-
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.
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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.
- 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.
- 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.
- 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.
- Nnext year I 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, 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: Sunday 28 April 2024.