WILLIAM GOLDMAN
    I am Professor in the Mathematics Department at the University of Maryland.
    • Office: 3106 William E. Kirwan Hall, 4176 Campus Drive, College Park, MD 20742-4015
    • TEL: (301)-405-5124, FAX: (301)-314-0827
    • EMAIL: wmg AT umd DOT edu
      • Most people refer to me by my nickname "Bill".
  • I am currently teaching ``Fudamental Concepts of Differential Geometry, (MATH740) which meets Tuesdays-Thursday at 11:00 in MTH1311.
  • I recently spoke at the annual Maryland Dynamics Conference, honoring Giovanni Forni's 60th birthday. Check out the slides from my talk.
  • On Tuesday, May 9 I speak in the Einstein Chair seminar and the Hyperbolic Geometry Seminar at the Graduate Center of CUNY.
    My title is ``Dynamical Systems arising from the Classification of Geometric Structures''.
  • I will be visiting the Max Planck Insitute in Leipzig, and speaking in the Geometry Seminar there on June 4.
  • I will be speaking at the Workshop on Hamiltonian Geometry and Quantization at the Fields Insitute, July 15-19,2024.
    This workshop honors the 60th birthdays of Lisa Jeffrey, Yael Karshon and Jonathan Weitsman.
  • Here is a recent preprint discussing how the deformation space of complete affine 2-manifolds relates to a twisted cubic cone in 4-space. This result was suggested by Pierre Deligne after I mentioned it in a lecture I gave at the Institute for Advanced Study during my 2021 sabbatical there. It gives an explicit proof of Oliver Baues's theorem that this deformation space is homeomorphic to a plane. This paper will appear in a Contemporary Mathematics volume celebrating Ravi Kulkarni's 80th birthday.
  • My first paper with my colleague Giovanni Forni, Mixing Flows on moduli spaces of flat bundles over sruraces appeared in Volume 2 of ``Geometry and Physics,'' dedicated to Nigel Hitchin's 70th birthday conferences in Oxford, Aarhus and Madrid. (I could only attend the conference in Oxford.) This paper outlines a program to study dynamical problems arising from the classification of geometric structures on manifolds by introducing a cocycle of symplectic moduli spaces over the Teichmueller geodesic flow and SL(2,R)-action.
  • I am currently investigating a remarkable family of real affine cubic surfaces which arise as relative SL(2)-character varieties for a one-holed torus. See if you can run the interactive Mathematica notebook I wrote with Ajeet Gary several years ago.
  • Next fall I will be teaching Math 431 (Geometry for Computer Applications), a course I've been developing for many years. In 2021 it was taught by my former doctoral student Justin Wyss-Gallifent.
  • I serve on the faculty of both the MATH and AMSC graduate programs at the University of Maryland and have supervised several doctoral dissertations
  • Co-director (with Rodrigo Trevino), Lab for Experimental Mathematics at MAryland (LEMMA). I cofounded this experiment with Richard Schwartz in 2000, when it was called the Experimental Geometry Lab. You can read about it here. I was one of the founding members of Geometry Labs United, and co-organized the Geometry Labs United Conference which took place at ICERM, 16-17 July 2020.
    • Computational Aspects of Discrete Subgroups of Lie groups, ICERM, 14-18 June 2021. Here are the slides from my talk, and written version here. In that talk I discuss mathematical developments arising from a 1992 REU project with then-undergraduate Robert Benedetto, when we discovered compact components of the SL(2,R)-character variety of a four-holed sphere.
  • Recent Administrative Activities:
    • Member-At-Large of the Council of the American Mathematical Society and member of the Committee on Publications.
    • Member, Scientific Advisory Board, Brin Mathematics Research Center at the University of Maryland.
    • I recently co-organized (with Steve Bradlow and Richard Wentworth) Brin MRC a workshop ``Advances in Higgs bundles." there, and next year will be co-organizing (with Karin Melnick, Charles Frances, Jill McGowan and Caleb Ashley) a workshop ``Affine and hyperbolic geoemetry" in memory of Todd Drumm.
    • Former member (with Patrick Brosnan and Abba Gumel), Department Colloquium Committee.
    • Administrative activities before 2015
    • Network Executive Committee (and original co-PI, and director of Maryland hub), GEAR Network, an NSF Research Network in the Mathematical Sciences.
    • Scientific Advisory Board (2020-2022), Institute for Computational and Experimental Research in Mathematics (ICERM), Brown University.
  • Curriculum Vitae
  • Research papers
  • Selected reviews
  • Previous research students; also see my listing on the Math Genealogy Project.
  • Check out Evan Goldman's art
  • Link to Ameridan Mathematical Society Bookstore for Geometric Structures on Manifolds, published in the AMS Graduate Studies in Mathematics volume 227. (li+409 pp. ISBN: [9781470471033]; [9781470471989]; [9781470471972] 57 (22 53-01)) Check out the recent review by the Mathematical Association of America and in Math Reviews (MathSciNet) from the American Mathematical Society.
  • Recent draft of Proper actions of discrete groups of affine transformations, coauthored with Jeffrey Danciger, Todd Drumm and Ilia Smilga, from the Margulis Festschrift, ``Dynamics, Geometry, Number Theory: The Impact of Margulis in Modern Mathematics," University of Chicago Press. See also http://arxiv.org/abs/2002.09520.
  • A preliminary draft of a recent survey, from ``Geometries in History" (S. Dani and A. Papadopoulos, eds. Springer 2019)

    • Last updated: Wednesday 24 April 2024.