Generic Polynomials

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The talk will focus on the classical question of finding a "canonical form" for degree n polynomials in one variable. For example, the quadratic polynomial x2 + ax + b can be transformed into one of the form x2 + c by completing the square. The latter can be viewed as a canonical form which depends on only one parameter (namely, c) rather than the two we started out with (namely, a and b). In general, we will show that any canonical form for degree n polynomials depends on at least [n/2] parameters. This result (obtained in collaboration with J. Buhler) generalizes a theorem of Felix Klein on quintic polynomials and is related to Hilbert's 13-th problem.

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Thursday, September 4, 1997
4:10 p.m. in MA 109
Coffee/Tea/Treats 3:30 p.m. in MA 104 (Lounge)

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