# 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

*Title:*Radial solutions of semilinear elliptic system with nonlinear gradient terms

**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:*Fatouâ€™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