Department Colloquium
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Speaker:
Dave Witte Morris Department of Mathematics and Computer Science University of Lethbridge, Alberta, Canada Time and Place: 3:30 p.m., Friday, January 11, 2008, 14 Allen Title: Some Arithmetic Groups that Cannot Act on the Line Abstract: It is known that finite-index subgroups of the arithmetic group SL(3,Z) have no (orientation-preserving) actions on the real line. This naturally led to the conjecture that most other arithmetic groups (of higher real rank) also cannot act on the line. This problem remains open, but joint work with Lucy Lifschitz verifies the conjecture for many examples. This includes all finite-index subgroups of SL(2,Z[alpha]), where alpha is any irrational, real algebraic integer. The proof is based on the fact, proved by D.Carter, G.Keller, and E.Paige, that every element of these groups is a product of a bounded number of elementary matrices. No familiarity with arithmetic groups will be assumed. Host: Ted Dobson, (662) 325-7153, dobson@math.msstate.edu Refreshments: 3:00-3:30 p.m., 467 Allen |