MATH SEMINAR:Disjoint Frequently Hypercyclic Operators

Speaker:Özgür Martin

Title: Disjoint Frequently Hypercyclic Operators

Date/Time: February 22, 2023 12:40PM 

Place: FENS G035

Abstract: Linear dynamics is a branch of functional analysis which studies orbits of continuous linear operators acting on infinite dimensional topological vector spaces. Two central notions in linear dynamics are frequent hypercyclicity and disjoint hypercyclicity. The former notion quantifies how often the orbit of a vector visits each nonempty open set, and the latter notion measures the independence of orbits of a vector under two linear operators. We will review these notions and their connections to other areas like topological dynamics, ergodic theory, and additive combinatorics. Then, we will introduce disjoint frequent hypercyclicity which merges these two notions and present recent results and open problems.

Bio: Özgür Martin is a faculty member in the Mathematics Department at Mimar Sinan University of Fine Arts. Before joining Mimar Sinan, he worked as a postdoc in Miami University, OH, and received his PhD from Bowling Green State University, OH. He is interested in functional analysis as well as theory and applications of machine learning.