# Analysis Seminar Archive for 2014-15

**Tuesday 30th September, 2014 **
(place: UCD
Ag1.01 )
4.00pm

*Speaker:* R. Smith

*Title:*Lipschitz-free spaces and the metric approximation property

**Abstract**
Given a metric space $M$ with distinguished point $0$, the
Lipschitz-free
space $\mathcal F(M)$ is the natural predual of the space of
Lipschitz
functions that vanish at $0$ (endowed with the Lipschitz norm). The
study
of these spaces is an emerging area of research. Despite their
elementary
definition, the linear structure of the spaces $\mathcal F(M)$ is
still
relatively poorly understood: in many cases it is not known whether
$\mathcal F(M)$ has the approximation property, a finite-dimensional
decomposition or a Schauder basis. In this talk we show that for
certain
subsets $M$ of $\mathbb R^N$ (such as all finite-dimensional compact
convex sets), the Lipschitz-free space $\mathcal F(M)$ has the metric
approximation property, independent of the choice of norm on
$\mathbb R^N$. This contrasts with the fact, proved by Godefroy and
Ozawa, that there exist infinite-dimensional compact convex sets $M$
such
that $\mathcal F(M)$ does not have the approximation property.

**Tuesday 7th October **
(place: UCD
Ag. 1.01 )
3:00pm

*Speaker:* M. Mackey

*Title:*Another random constant

**Tuesday 7th October **
(place: UCD
Ag. 1.01 )
4:15pm

*Speaker:* R. Timoney

*Title:*Square and square-free W*TROs

**Tuesday 14th October **
(place: UCD
Ag. 1.01 )
3:00pm

*Speaker:* H. Render

*Title:*On uniqueness of polyharmonic approximation on hyperplanes

**Tuesday 14th October **
(place: UCD
Ag. 1.01 )
4:15pm

*Speaker:* S. J. Gardiner

*Title:*A convergence theorem for harmonic measures with applications to Taylor series I

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

*Speaker:* S. J. Gardiner

*Title:*A convergence theorem for harmonic measures with applications to Taylor series II

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

*Speaker:* C. Boyd

*Title:*Geometry of Marcinkiewicz function spaces

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

*Speaker:* G. Singh

*Title:*Maximum principle in 2nd order PDEs

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

*Speaker:* M. Ghergu

*Title:*Behaviour around singularities for systems of PDEs

**Tuesday 4th November **
(place: TCD
WR20 )
2:30pm

*Speaker:* V. Bible

*Title:*Renorming a Banach space whose norm is LFC

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

*Speaker:* S. Buckley (Maynooth)

*Title:*Boundaries at infinity of Gromov and CAT(0) spaces

**Tuesday 11th November **
(place: UCD
Ag. 1.01 )
3:00pm

*Speaker:* A. Proch\'azka (UFC, Besan\c con)

*Title:*On existence of maps with distortion strictly less than 2

**Abstract**
We will see an example of a metric space $M$ with the following
property: If $M$ embeds into a Banach space bi-Lipschitz with distortion
strictly less than $2$ then $X$ linearly contains $\ell_1$. A refinement
of the construction of $M$ allows for a proof of the following theorem:
$C([0,\omega^\alpha])$ does not embed bi-Lipschitz with distortion
strictly less than $2$ into $C([0,\omega^\beta])$ if $\beta<\alpha$. Joint
work with Luis Sanchez-Gonzalez.

**Tuesday 11th November **
(place: UCD
Ag. 1.01 )
4:15pm

*Speaker:* R. Levene

*Title:*Hyperreflexivity and idempotent Schur multipliers

**Tuesday 18th November **
(place: TCD
WR20 )
2:30pm

*Speaker:* N. Snigireva

*Title:*Quantization for recurrent self-similar measures

**Tuesday 18th November **
(place: TCD
WR20 )
4:00pm

*Speaker:* J. Boland

*Title:*Limits of hypercyclic operators

**Tuesday 25th November **
(place: TCD
WR20 )
2:30pm

*Speaker:* A. Brown

*Title:*Norms of mappings between spaces of non-homogeneous polynomials

**Tuesday 25th November **
(place: TCD
WR20 )
4:00pm

*Speaker:* M. Daws (Leeds)

*Title:*A non-commutative notion of separate continuity

**Abstract**
The classical Gelfand theory of communicate C*-algebras tells us
that communicate C*-algebras are nothing but the algebras C_0(K),
the algebra of complex valued functions, vanishing at infinity, on
a locally compact Hausdorff space. This, in some sense, is the
motivating example behind non-commutative geometry / topology. How
might we similarly consider separate continuity from a C*-algebra
framework? We present one way to do this-- the naive "non-commutative"
definition thus resulting doesn't quite work, but we will show that
while our candidate set is not an algebra, in general, it does
always contain a "maximum" C*-subalgebra. Time allowing, I will
present some applications to the study of "quantum" topological
semigroups.

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

*Speaker:* E. Kakariadis (Newcastle)

*Title:*Semigroup actions on operator algebras

**Abstract**
The study of operator algebras arising from dynamical systems is
almost as old as the study of operator algebras themselves. Recently
the research has turned the focus to actions of semigroups on an
arbitrary operator algebra by endomorphisms and their dilation to
group actions. In this talk we will present recent findings for the
semigroup $\mathbb Z_+^n$. These include the Cuntz-Nica-Pimsner
algebra that generalises the Cuntz-Pimsner algebra of the one variable
case and the usual C*-crossed product for group actions. In particular
we will give a dilation technique from $n$ commuting endomorphisms to
$n$ commuting automophisms on a larger C*-algebra such that the
corresponding (minimal) Cuntz-Nica-Pimsner algebras are strong Morita
equivalent. Hence we can reduce problems on semigroup actions to
problems on group actions. Further consequences of our analysis
include the association of the ideal structure/nuclearity/exactness of
the Nica-Pimsner algebras with
minimality-freeness/nuclearity/exactness of the C*-dynamics.
The talk is based on a joint work with Ken Davidson and Adam Fuller.

**Tuesday 27th January, 2015 **
(place: TCD
WR20 )
4.00pm

*Speaker:* I. Gogic

*Title:*Noncommutative branched coverings

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

*Speaker:* J. Kaiser (Passau)

*Title:*Real geometry and potential theory

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

*Speaker:* M. Ghergu

*Title:*Behavior at isolated singularities for solutions of nonlocal
elliptic systems

**Tuesday 10th February, 2015 **
(place: TCD
WR20 )
4.00pm

*Speaker:* R. Timoney

*Title:*NC versions of Cartan uniqueness

**Tuesday 17th February, 2015 **
(place: UCD
Ag 1.01 )
3.00pm

*Speaker:* H. Render

*Title:*Error estimates for spherical product rules and a new cubature on the
disk

**Tuesday 24th February **
(place: TCD
WR20 )
2:30pm

*Speaker:* R. Harte

*Title:*Non commutative Taylor spectral theory

**Tuesday 24th February **
(place: TCD
WR20 )
4:00pm

*Speaker:* D. Kitson (Lancaster)

*Title:*An operator-theoretic approach to geometric rigidity

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

*Speaker:* R. Levene

*Title:*Positive extensions

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

*Speaker:* C. Boyd

*Title:*Copies of $\ell_1$ in Injective Tensor Products of Tree Spaces

**Tuesday 10th March **
(place: TCD
WR20 )
2:30pm

*Speaker:* N. Snigireva

*Title:*Quantization for probability measures associated with infinite
iterated function systems

**Tuesday 10th March **
(place: TCD
WR20 )
4:00pm

*Speaker:* M. Golitsyna (Kharkov)

*Title:*Analytic closure of the sets of real hyperbolic polynomials with
separated roots

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

*Speaker:* P. Mellon

*Title:*Denjoy-Wolff theory and extensions of a classical result of Herv\'e
on finite dimensional domains

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

*Speaker:* S. Gardiner

*Title:*Boundary Behaviour of Dirichlet Series and Universality

**Tuesday 31st March **
(place: UCD
Ag. 1.01 )
3:00pm

*Speaker:* P. Massopust (TU M\"unchen)

*Title:*Local Iterated Function Systems (IFSs) and Self-Referential Functions

**Abstract**
We present the concept of local IFS and highlight some of their
properties. As a special but nonetheless very important subclass
of local IFSs we consider those whose attractors are graphs of
functions. We associate with this subclass of local IFSs a
function-valued operator and derive conditions under which this
operator maps certain classes of function spaces into themselves.
Finally, we introduce fractels (= fractal elements) for both IFSs
and functions, and show that fractels give a more intrinsic
characterization of self-referentiabiity.

**Tuesday 31st March **
(place: UCD
Ag. 1.01 )
4:15pm

*Speaker:* R. Levene

*Title:*Positive extensions II

**Tuesday 7th April **
(place: UCD
Ag. 1.01 )
3:00pm

*Speaker:* J. M. Rigby (Queen Mary UL)

*Title:*Iteration of Holomorphic maps

**Tuesday 7th April **
(place: UCD
Ag. 1.01 )
4:15pm

*Speaker:* V. Bible

*Title:*Smooth approximations of norms on Banach spaces

**Tuesday 14th April **
(place: TCD
WR20 )
4.00pm

*Speaker:* D. C. Moore (Nottingham)

*Title:*Similarity mechanisms and essential spectra

**Abstract**
In this talk, I discuss the derivation of an apparently
new
`three spaceâ€™ result for the essential spectra of bounded linear
operators
on complex Banach spaces, and examine some of its consequences for the
study of composition operators on some Banach function spaces. If time
permits, I may also discuss some examples and open questions.

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

*Speaker:* H. Shahgholian (KTH)

*Title:*Free boundaries arriving from semi- and quasilinear PDEs

**Abstract**
In this talk I shall review some classical free boundary problems, as
well as a few new ones, arising in semi-and quasi-linear problems.
I shall present a general framework for how the regularity theory
works in such problems.

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

*Speaker:* R. Smith

*Title:*A charcterisation of isomorphic polyhedrality in separable Banach
spaces

**Tuesday 5h May, 2015 **
(place: TCD
2.6 )
4.00pm

*Speaker:* N. Dobbs (Geneva)

*Title:*Line, spiral, dense

**Abstract**
Generic analytic curves are dense in the plane. For particular
parametrised families of analytic curves, this need not be true
(e.g. graphs of complex polynomials), or something stronger could
be true (e.g. under the zeta-function, the image of every vertical
line in the critical strip is dense). Not many classes of explicit
dense curves were known. We show that exponential of exponential
of almost every line in the complex plane is dense in the plane,
along with some related results.

**Tuesday 2nd June, 2015 **
(place: UCD
231 Science North )
3:00pm

*Speaker:* L. Moraes (UFRJ)

*Title:*Tauberian Polynomials

**Tuesday 2nd June, 2015 **
(place: UCD
231 Science North )
4:20pm

*Speaker:* R. Ryan (NUIGalway)

*Title:*Free Banach Lattices

**Tuesday 12th June, 2015 **
(place: UCD
231 Science North )
12:00

*Speaker:* Arthur Danielyan (University of South Florida)

*Title:*Bounded approximation by polynomials and the Rudin-Carleson theorem