Friday, September 27, 201312:30 pmModel theory seminarGC 6417

Finite forms of Gowers’ Theorem on the oscillation stability of c_0

Diana Ojeda Aristizabal

Cornell University

Diana Ojeda Aristizabal

We give a constructive proof of the finite version of Gowers’ FIN_k Theorem and analyze the corresponding upper bounds. The FIN_k Theorem is closely related to the oscillation stability of c_0. The stabilization of Lipschitz functions on arbitrary finite dimensional Banach spaces was proved well before by V. Milman. We compare the finite FIN_k Theorem with the Finite Stabilization Principle found by Milman in the case of spaces of the form ell_{infty}^n, ninN, and establish a much slower growing upper bound for the finite stabilization principle in this particular case.

Diana Ojeda Aristizabal is a Ph.D. candidate in mathematics at Cornell University, working with Justin Moore in the area of Ramsey theory and geometry of Banach spaces.