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 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