# Analysis Seminars

### Analysis Seminars for this Semester

Tuesday 7th February, 2017 (place: UCD Ag 1.01 ) 4.15pm

Speaker: N. Dobbs
Title: Diabolical Entropy

Tuesday 14th February, 2017 (place: UCD Ag 1.01 ) 4.00pm

Speaker: R. Timoney
Title: The universal TRO of a Hilbert space

Abstract A report on recent work in progress with L. Bunce to elucidate the structure of the universal TRO $T$ for a Hilbertian JC*-triple $E$ (of infinite dimension). Ideals and factor representations of $T$ can be connected to those of the right C*-algebra $A$ of $T$. We show that $A$ is antiliminal, prime and has injective factor representations of types I, II and III when $E$ is separable. Similar results hold for $T$.

Tuesday 21st February (place: UCD Ag. 1.01 ) 3:00pm

Speaker: M. Golitsyna
Title: Universal Laurent expansions of harmonic functions

Tuesday 21st February (place: UCD Ag. 1.01 ) 4:15pm

Speaker: H. Render
Title: Products of Bessel functions (II)

Tuesday 15th November, 2016 (place: UCD Ag 1.01 ) 4.00pm

Speaker: A. Korepanov (Warwick)
Title: Strong approximation of deterministic dynamical systems by Brownian motion

Tuesday 28th March (place: UCD Ag. 1.01 ) 3:00pm

Speaker: M. Ghergu
Title: Some methods in the study of semilinear elliptic problem

Tuesday 28th March (place: UCD Ag. 1.01 ) 4:15pm

Speaker: G. Singh
Title: On a class of mixed Choquard-Schr\"odinger Poisson systems

Tuesday 4th April (place: UCD Ag. 1.01 ) 3:00pm

Speaker: S. Gardiner
Title: Analytic content and the isoperimetric inequality

Tuesday 4th April (place: UCD Ag. 1.01 ) 4:15pm

Speaker: A. McCluskey (NUIG)
Title: A framework for the notion of betweenness

Tuesday 18th April (place: UCD Ag. 1.01 ) 3:00pm

Speaker: J. Buckley (IMS Madrid; KCL)
Title: On the number of nodal domains of toral eigenfunctions

Tuesday 18th April (place: UCD Ag. 1.01 ) 4:15pm

Speaker: A. T\"ornquist (Copenhagen)
Title: Fraisse theory: The Poulsen simplex and other examples

Tuesday 25th April, 2017 (place: UCD Ag 1.01 ) 4.15pm

Speaker: M. Golitsyna
Title: Sequences of real-rooted polynomials that converge in three points and the Laguerre-Polya class

Tuesday 2nd May, 2017 (place: UCD Ag 1.01 ) 4.15pm

Speaker: R. Smith
Title: Approximation of norms in preduals of Lorentz spaces

Tuesday 9th May, 2017 (place: UCD Ag 1.01 ) 4.15pm

Speaker: C. Gilmore
Title: Growth rates of frequently hypercyclic harmonic functions

Abstract The notion of frequent hypercyclicity stems from ergodic theory and has been an active area of research since it was introduced by Bayart and Grivaux (2004). Many natural continuous linear operators are frequently hypercyclic, for instance the differentiation operator on the space of entire functions. We will begin by recalling some basic examples and the pertinent notions of frequent hypercyclicity. We then consider the partial differentiation operator acting on the space of harmonic functions on $R^n$. Our primary goal is to identify sharp growth rates, in terms of the $L^2$-norm, of harmonic functions that are frequently hypercyclic vectors for the basic partial differentiation operator. This answers a question posed by Blasco et al. (2010). This is joint work with Eero Saksman and Hans-Olav Tylli.