Welcome

This semester I am teaching m362k (first semester probability) and m427l (vector calculus). 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.

  Complex hyperbolic geometry and the monster simple group (conjectural)
      to appear in Oberwolfach Reports
      Download PDF
  Triangles of Baumslag-Solitar groups
      preprint 2008
      Download PDF
  A Banach space determined by the Weil height
      with Jeffrey Vaaler, to appear in Acta Arithmetica
      Download PDF
  Monodromy groups of Hurwitz-type problems
      with Chris Hall; submitted 2008
      Download PDF
  On the Y₅₅₅ complex reflection group
      submitted 2008
      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; to appear in Ann. Ecole Norm. Sup.
      Download PDF
  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.
      Download PDF
  A monstrous proposal
      To appear in Groups and symmetries: From the Neolithic Scots to John McKay, ed. J. Harnad.
      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, 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.
      Download PDF
  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
      Download PDF, ps or tar.gz
  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
      Download PDF, ps, dvi or tex
  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
      Download PDF, ps, dvi or tex
  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
Department of Mathematics
University of Texas at Austin
1 University Station C1200
Austin TX, 78712

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