# 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

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 space’ 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