Richard Schwartz

Richard Evan Schwartz ( born August 11, 1966 in Los Angeles ) is an American mathematician who deals with geometric group theory, geometry and dynamical systems of billiard type.

Schwartz studied at the University of California, Los Angeles ( BA, 1987) and in 1991 received his doctorate from Princeton University with William Thurston (The limit sets of some infinitely generated Schottky groups). He taught at the University of Maryland and is a professor at Brown University.

In 1992 he introduced the pentagram image ( Pentagram map ), a map of closed convex polygons (on the polygon which is formed by the interfaces of the shortest diagonal ) in the real projective plane, which can be regarded as a discrete dynamic system. It is even exactly integrable

In 1989 he proved a conjecture of Goldman and John Parker, which provides a complete description of the moduli space of the complex hyperbolic ideal triangle group.

In 2007 he proved the existence of unbounded orbits of outer billiards ( a dynamic system, which was introduced in the 1950s by Bernhard Neumann as a toy model for celestial mechanics ).

He wrote a children's book about mathematics, originated from comics, which he drew for his daughter.

In 2002 he was invited speaker at the International Congress of Mathematicians in Beijing ( Complex hyperbolic triangle groups).

Writings

• Spherical CR Geometry and Dehn Surgery, Annals of Mathematics Studies 165, Princeton University Press 2007
• Outer Billiards on Kites, Annals of Mathematics Studies, 171, Princeton University Press 2009
• You Can Count on Monsters A.K. Peters Ltd. , 2010 (Mathematical children's book )
• Mostly Surfaces, American Math Society, 2011
• Elementary surprises in projective geometry, Mathematical Intelligencer 2010