Welcome

In fall 2009 I am teaching m408d (calculus 2). In spring 2010 I will teach an undergraduate topics course (computational group theory) and a graduate topics course (finite groups). 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)
      Oberwolfach Reports 5 (2008) 2586-2588
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  Triangles of Baumslag-Solitar groups
      preprint 2008
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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; submitted 2008
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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; to appear in Ann. Sci. Ecole Norm. Sup.
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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.
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  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.
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  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.
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  Orbits in the Leech Lattice
      Experimental Math. 14 (2005) 491-509
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  Real cubic surfaces and real hyperbolic geometry
      with J. Carlson and D. Toledo; CRAS 337 (2003) 185-188
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  Orthogonal Complex Hyperbolic Arrangements
      with J. Carlson and D. Toledo; Symposium in Honor of C. H. Clemens, Contemp. Math. 312 (2002) 1-8
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  The moduli space of cubic threefolds
      J. Alg. Geom. 12 (2003) 201-223
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  The complex hyperbolic geometry of the moduli space of cubic surfaces
      with J. Carlson and D. Toledo; J. Alg. Geom. 11 (2002) 659-724
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  Cubic surfaces and Borcherds products
      with E. Freitag; Comm. Math. Helv. 77 (2002) 270-296
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  The period lattice for Enriques surfaces
      Math. Ann. 317 (2000) 483-488
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  Asphericity of moduli spaces via curvature
      J. Diff. Geom. 55 (2000) 441-451
      previously entitled Metric curvature of infinite branched covers
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  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
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  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
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  A homological characterization of hyperbolic groups
      with S. Gersten, Invent. Math. 135 (1999) 723-742
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  Reflection groups on the octave hyperbolic plane
      J. Alg. 213 (1999) 467-498
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  New complex- and quaternion-hyperbolic reflection groups
      Duke Math. J. 103 (2000) 303-333
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  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
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  Spotting infinite groups
      Math. Proc. Camb. Phil. Soc. 125 (1999) 39-42
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Expository notes:

  Hilbert's Nullstellensatz
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  The finite reflection groups
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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