Welcome

Daniel Allcock Professor, Mathematics, U.T Austin (hook 'em horns!) PMA 9.112 (formerly RLM 9.112). Black Lives Matter! (and what about All Lives Matter?) In Fall 2021, I will teach a graduate course in Lie groups and Lie algebras. In spring 2021 I am teaching M373K (Algebraic Structures). (students: please access it via canvas) Student quote about n!: "You're not allowed to get excited in math, because someone decided numbers get real big when you do that." A few links that inspire me---maybe you too? The story of our own Bill Wolesensky Arnold Schwarzeneggar's July 4 message (2020) Lessons by a young man, for one much older Here is my CV and below are my papers. At the bottom of this page there are also some expository notes. Please email me at allcock at math.utexas.edu if you have trouble downloading, printing or understanding my papers. As part of a grant application I had to summarize five years of research in two pages. I'm posting the summary here in case it is interesting to someone. (I'm afraid it will only be readable to mathematicians.)

  Most big mapping class groups fail the Tits Alternative
      submitted 2020
      Download PDF
  Variations on Glauberman's ZJ Theorem
      submitted 2020
      Download PDF
  Moduli spaces of tropical curves are simply connected
      with Daniel Corey and Sam Payne; submitted 2019
      Download PDF
  Best play in Dots and Boxes endgames
      To appear in Intl. J. Game Theory
      Download PDF
  The tetrahedron and automorphisms of Enriques and Coble surfaces of Hessian type
      with Igor Dolgachev, Annales Henri Lebesgue 3 (2020) 1133-1159
      Download PDF
  Generators for a complex hyperbolic braid group
      with Tathagata Basak, Geometry & Topology 20 (2018) 747-778.
      Download PDF
  Congruence subgroups and Enriques surface automorphisms
      J. Lond. Math. Soc. 98 (2018) 1-11.
      Download PDF
  The Conway-Sloane calculus for 2-adic lattices
      with Itamar Gal and Alice Mark; to appear in L'Enseignement mathematique (arxiv 1511.04614)
      Download PDF
  Spherical space forms revisited
      Transactions of the A.M.S. 370 (2018) 5561-5582.
      Download PDF
  A fake projective plane via 2-adic uniformization with torsion
      with Fumiharu Kato, Tohoku Math. J. 69 (2017) 221-237
      Download PDF
  Prenilpotent pairs in the E10 root system
      Math. Proc. Camb. Phil. Soc. 164 (2018) 473-483.
      Download PDF
  Presentation of hyperbolic Kac-Moody groups over rings
      with Lisa Carbone, J. Algebra 445 (2016) 232-243
      Download PDF
  Presentation of affine Kac-Moody groups over rings
      Algebra and Number Theory 10 (2016) 533-556
      Download PDF
  Geometric generators for braid-like groups
      with Tathagata Basak
      Geometry and Topology 20 (2016) 747-778
      Download PDF
  Steinberg groups as amalgams
      Algebra & Number Theory 10 (2016) 1791-1843
      Download PDF
  Binary Relations from Tournament Solutions, and Back Again
      with Scott Moser; submitted 2013
      Download PDF
  Root systems for Lorentzian Kac-Moody algebras in rank 3
      Bull. Lond. Math. Soc. 47 (2015) 325-342
      Download PDF
  Reflection centralizers in Coxeter groups
      Transformation Groups 18 (2013) 599-613
      Download PDF
  Completions, branched covers, Artin groups and Singularity Theory
      Duke Math. J. 162 (2013) 2645-2689.
      Download PDF
  The densest lattices in PGL₃(Q₂)
      with Fumiharu Kato, Advances in Math. 242 (2013) 102-115
      Download PDF
  Normalizers of parabolic subgroups of Coxeter groups
      Algebraic & Geometric Topology 12 (2012) 1137-1143
      Download PDF
  The reflective Lorentzian lattices of rank 3
      Memoirs of the A.M.S. 220 (number 1033) (2012). Erratum.
      Download PDF, tex/perl or the (huge) unabridged table PDF or tex/perl
  Complex hyperbolic geometry and the monster simple group (conjectural)
      Oberwolfach Reports 5 (2008) 2586-2588
      Download PDF
  Triangles of Baumslag-Solitar groups
      Canadian J. of Math. 64 (2012) 241-253
      Download PDF
  A Banach space determined by the Weil height
      with Jeffrey Vaaler, Acta Arithmetica 136 (2009), 279-298
      Download PDF
  Monodromy groups of Hurwitz-type problems
      with Chris Hall; Advances in Mathematics 225 (2010) 69-80.
      Download PDF
  On the Y₅₅₅ complex reflection group
      J. Alg. 322 (2009) 1454-1465
      Download PDF
  A new approach to rank one linear algebraic groups
      J. Algebra 321 (2009) 2540-2544.
      Download PDF
  Hyperbolic geometry and moduli of real cubic surfaces
      with J. Carlson and D. Toledo, Ann. Sci. Ecole Norm. Sup. 43 (2010) 69-115
      Download PDF
  The moduli space of cubic threefolds as a ball quotient
      with J. Carlson and D. Toledo, Memoirs of the A.M.S. 209 (2011) no. 985
      Download PDF
  A monstrous proposal
      in Groups and symmetries, CRM Proc. Lecture Notes 47 (2009) 17-24
      Download PDF
  Non-arithmetic uniformization of some real moduli spaces
      with J. Carlson and D. Toledo; Geometriae Dedicata 122 (2006) 159-169. Erratum 122 (2006) 171.
      Download PDF
  Hyperbolic geometry and the moduli space of real binary sextics
      with J. Carlson and D. Toledo; in Algebra and Geometry around Hypergeometric Functions, R.P. Holzapfel, A.M. Uludag, M. Yoshida (editors), Progress in Mathematics series v. 260, Birkauser, 1-22.
      Download PDF
  Infinitely many hyperbolic Coxeter groups through dimension 19
      Geometry and Topology 122 (2006), 159-169.
      Download PDF
  Hyperbolic surfaces with prescribed infinite symmetry groups
      Proc. Amer. Math. Soc. 134 (2006) 3057-3059.
      Download PDF
  Orbits in the Leech Lattice
      Experimental Math. 14 (2005) 491-509
      Download PDF or check the errata
  Real cubic surfaces and real hyperbolic geometry
      with J. Carlson and D. Toledo; CRAS 337 (2003) 185-188
      Download PDF
  Orthogonal Complex Hyperbolic Arrangements
      with J. Carlson and D. Toledo; Symposium in Honor of C. H. Clemens, Contemp. Math. 312 (2002) 1-8
      Download PDF or Check the addendum
  The moduli space of cubic threefolds
      J. Alg. Geom. 12 (2003) 201-223
      Download PDF
  The complex hyperbolic geometry of the moduli space of cubic surfaces
      with J. Carlson and D. Toledo; J. Alg. Geom. 11 (2002) 659-724
      Download PDF
  Cubic surfaces and Borcherds products
      with E. Freitag; Comm. Math. Helv. 77 (2002) 270-296
      Download PDF
  The period lattice for Enriques surfaces
      Math. Ann. 317 (2000) 483-488
      Download PDF
  Asphericity of moduli spaces via curvature
      J. Diff. Geom. 55 (2000) 441-451
      previously entitled Metric curvature of infinite branched covers
      Download PDF
  Braid pictures for Artin groups
      Trans. A.M.S. 354 (2002) 3455-3474
      Download PDF
  Ideals in the integral octaves
      J. Alg. 220 (1999) 396-400
      Download PDF
  A complex hyperbolic structure for moduli of cubic surfaces
      with J. Carlson and D. Toledo, CRAS 326 (1998) 49-54
      Download PDF
  The Leech lattice and complex hyperbolic reflections
      Invent. Math. 140 (2000) 283-301
      Download PDF or check the erratum
  A homological characterization of hyperbolic groups
      with S. Gersten, Invent. Math. 135 (1999) 723-742
      Download PDF
  Reflection groups on the octave hyperbolic plane
      J. Alg. 213 (1999) 467-498
      Download PDF or check the erratum
  New complex- and quaternion-hyperbolic reflection groups
      Duke Math. J. 103 (2000) 303-333
      Download PDF
  An isoperimetric inequality for the Heisenberg groups
      GAFA 8 (1998) 219-233
      Download PDF
  Identifying models of the octave projective plane
      Geom. Dedicata 65 (1997) 215-217
      Download PDF
  Spotting infinite groups
      Math. Proc. Camb. Phil. Soc. 125 (1999) 39-42
      Download PDF

Expository notes:

  Hilbert's Nullstellensatz
      Download PDF
  The finite reflection groups
      Download PDF

My current research is supported by a Simons Foundation Collaboration Grant
Here is a Dots & Boxes board.
You can play Euclid: The Game! to challenge yourself with compass and ruler constructions.
Daniel Allcock
University of Texas at Austin
Department of Mathematics, RLM 8.100
2515 Speedway Stop C1200
Austin, Texas 78712-1202

phone (512) 471-1120
fax (512) 471-9038
email: allcock at math.utexas.edu