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
- Since April 1st, 2020, I am at the TU Kaiserslautern
Research Interests
- Geometry: Tits buildings, automorphisms, involutions, flips
- Groups: Algebraic groups, amalgams, Kac-Moody groups, groups of lie type
- Computer algebra with focus on algorithmic group theory
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
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The complete Phan-type theorem for $Sp(2n,q)$J. Group Theory 9 (2006), no. 5, 603–626
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Odd-dimensional orthogonal groups as amalgams of unitary groups. Part 2: machine computationsJ. Algebra 316 (2007), no. 2, 591–607
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On the Phan system of the Schur cover of $SU(4,3^2)$Designs, Codes and Cryptography 47 (2008), 243–247
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Intransitive geometries and fused amalgamsJ. Group Theory 11 (2008), 443–464
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Iwasawa decompositions of split Kac-Moody groupsJ. Lie Theory 19 (2009), no. 2, 311–337
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Abstract involutions of algebraic groups and of Kac-Moody groupsJ. Group Theory 14 (2011), 213–249
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Lie algebras and 3-transpositionsJ. Algebra 368 (2012), 21–39
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Schur multipliers and the Lazard correspondenceArchiv der Mathematik 99 (2012), no. 3, 217–226
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The construction of finite solvable groups revisitedJ. Algebra 408 (2014), 166–182
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Second cohomology of Lie rings and the Schur multiplierIntl. J. Group Theory 3 (2014), no. 2, 9–20
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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
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Simple Connectivity in Polar SpacesForum Mathematicum 28 (2015), no. 3, 491–505
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Isomorphisms and rigidity of arithmetic Kac-Moody groupsJ. Lie Theory 26 (2016), no. 2, 1079–1105
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Moufang twin trees of prime orderAdv. Math. 302 (2016), 1–24
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Spin covers of maximal compact subgroups of Kac-Moody groups, and Spin-extended Weyl groupsJ. Group Theory 20 (2017), no. 3, 401–504
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Constructing groups of ‘small’ order: Recent results and open problemsChapter in "Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory", Springer (2017), –
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Kac-Moody symmetric spacesMünster J. of Math 13 (2020), 1–114
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Decompositions of Kac-Moody groupsin preparation
Conference proceedings
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Computing polycyclic quotients of finitely (L-)presented groups via Groebner bases
Other (non-refereed) publications
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The GAP package SingularInterface.Computeralgebra-Rundbrief 55 (2014), 29–33
Students
- Master students
- Christian Hoffmeister (2012): Posets of twisted involutions in Coxeter groups
- Anne Hukelmann (2015): Das Isomorphieproblem polyzyklischer Gruppen
- Nina Wagner (2017): Symbolic Collection in Polycyclic Groups
- Romina Heukäufer (2017): Stark reguläre Graphen
- Thi-Ngoc-Bich Le (2017): Schoofs Algorithmus
- Sebastian Bischof (2018): The extension theorem for twin buildings
- Katharina Liehr (2018): Gruppen, Ringe, Moduln
- Bachelor students
- Romina Heukäufer (2015): Klassifikation endlicher Spiegelungsgruppen
- Janina Erb (2016): Zopfgruppen
- Katharina Liehr (2016): Diskrete Bewertungsringe
- Sebastian Bischof (2016): Bäume und Amalgame
- Daniel Kaulbach (2016): Automatisiertes Beweisen geometrischer Sätze
- Benjamin Manns (2018): Elliptische Kurven in der Kryptographie
- Paul Merz (2018): NTRUEncrypt
- Charlotte Thurn (2018): Termersetzungssysteme und der Knuth-Bendix-Algorithmus
Conference talks
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December 11, 2004
"Computations with geometric amalgams"
Nikolauskonferenz 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 Gruppentheorie-Kolloquium 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, China) -
December 12, 2009
"Fischer Spaces and Lie Algebras"
Nikolauskonferenz 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) -
May 28, 2011
"Involutionen von Moufangpolygonen"
Reinhold-Baer-Kolloquium (TU Braunschweig, 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) -
March 18, 2013
"libsing: A new interface between GAP and Singular"
3. Jahrestagung DFG-Schwerpunktprogramm 1489 (Uni Konstanz, Germany) -
March 21, 2013
"Constructing finite solvable groups"
3. Jahrestagung DFG-Schwerpunktprogramm 1489 (Uni Konstanz, Germany) -
May 23, 2013
"Solvable group generation"
Questions, Algorithms, and Computations in Abstract Group Theory (TU Braunschweig, Germany) -
October 8, 2013
"Decompositions of Kac-Moody groups"
Buildings 2013 (Uni Münster, Germany) -
November 26, 2013
"Spin covers of "maximal compact" subgroups of real Kac-Moody groups"
Workshop "Generalizations of Symmetric Spaces" (Lorentz Center Leiden, Netherlands) -
March 6, 2014
"Symbolic computations with p-groups and Lie rings"
4. Jahrestagung DFG-Schwerpunktprogramm 1489 (Bad Boll, Germany) -
March 26, 2014
"Symbolic computations with p-groups and Lie rings"
Workshop "Experimental Methods in Computational Algebra" (Uni Hannover, Germany) -
May 16, 2014
"Solvable group generation"
Tagung Fachgruppe Computeralgebra (Uni Kassel, Germany) -
May 30, 2014
"Generalized spin groups"
47th Seminar Sophus Lie (Schloß Rauischolzhausen, Germany) -
July 12, 2014
"Generalized Spin groups"
Norddeutsches Gruppentheorie-Kolloquium 2014 (Uni Bielefeld, Germany) -
September 30, 2014
"Cartan-Bott periodicity for compact forms of Kac-Moody algebras of type $E_n$"
Buildings 2014 (Uni Münster, Germany) -
February 16, 2015
"Cartan-Bott periodicity for maximal compact subalgebras of real Kac-Moody algebras of type $E_n$"
CoGrAl2015 (Uni Jena, Germany) -
May 7, 2015
"Generalized spin representations"
Groups and Geometries (Banff, Kanada, Canada) -
May 15, 2015
"The Normaliz interface of GAP"
Normaliz Workshop (Uni Osnabrück, Germany) -
June 22, 2015
"Generalized spin representations"
Workshop on Generalizations of Symmetric Spaces (Nahsholim, Israel, Israel) -
September 26, 2017
"Kac-Moody symmetric spaces"
Buildings and Symmetry (University of Western Australia, ) -
January 20, 2018
"Kac-Moody symmetric spaces"
Reinhold-Baer-Kolloquium (TU Braunschweig, Germany)
Talks at other universities
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May 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 -
December 10, 2014
"Cartan-Bott periodicity for compact forms of Kac-Moody algebras of type $E_n$"
TU Eindhoven, Netherlands -
April 29, 2016
"Towards Kac-Moody symmetric spaces"
Uni Erlangen, Germany -
July 13, 2017
"Symbolische Berechnungen in Gruppen und Ringen"
Uni Würzburg, Germany
Non-mathematical talks
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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
- Norddeutsches Gruppentheorie-Kolloquium 2012, June 29-30, 2012, TU Braunschweig, Germany (with Bettina Eick)
- First GAP Days 2014, August 25-29, 2014, RWTH Aachen, Germany (with Mohamed Barakat, Frank Lübeck)
- Second GAP Days 2015, March 16-20, 2015, RWTH Aachen, Germany (with Mohamed Barakat, Frank Lübeck)
- Third GAP Days 2015, September 14-23, 2015, NTNU Trondheim, Norway (with Mohamed Barakat, Øyvind Solberg)
- First Joint GAP-SageMath Days,, January 18-22, 2016, University of St Andrews, Scotland (with Alexander Konovalov, Dmitrii Pasechnik, Markus Pfeiffer)
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Session on
Computational aspects of homological algebra, group, and representation theory
at the ICMS 2016, July 11-14, 2016, Berlin, Germany (with Mohamed Barakat) - Norddeutsches Gruppentheorie-Kolloquium 2017, June 9-10, 2017, JLU Gießen, Germany (with Ralf Köhl, Bernhard Mühlherr)
- GAP Days Fall 2017, August 30 - September 8, 2017, University of Siegen, Germany (with Mohamed Barakat)
- GAP Days Fall 2018, September 17-21, 2018, Uni Siegen, Germany (with Mohamed Barakat)
- GAP Days Fall 2019 (as part of the GAP Singular Meeting), August 20-23, 2019, PfalzAkademie, Lambrecht, Germany
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GAP Days Spring 2020,
March 23-27, 2020,
St Andrews, UKVirtual/Remote/Home Offices, (with Ruth Hoffmann, Chris Jefferson)
Teaching
- Seminar "Commutative Algebra and Algebraic Geometry" (summer term 2006)
- MCS Introductory Course (winter term 2006/2007)
- Seminar "Number Theory and Cryptography" (summer term 2007)
- Seminar "Tits Buildings" (winter term 2007/2008)
- Lecture "Gruppentheorie" (winter term 2009/2010)
- Lecture "Algorithmische Gruppentheorie" (summer term 2010)
- Lecture "Darstellungstheorie" (winter term 2010/2011)
- Lecture "Computeralgebra" (winter term 2011/2012)
- Lecture "Einführung in die Gruppentheorie" (winter term 2012/2013)
- Lecture "Algorithmische Algebra" (summer term 2013)
- Lecture "Lineare Algebra I" (winter term 2013/2014)
- Lecture "Lineare Algebra II" (summer term 2014)
- Seminar/Proseminar "Computeralgebra" (summer term 2014), Announcement (german)
- Lecture "Algebra" (winter term 2014/2015)
- Rechenkurs "Algebra mit GAP" (winter term 2014/2015), Announcement (german), worksheets
- Lecture and seminar "Computeralgebra" (summer term 2015), Announcement (german)
- Lecture "Algorithmische Gruppentheorie" (winter term 2015/2016)
- Reading course "Algorithmische Invariantentheorie" (winter term 2015/2016)
- Lecture "Gruppentheorie" (summer term 2016)
- Seminar "Algebra" (summer term 2016)
- Lecture "Homologische Algebra" (winter term 2016/2017)
- Lecture "Algorithmische Zahlentheorie" (summer term 2017)
- Seminar "Zahlentheorie und Kryptographie" (summer term 2017)
- Lecture "Computeralgebra" (winter term 2017/2018)
- Rechenkurs "Algebra mit GAP" (winter term 2017/2018)
- Lecture "Algorithmische Gruppentheorie" (summer term 2018)
- Lecture "Gruppentheorie" (summer term 2019)