Events for 08/01/2016 from all calendars
Workshop in Analysis and Probability Seminar
Time: 2:00PM - 2:50PM
Location: BLOC 220
Speaker: Daniel Freeman, St. Louis University
Title: The discretization problem for continuous frames
Abstract: There is a long history of creating frames for Hilbert spaces by sampling continuous frames. For instance, Gabor frames are formed by sampling the short time Fourier transform at a lattice. Continuous frames often arise naturally in mathematics and physics, but the sampled frames are usually more useful for applications and computations. Using the results of Marcus-Spielman-Srivastava in their solution of the Kadison-Singer problem, we solve the discretization problem for continuous frames by characterizing exactly when a continuous frame may be sampled to obtain a frame. In particular, we prove that every bounded continuous frame may be sampled to obtain a frame. This is joint work with Darrin Speegle.
Linear Analysis Seminar
Time: 3:00PM - 4:00PM
Location: BLOC 220
Speaker: Igor Klep, University of Auckland
Title: Domains of noncommutative rational functions and their matrix pencil realizations
Abstract: A noncommutative (nc) rational function r is defined through evaluations of formal nc rational expressions on tuples of matrices, giving rise to its domain r. Nc rational functions arise and are used e.g. in automata theory, algebraic combinatorics, control theory, free analysis and free probability. They form a skew field, the so-called universal skew field of fractions of a free algebra, and were first constructed by Amitsur and later studied by Cohn and many others. In this talk we shall discuss domains of nc rational functions. We will characterize regular functions whose domain is everything, and explain when two domains are comparable. This in turn will allow us to describe nc rational functions with a given domain. A key tool in this pursuit are matrix pencil realizations of nc rational functions. The talk is based on joint works with Victor Vinnikov, Jurij Volcic and James Pascoe.