Richard Schwartz

Richard Schwartz is currently a professor of mathematics at Brown University. His accomplishments include a proof of the Goldman-Parker conjecture, and a proof that every triangle all of whose angles are less than 100 degrees has a periodic billiard orbit. The latter statement means that, given a billiards table whose shape is a triangle meeting the angle requirements described, and considering an idealized billiards ball that never slows down once it is hit, there is a path that the billiards ball can follow on that table that repeats itself. An example is that for a 45-45-90 triangle, any orbit that starts with the ball rolling perpendicular to one of the edges of the triangle is a periodic billiard orbit.

elected publications

*Richard Schwartz, "The Quasi-Isometry Classification of Rank One Lattices Publ. Math. IHES (1995) 82 133–168
*Richard Schwartz, "Ideal triangle groups, dented tori, and numerical analysis." Ann. of Math. (2) 153 (2001), no. 3, 533–598. (original proof of the Goldman-Parker conjecture)
*Richard Schwartz, "A better proof of the Goldman-Parker conjecture." Geom. Topol. 9 (2005), 1539–1601

External links

* [http://www.math.brown.edu/~res/ Richard Schwartz's Homepage]
* [http://www.cmps.umd.edu/goldman_parker.htm Solving the Goldman/Parker Conjecture]