The Laurent phenomenon

A composition of birational maps given by Laurent polynomials need not be given by Laurent polynomials; however, sometimes---quite unexpectedly---it does. We suggest a unified treatment of this phenomenon, which covers a large class of applications. In particular, we settle in the affirmative the Gale-Robinson conjecture on integrality of generalized Somos sequences, and prove the Laurent property for several multidimensional recurrences, confirming conjectures by J.Propp, N.Elkies, and M.Kleber.

This is joint work with Andrei Zelevinsky (math.CO/0104241).

The talk will be followed at 8 p.m. by a performance of Beethoven's Symphonies No. 5 and 6 by the Berlin Philharmonic at the Hill Auditorium, maestro Claudio Abbado conducting. (Tickets not included with seminar attendance.)