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 ed
Most people refer to me by my nickname "Bill".
I recently spoke at the annual Maryland Dynamics Conference.
See my slides .
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.
I am currently teaching ``Fudamental Concepts of Differential Geometry,
(MATH740) which meets Tuesdays-Thursday at 11:00 in MTH1311.
I serve on the faculty of both the
MATH and
AMSC
graduate programs at the University of Maryland and have
supervised several doctoral dissertations.
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.