Richard Schwartz

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For the vegetarian and animal welfare activist, see Richard H. Schwartz. For the film producer, see Rick 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.

[edit] Selected 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