On the interplay of hypercyclicity with Szemeredi's theorem

04/11/2017 - 12:15pm
04/11/2017 - 1:10pm
Yunied Puig de Dios (Ben Gurion University, Israel)

Linear dynamics is a very young and active branch of functional analysis, mainly concerned with the iterates of continuous linear operators. One of its most studied objects is the notion of hypercyclicity. An operator T acting on a topological vector space X is said to be hypercyclic if there exists x\in X such that the T-orbit of x, O(x, T) = {T^nx: n \geq 0 } is dense in X. One distinctive characteristic of linear dynamics is its strong connections with other fields of mathematics like operator theory, geometry of Banach spaces and probability. In this talk, we will see very recent results that point to a rather unexpected connection of linear dynamics with ergodic Ramsey theory through a kind of Szemeredi's theorem for generalized polynomials.

Millikan 2099, Pomona College