Mathematics Colloquium

Thursday, October 26, 1995, 4:00pm

102 Bradley Hall

Professor Martin Goldstern

Rutgers University

speaks on

Interpolation in lattices

Abstract. A lattice is a partial order in which any two elements a,b have a least upper bound a+b and a greatest lower bound a*b. Polynomials are defined as usual by applying these operations to variables x,y, ... and constants a,b,... from the lattice, e.g. p(x) = ((x*b)+(c+x))*(d*a). Functions which are described by a polynomail are called polynomial functions. Similarly to the case of fields, polynomial functions are of interest because they can be easily computed. Polynomial functions are always monotone, so the question arises whether this property characterizes polynomial functions. Can it be that *all* monotone functions are polynomial, or can at least be approximated or interpolated by polynomials? The answer is known for finite lattices. We will discuss this question mainly for infinite lattices.

Tea. High tea will be served at 3:30pm in the Lounge.
Emmy's. Certain refreshments will be available at the Emmy's after the talk.
Host. Jim Baumgartner will be the host, anybody interested in having dinner with the speaker should contact Jim (Ext. 6-3559).