Recent results and open problems
    Chapter in "Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory", Springer (2017),
    PDFDOIURL
  17. Walter Freyn, Tobias Hartnick, Max Horn, Ralf Köhl
    Kac-Moody symmetric spaces
    Münster J. of Math 13 (2020), 1–114
    arXivDOIURL
  18. Max Horn
    Decompositions of Kac-Moody groups
    in preparation


Conference proceedings

  1. Bettina Eick, Max Horn
    Computing polycyclic quotients of finitely (L-)presented groups via Groebner bases


Other (non-refereed) publications

  1. Mohamed Barakat, Max Horn, Frank Lübeck, Oleksandr Motsak, Max Neunhöffer, Hans Schönemann
    The GAP package SingularInterface.
    Computeralgebra-Rundbrief 55 (2014), 29–33


Students



Conference talks

  1. December 11, 2004
    "Computations with geometric amalgams"
    Nikolauskonferenz 2004 (RWTH Aachen, Germany)
  2. June 16, 2005
    "Computations with amalgams of unitary groups"
    2nd Joint Meeting of AMS, DMV, OeMG (Uni Mainz, Germany)
  3. September 14, 2006
    "Phan amalgams"
    Finite Geometries, Second Irsee Conference (Kloster Irsee, Germany)
  4. October 10, 2006
    "Flips of algebraic groups"
    Buildings 2006 (Uni Münster, Germany)
  5. October 11, 2007
    "Non-standard geometric covering theory"
    Buildings 2007 (Uni Münster, Germany)
  6. July 19, 2008
    "Involutionen von algebraischen und Kac-Moody Gruppen"
    Norddeutsches Gruppentheorie-Kolloquium 2008 (Uni Kiel, Germany)
  7. September 30, 2008
    "Involutions of algebraic and Kac-Moody groups"
    Buildings 2008 (Uni Münster, Germany)
  8. November 16, 2008
    "Involutions of algebraic and Kac-Moody groups"
    Mini-Workshop: Symmetric Varieties and Involutions of Algebraic Groups (Oberwolfach, Germany)
  9. 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, China)
  10. December 12, 2009
    "Fischer Spaces and Lie Algebras"
    Nikolauskonferenz 2009 (RWTH Aachen, Germany)
  11. June 26, 2010
    "Computing polycyclic quotients of finitely (L-)presented groups"
    ACA 2010 (University of Vlora, Albania)
  12. September 16, 2010
    "Computing polycyclic quotients of finitely (L-)presented groups via Gröbner bases"
    ICMS 2010 (Kobe University, Japan)
  13. October 6, 2010
    "From Fischer spaces to (Lie) algebras"
    Buildings 2010 (Uni Münster, Germany)
  14. May 28, 2011
    "Involutionen von Moufangpolygonen"
    Reinhold-Baer-Kolloquium (TU Braunschweig, Germany)
  15. August 2, 2011
    "Polycyclic quotients and non-commutative Gröbner bases"
    Conference on Group Theory (Harlaxton College, England)
  16. September 19, 2011
    "Polyzyklische Quotienten und nicht-kommutative Gröbnerbasen"
    DMV Tagung 2011, Minisymposium "Algorithmische Algebra" (Uni Köln, Germany)
  17. April 12, 2012
    "Double coset decompositions of Kac-Moody groups"
    Mini-Workshop: Generalizations of Symmetric Spaces (Oberwolfach, Germany)
  18. May 10, 2012
    "Computing Schur multipliers of p-groups and Lie rings"
    Tagung der Fachgruppe Computeralgebra (Uni Kassel, Germany)
  19. March 18, 2013
    "libsing: A new interface between GAP and Singular"
    3. Jahrestagung DFG-Schwerpunktprogramm 1489 (Uni Konstanz, Germany)
  20. March 21, 2013
    "Constructing finite solvable groups"
    3. Jahrestagung DFG-Schwerpunktprogramm 1489 (Uni Konstanz, Germany)
  21. May 23, 2013
    "Solvable group generation"
    Questions, Algorithms, and Computations in Abstract Group Theory (TU Braunschweig, Germany)
  22. October 8, 2013
    "Decompositions of Kac-Moody groups"
    Buildings 2013 (Uni Münster, Germany)
  23. November 26, 2013
    "Spin covers of "maximal compact" subgroups of real Kac-Moody groups"
    Workshop "Generalizations of Symmetric Spaces" (Lorentz Center Leiden, Netherlands)
  24. March 6, 2014
    "Symbolic computations with p-groups and Lie rings"
    4. Jahrestagung DFG-Schwerpunktprogramm 1489 (Bad Boll, Germany)
  25. March 26, 2014
    "Symbolic computations with p-groups and Lie rings"
    Workshop "Experimental Methods in Computational Algebra" (Uni Hannover, Germany)
  26. May 16, 2014
    "Solvable group generation"
    Tagung Fachgruppe Computeralgebra (Uni Kassel, Germany)
  27. May 30, 2014
    "Generalized spin groups"
    47th Seminar Sophus Lie (Schloß Rauischolzhausen, Germany)
  28. July 12, 2014
    "Generalized Spin groups"
    Norddeutsches Gruppentheorie-Kolloquium 2014 (Uni Bielefeld, Germany)
  29. September 30, 2014
    "Cartan-Bott periodicity for compact forms of Kac-Moody algebras of type $E_n$"
    Buildings 2014 (Uni Münster, Germany)
  30. February 16, 2015
    "Cartan-Bott periodicity for maximal compact subalgebras of real Kac-Moody algebras of type $E_n$"
    CoGrAl2015 (Uni Jena, Germany)
  31. May 7, 2015
    "Generalized spin representations"
    Groups and Geometries (Banff, Kanada, Canada)
  32. May 15, 2015
    "The Normaliz interface of GAP"
    Normaliz Workshop (Uni Osnabrück, Germany)
  33. June 22, 2015
    "Generalized spin representations"
    Workshop on Generalizations of Symmetric Spaces (Nahsholim, Israel, Israel)
  34. September 26, 2017
    "Kac-Moody symmetric spaces"
    Buildings and Symmetry (University of Western Australia, )
  35. January 20, 2018
    "Kac-Moody symmetric spaces"
    Reinhold-Baer-Kolloquium (TU Braunschweig, Germany)


Talks at other universities

  1. May 4, 2005
    "Amalgame"
    Uni Braunschweig, Germany
  2. February 10, 2009
    "Involutions of Kac-Moody groups"
    Cornell University, USA
  3. February 17, 2009
    "Involutions of Kac-Moody groups"
    Martin-Luther-Universität Halle-Wittenberg, Germany
  4. February 20, 2009
    "Unitary forms of Kac-Moody groups"
    Cornell University, USA
  5. March 12, 2009
    "Unitary forms of Kac-Moody groups"
    Binghamton University, USA
  6. July 1, 2009
    "The geometry of involutions of algebraic groups and of Kac-Moody groups"
    TU Eindhoven, Netherlands
  7. January 14, 2010
    "Fischer Spaces, 3-transposition groups and Lie Algebras"
    Leibniz Universität Hannover, Germany
  8. December 21, 2010
    "Polyzyklische Quotienten und nicht-kommutative Gröbnerbasen"
    Friedrich-Schiller-Universität Jena, Germany
  9. January 19, 2011
    "Connectedness of flip-flop systems"
    Universiteit Gent, Belgium
  10. December 10, 2014
    "Cartan-Bott periodicity for compact forms of Kac-Moody algebras of type $E_n$"
    TU Eindhoven, Netherlands
  11. April 29, 2016
    "Towards Kac-Moody symmetric spaces"
    Uni Erlangen, Germany
  12. July 13, 2017
    "Symbolische Berechnungen in Gruppen und Ringen"
    Uni Würzburg, Germany


Non-mathematical talks

  1. 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)


Conference organization



Teaching

  1. Seminar "Commutative Algebra and Algebraic Geometry" (summer term 2006)
  2. MCS Introductory Course (winter term 2006/2007)
  3. Seminar "Number Theory and Cryptography" (summer term 2007)
  4. Seminar "Tits Buildings" (winter term 2007/2008)
  5. Lecture "Gruppentheorie" (winter term 2009/2010)
  6. Lecture "Algorithmische Gruppentheorie" (summer term 2010)
  7. Lecture "Darstellungstheorie" (winter term 2010/2011)
  8. Lecture "Computeralgebra" (winter term 2011/2012)
  9. Lecture "Einführung in die Gruppentheorie" (winter term 2012/2013)
  10. Lecture "Algorithmische Algebra" (summer term 2013)
  11. Lecture "Lineare Algebra I" (winter term 2013/2014)
  12. Lecture "Lineare Algebra II" (summer term 2014)
  13. Seminar/Proseminar "Computeralgebra" (summer term 2014), Announcement (german)
  14. Lecture "Algebra" (winter term 2014/2015)
  15. Rechenkurs "Algebra mit GAP" (winter term 2014/2015), Announcement (german), worksheets
  16. Lecture and seminar "Computeralgebra" (summer term 2015), Announcement (german)
  17. Lecture "Algorithmische Gruppentheorie" (winter term 2015/2016)
  18. Reading course "Algorithmische Invariantentheorie" (winter term 2015/2016)
  19. Lecture "Gruppentheorie" (summer term 2016)
  20. Seminar "Algebra" (summer term 2016)
  21. Lecture "Homologische Algebra" (winter term 2016/2017)
  22. Lecture "Algorithmische Zahlentheorie" (summer term 2017)
  23. Seminar "Zahlentheorie und Kryptographie" (summer term 2017)
  24. Lecture "Computeralgebra" (winter term 2017/2018)
  25. Rechenkurs "Algebra mit GAP" (winter term 2017/2018)
  26. Lecture "Algorithmische Gruppentheorie" (summer term 2018)
  27. Lecture "Gruppentheorie" (summer term 2019)


Miscellaneous