Welcome

In fall 2012 I am teaching M328K and a graduate topics course on quadratic forms. Here is my CV and below are my papers. I have written a fairly complete summary of my research, aimed mainly at other mathematicians. At the bottom of the 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.

  Root systems for Lorentzian Kac-Moody algebras in rank 3
      preprint, 2012
      Download PDF
  Reflection centralizers in Coxeter groups
      preprint, 2011
      Download PDF
  Completions, branched covers, Artin groups and Singularity Theory
      To appear in Duke Math. J.
      Download PDF
  The densest lattices in PGL₃(Q₂)
      with Fumiharu Kato, to appear in Advances in Math.
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  Normalizers of parabolic subgroups of Coxeter groups
      Algebraic & Geometric Topology 12 (2012) 1137-1143
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  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
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  Triangles of Baumslag-Solitar groups
      to appear in Canadian J. of Math.
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  A Banach space determined by the Weil height
      with Jeffrey Vaaler, Acta Arithmetica 136 (2009), 279-298
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  Monodromy groups of Hurwitz-type problems
      with Chris Hall; Advances in Mathematics 225 (2010) 69-80.
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  On the Y₅₅₅ complex reflection group
      J. Alg. 322 (2009) 1454-1465
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  A new approach to rank one linear algebraic groups
      J. Algebra 321 (2009) 2540-2544.
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  Hyperbolic geometry and moduli of real cubic surfaces
      with J. Carlson and D. Toledo, Ann. Sci. Ecole Norm. Sup. 43 (2010) 69-115
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  The moduli space of cubic threefolds as a ball quotient
      with J. Carlson and D. Toledo; to appear in Memoirs of the A.M.S.
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  A monstrous proposal
      in Groups and symmetries, CRM Proc. Lecture Notes 47 (2009) 17-24
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  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, ps, dvi or latex
  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 or tar.gz
  Infinitely many hyperbolic Coxeter groups through dimension 19
      Geometry and Topology 122 (2006), 159-169.
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  Hyperbolic surfaces with prescribed infinite symmetry groups
      Proc. Amer. Math. Soc. 134 (2006) 3057-3059.
      Download PDF, ps, dvi or latex
  Orbits in the Leech Lattice
      Experimental Math. 14 (2005) 491-509
      Download PDF, ps, dvi or latex or check the errata
  Real cubic surfaces and real hyperbolic geometry
      with J. Carlson and D. Toledo; CRAS 337 (2003) 185-188
      Download PDF, ps or tar.gz
  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, ps, dvi or latex, or check the addendum
  The moduli space of cubic threefolds
      J. Alg. Geom. 12 (2003) 201-223
      Download PDF, ps or tar.gz
  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, ps, dvi or tex
  Cubic surfaces and Borcherds products
      with E. Freitag; Comm. Math. Helv. 77 (2002) 270-296
      Download PDF, ps, dvi or latex
  The period lattice for Enriques surfaces
      Math. Ann. 317 (2000) 483-488
      Download PDF, ps, dvi or tex
  Asphericity of moduli spaces via curvature
      J. Diff. Geom. 55 (2000) 441-451
      previously entitled Metric curvature of infinite branched covers
      Download PDF, ps, dvi or tex
  Braid pictures for Artin groups
      Trans. A.M.S. 354 (2002) 3455-3474
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  Ideals in the integral octaves
      J. Alg. 220 (1999) 396-400
      Download PDF, ps, dvi or tex
  A complex hyperbolic structure for moduli of cubic surfaces
      with J. Carlson and D. Toledo, CRAS 326 (1998) 49-54
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  The Leech lattice and complex hyperbolic reflections
      Invent. Math. 140 (2000) 283-301
      Download PDF, ps, dvi or tex, or check the erratum
  A homological characterization of hyperbolic groups
      with S. Gersten, Invent. Math. 135 (1999) 723-742
      Download PDF, ps, dvi or amstex
  Reflection groups on the octave hyperbolic plane
      J. Alg. 213 (1999) 467-498
      Download PDF, ps, dvi or tex, or check the erratum
  New complex- and quaternion-hyperbolic reflection groups
      Duke Math. J. 103 (2000) 303-333
      Download PDF, ps, dvi or tex
  An isoperimetric inequality for the Heisenberg groups
      GAFA 8 (1998) 219-233
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  Identifying models of the octave projective plane
      Geom. Dedicata 65 (1997) 215-217
      Download PDF, ps, dvi or tex
  Spotting infinite groups
      Math. Proc. Camb. Phil. Soc. 125 (1999) 39-42
      Download PDF, ps, dvi or tex

Expository notes:

  Hilbert's Nullstellensatz
      Download PDF, ps, dvi or latex
  The finite reflection groups
      Download PDF, ps, dvi or tex

My current research is supported by NSF grant DMS-0245120.
My previous research was supported by an NSF postdoctoral fellowship and by NSF grants DMS-0070930 and DMS-0231585.

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