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Graduate Seminar Sebastien Vasey
Carnegie Mellon University
Abstract: Imagine living in a world where every set of reals is a finite union of intervals and points. How much easier would life then be?The talk will make this question precise by introducing the notion of o-minimality. I will show that in this universe, many dreams come true. For example, every real-valued function is piecewise continuous, and every subset of the plane can be decomposed into finitely many very simple sets, the so-called cells.As an application, I will outline a proof of the following result of Khovanskii: For any k and n, there exists C such that if p is a real polynomial with n variables, k non-zero terms (but unbounded degree), and finitely many real roots, then it has fewer than C such roots.
Date: Wednesday, February 19, 2014
Time: 5:30 pm
Location: Wean Hall 8220
Submitted by: Brian Kell