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 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 spoke at the Einstein Chair seminar and the Hyperbolic Geometry Seminar at the Graduate Center of CUNY.
• I visited the Max Planck Insitute in Leipzig, and spoke in the Geometry Seminar on June 4.
• I spoke at the Workshop on Hamiltonian Geometry and Quantization at the Fields Insitute, July 15-19,2024.
  This workshop honored the 60th birthdays of Lisa Jeffrey, Yael Karshon and Jonathan Weitsman.
• On September 4, I spoke at both the Boston College Geometry, Topology and Dynamics Seminar and the seminar for the Experimental Mathematics Lab at Boston College..

• 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. A second paper, with Forni and Carlos Matheus and Sean Lawton, may be found here.
• The paper, by Rachel (Nakyung) Lee and Karin Melnick, extends Lee's 2023 award-winning doctoral dissertation classifying Lorentzian conformal structures with unipotent holonomy on closed manifolds. This is the first major progress on the classifiction of arabolic-geometry structures on closed manifolds with nilpotent holonomy since my 1983 paper on conformally flat manifolds with nilpotent holonomy.
• A part of the introduction for the Festschrift for Toshiyuki Kobayashi dealing with his work on proper actions in pseudo-Riemannian geometry.
• A ZblMath review of Michael Magee's article "Random Unitary Representations of Surface Groups I:Asymptotic Expansions."
• Current and past experimental projects
• 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 when he was an undergraduate at Maryland.
• 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.
• Another project in 1992 with Sergey Brin in the Undergraduate Apprecenticeship in Research and Scholarship, concerned Visualizing Pappus's Theorem in Projective Geometry.

• Member-At-Large of the Council of the American Mathematical Society and member of the Committee on Publications.
• Brin Mathematics Research Center at the University of Maryland.
• Member, Scientific Advisory Board.
• I recently co-organized (with Steve Bradlow and Richard Wentworth) Brin MRC a workshop ``Advances in Higgs bundles." there.
• Former member (with Patrick Brosnan and Abba Gumel), Department Colloquium Committee.
• Administrative activities before 2015
• Network Executive Committee (original co-PI, and director of Maryland hub), GEAR Network, an NSF Research Network in the Mathematical Sciences, 2011-2022; with Steve Bradlow, Steve Kerkchff, Richard Wentworth and Anna Wienhard.
• Scientific Advisory Board (2020-2022), Institute for Computational and Experimental Research in Mathematics (ICERM), Brown University.

Last updated: Tuesday 22 October 2024.