Department of Mathematics

University of Maryland

301-405-5156

In 1989 I moved to the University of Maryland and began working with Misha Kapovich. Misha and I have written 17 papers to date. They started with work on configurations spaces of elementary geometric objects, polygonal linkages in the plane and in space and arrangements of lines in the projective plane. We gave the first published proof of theorem first announced by Thurston in the 1990's that, given an compact smooth manifold M there is a planar linkage whose configuration space is a disjoint union of a number of copies of M (it is not true that one can get just one copy of M in general). We later carried over our work to Euclidean buildings where we found applications to saturation problems for structure constants of representation rings and spherical Hecke algebras associated to reductive algebraic groups defined over the rational numbers.

The work with Kapovich led me into a four way collaboration with Ben Howard, Andrew Snowden and Ravi Vakil which resulted in the solution of a one hundred year old problem in classical invariant theory. In 1894 A. Kempe found generators for the ring of projective invariants of n ordered points on the projective line (the lowest degree invariants generate the ring). In his famous book "The Classical Groups" H. Weyl emphasized the importance of computing both the generators (First Main Theorem) and relations (Second Main Theorem) for such classical problems. In 2009, HMSV computed the relations among Kempe's generators, thereby proving the "Second Main Theorem" for ordered points on the line 115 years after the First Main Theorem was proved.

In 2010 I was asked by S.T. Yau and Lizhen Ji to write an article about my career for a book honoring Chern's hundredth birthday (Chern was my teacher in Berkeley) . You can download my article immediately below: Chern hundredth birthday article

I have been an avid golfer since my teens and have recently taken up fly-fishing and skiing.