# Analysis Seminar Archive for 2015-16

Tuesday 29th September, 2015 (place: TCD WR20 ) 3.30pm

Speaker: A. Nicoara
Title:Failure of the Weierstrass Preparation Theorem in Quasi-analytic Denjoy-Carleman Rings

Abstract In 1976 Childress proved Weierstrass Division failed in quasi-analytic Denjoy-Carleman rings. While Weierstrass Division implies the Weierstrass Preparation Theorem, the reverse is not known to hold. The question of whether the Weierstrass Preparation Theorem held for Denjoy-Carleman functions or not remained open for over 30 years. In joint work with Francesca Acquistapace, Fabrizio Broglia, Michail Bronshtein, and Nahum Zobin, we showed the Weierstrass Preparation Theorem fails for Denjoy-Carleman functions by proving a strong non-extension result.

Tuesday 6th October (place: UCD Ag. 1.01 ) 3:00pm

Speaker: R. Levene
Title:Complementarity \& privacy in quantum information theory

Tuesday 6th October (place: UCD Ag. 1.01 ) 4:15pm

Speaker: R. Timoney
Title:Morita equivalence via ternary rings

Tuesday 13th October (place: TCD WR20 ) 2:30pm

Speaker: C. Boyd
Title:The bidual of a tree space

Tuesday 13th October (place: TCD WR20 ) 4:00pm

Speaker: C. \'O D\'unlaing
Title:Compact families of Jordan curves

Tuesday 20th October (place: UCD Ag. 1.01 ) 3:00pm

Speaker: N. Snigireva
Title:On zeros of polynomials on Banach spaces

Tuesday 20th October (place: UCD Ag. 1.01 ) 4:15pm

Speaker: M. Manolaki
Title:On zero sets of analytic functions

Tuesday 27th October (place: TCD WR20 ) 2:30pm

Speaker: I. Gogic
Title:Uniform approximation by two-sided multiplication maps

Tuesday 27th October (place: TCD WR20 ) 4:00pm

Speaker: J. Boland
Title:Norm closure of hypercyclic operators on Argyros-Haydon space

Tuesday 3rd November (place: UCD Ag. 1.01 ) 3:00pm

Speaker: H. Render
Title:The Dirichlet problem for quadratic surfaces and entire data

Tuesday 3rd November (place: UCD Ag. 1.01 ) 4:15pm

Speaker: S. Dineen
Title:Hyperbolic manifolds

Tuesday 10th November (place: UCD Ag. 1.01 ) 3:00pm

Speaker: G. Singh

Tuesday 10th November (place: UCD Ag. 1.01 ) 4:15pm

Speaker: M. Ghergu
Title:Elliptic inequalities in exterior domains for biharmonic problems

Tuesday 17th November (place: TCD WR20 ) 2:30pm

Speaker: M. Mackey
Title:Random intervals of exhaustion

Tuesday 17th November (place: TCD WR20 ) 4:00pm

Speaker: P. Hoffman (Maynooth)
Title:The nesting problem in forward automatic differentiation

Tuesday 24th November (place: UCD Ag. 1.01 ) 3:00pm

Speaker: S. Gardiner
Title:Harmonic functions which vanish on a cylindrical surface

Tuesday 24th November (place: UCD Ag. 1.01 ) 4:15pm

Speaker: R. Smith
Title:Approximation of arbitrary norms by smooth and polyhedral norms on $c_0(\Gamma)$

Tuesday 1st December (place: UCD Ag. 1.01 ) 3:00pm

Speaker: V. Evdoridou (OU)
Title:Fatou’s web and non-escaping endpoints

Tuesday 1st December (place: UCD Ag. 1.01 ) 4:15pm

Speaker: D. Mart\'i-Pete (OU)
Title:The escaping set of transcendental self-maps of the punctured plane

Tuesday 26th January, 2016 (place: TCD WR20 ) 4.00pm

Speaker: A. T\"ornquist (Copenhagen)
Title:A descriptive set-theoretic view of classification problems in operator algebras

Abstract In the past 20 years, descriptive set theorists have developed a theory that provides a measure of relative complexity of equivalence relations. This theory has its roots in classical smooth/non-smooth distinction of Mackey, but provides a much more refined view of the complexity of concrete classification problems. In recent years, the complexity of classification problems in operator algebras (of von Neumann factors and of nuclear simple separable C* algebras) have been examined from the descriptive set-theoretic perspective. In this talk, I will give an overview of these developments.

Tuesday 2nd February (place: UCD Ag. 1.01 ) 3:00pm

Speaker: H. Render
Title:On products of Bessel functions

Tuesday 2nd February (place: UCD Ag. 1.01 ) 4:15pm

Speaker: J. Ratzkin (Cape Town \& UCC
Title:Eigenvalues and Best Sobolev Constants of Moving Domains

Abstract Let D be a bounded domain in Euclidean space, and suppose its boundary moves outward. It follows from definitions that the fundamental frequency of D is a nonincreasing function of time. I will present some estimates of this rate of decrease, and characterize the case of equality. This is joint work with Tom Carroll of the University of Cork and Moustapha Fall of AIMS Senegal.

Tuesday 9th February, 2016 (place: TCD WR20 ) 4.00pm

Speaker: I. Gogi\'c
Title:When are the lengths of elementary operators uniformly bounded?

Tuesday 16th February (place: UCD Ag. 1.01 ) 3:00pm

Speaker: M. Manolaki
Title:Universal Dirichlet series and their derivatives

Tuesday 16th February (place: UCD Ag. 1.01 ) 4:15pm

Speaker: K. Piszczek (Poznan)
Title:The noncommutative Schwartz space. Is it interesting?

Abstract The question What is the noncommutative space of smooth functions' has been of interest for some time. We will focus on a concrete object that might play such a role. Motivation towards the research and properties of this object will be considered. In particular, we will try to describe some amenability properties of this noncommutative Frechet algebra.

Tuesday 23rd February, 2016 (place: TCD WR20 ) 4.00pm

Speaker: S. Morley (Nottingham)
Title:F-differentiable functions and F-quasianalyticity

Abstract Let X be a perfect, compact subset of the complex plane. We usually study those continuous, complex-valued functions f on X such that f has a continuous derivative at all points of X. Unfortunately, the collection of all such functions on X does not have desirable properties as a normed algebra of functions. In 2003, Bland and Feinstein introduced larger collections of continuous functions on X which have much more desirable properties as normed algebras. They studied those continuous functions on X for which there is an associated continuous function on X which integrates correctly' along each path in a given collection F of rectifiable paths in X. We call these functions F-differentiable functions and they have similar properties to the continuous differentiable functions on X. In this talk, we discuss the algebras of F-differentiable functions, their properties, and a notion of quasianalyticity for these algebras.

Tuesday 1st March (place: UCD Ag. 1.01 ) 3:00pm

Speaker: M. Ghergu
Title:Semilinear elliptic inequalities in a new setting

Tuesday 1st March (place: UCD Ag. 1.01 ) 4:15pm

Speaker: G. Singh
Title:Weak solutions for singular quasi-linear systems

Tuesday 8th March, 2016 (place: TCD WR20 ) 4.00pm

Speaker: R. Timoney
Title:What is the future of analysis?

Tuesday 22nd March (place: UCD Ag. 1.01 ) 3:00pm

Speaker: R. Levene
Title:Weighted Shift Directed Graph Operator Algebras

Tuesday 22nd March (place: UCD Ag. 1.01 ) 4:15pm

Speaker: M. Venkova (DIT)
Title:Approximation of Monomials in spaces of non-homogeneous polynomials

Tuesday 29th March (place: TCD WR20 ) 4:00pm

Speaker: J. Boland
Title:Approximating quasinilpotents by generalised nilpotents

Tuesday 5th April (place: UCD Ag. 1.01 ) 3:00pm

Speaker: M. Mathieu (QUB)
Title:Elementary operators---still not elementary?"

Abstract Many properties of elementary operators on Banach algebras have been studied extensively by a large number of authors over several decades but still they defy a full structural understanding maybe the reason being that they appear naturally in many guises in many situations. I shall report on recent work with Nadia Boudi (2015) and my latest PhD student Matthew Young (2015/16) in which we try to understand when elementary operators are spectrally bounded or spectrally isometric. As so often, definitive results are only achieved for elementary operators of small length.

Tuesday 5th April (place: UCD Ag. 1.01 ) 4:15pm

Speaker: S. Gardiner
Title:A reflection result for harmonic functions which vanish on a cylindrical surface