Richard Schwartz (mathematician): Difference between revisions
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'''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. |
'''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. |
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==Selected publications== |
==Selected publications== |
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Revision as of 05:57, 6 June 2007
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.
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
External links
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