# Diana Ojeda: Finite forms of Gowers’ Theorem on the oscillation stability of $c_0$

5 September 2014, 13:30–15:00

Fields institute, Room 210

Speaker: Diana Ojeda

Title:  Finite forms of Gowers’ Theorem on the oscillation stability of $c_0$
Abstract: 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 $\ell_{\infty}^n$, $n\in N$, and establish a much slower growing upper bound for the finite stabilization principle in this particular case.