Analysis Seminar Archive for 2016 - 17

Tuesday 27th September (place: UCD Ag. 1.01 ) 3:00pm

Speaker: C. Gillmore (Helsinki)
Title:Hypercyclicity of Derivations

Abstract Linear dynamics has been a rapidly evolving area of operator theory since the late 1980s. I will begin by recalling some basic examples and the pertinent notions of hypercyclicity in order to discuss the dynamics of bounded linear operators in the infinite-dimensional setting. The primary goal is to examine the hypercyclicity of generalised derivations $S \mapsto AS-SB$, for fixed operators $A,B$, on spaces of operators. Hitherto the principle result in this setting has been the characterisation of the hypercyclicity of the left and right multipliers. The main example I will show is the existence of non-trivial hypercyclic generalised derivations on separable ideals of operators

Tuesday 27th September (place: UCD Ag. 1.01 ) 4:15pm

Title:Ergodic and geometric properties for systems with overlaps

Abstract I will present several recent results in the dynamics and ergodic theory of smooth transformations and their invariant probability measures on fractals with overlaps. Among the classes of maps considered there are hyperbolic endomorphisms, iterated function systems with overlaps, and maps on projective spaces. In this context we study the dimensions of these fractals and of the equilibrium measures supported on them, and some connections with exact dimensionality and 1-sided Bernoullicity.

Tuesday 4th October, 2016 (place: UCD Ag 1.01 ) 4.00pm

Speaker: M. Ghergu
Title:Isolated singulatities for nonlocal elliptoc PDEs

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

Speaker: H. Render
Title:Fischer operators

Tuesday 18th October (place: UCD Ag. 1.01 ) 3:00pm

Speaker: R. Ryan (NUIG)
Title:Some recent results for real and complex analytic functions

Tuesday 18th October (place: UCD Ag. 1.01 ) 4:15pm

Speaker: M. Mackey
Title:Spectrum of one operator

Tuesday 1st November, 2016 (place: UCD Ag 1.01 ) 4.00pm

Speaker: M. Golitsyna
Title:Universal Laurent series

Tuesday 8th November, 2016 (place: UCD Ag 1.01 ) 4.00pm

Speaker: R. Levene
Title:Grothendieck's inequality in the non-commutative Schwarz space

Tuesday 15th November, 2016 (place: UCD Ag 1.01 ) 4.00pm

Speaker: R. Harte
Title:The Gelfand theory unplugged

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

Speaker: S. Gardiner
Title:Harmonic functions which vanish on coaxial cylinders

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

Speaker: A. T\"ornquist (Copenhagen)
Title:The descriptive set theory of unitary representations

Abstract Classifying the irreducible unitary representations of, say, a countable discrete group is a classical problem that motivated the work in the 1950s and 1960s of Mackey, Glimm, Effros, and others. Famously, Glimm showed that as soon as a group is not type 1, which turns out to be the same as not Abelian-by-finite, then the unitary dual is not "smooth". What this means is: there is no concrete parametrization of the irreducible representations of such a group. In the last decade, descriptive set theorists have attempted to apply their tools to say something more precise about the isomorphism relation on unitary representations, irreducible or otherwise. It turns out that when things are "bad", that is, in the non-type 1 case, one can say a great deal more about "how bad" things really are, but there are still several interesting open questions. In this talk I will give an overview of these developments.

Tuesday 29th November (place: UCD Ag. 1.01 ) 3:00pm

Speaker: N. Snigireva
Title:Gaussian measures and analytic functions

Tuesday 29th November (place: UCD Ag. 1.01 ) 4:15pm

Speaker: C. Boyd
Title:Invertibility and the trace class

Tuesday 7th February, 2017 (place: UCD Ag 1.01 ) 4.15pm

Speaker: N. Dobbs
Title: Diabolical Entropy

Tuesday 14th February, 2017 (place: UCD Ag 1.01 ) 4.00pm

Speaker: R. Timoney
Title: The universal TRO of a Hilbert space

Abstract A report on recent work in progress with L. Bunce to elucidate the structure of the universal TRO $T$ for a Hilbertian JC*-triple $E$ (of infinite dimension). Ideals and factor representations of $T$ can be connected to those of the right C*-algebra $A$ of $T$. We show that $A$ is antiliminal, prime and has injective factor representations of types I, II and III when $E$ is separable. Similar results hold for $T$.

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

Speaker: M. Golitsyna
Title: Universal Laurent expansions of harmonic functions

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

Speaker: H. Render
Title: Products of Bessel functions (II)

Tuesday 15th November, 2016 (place: UCD Ag 1.01 ) 4.00pm

Speaker: A. Korepanov (Warwick)
Title: Strong approximation of deterministic dynamical systems by Brownian motion

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

Speaker: M. Ghergu
Title: Some methods in the study of semilinear elliptic problem

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

Speaker: G. Singh
Title: On a class of mixed Choquard-Schr\"odinger Poisson systems

Tuesday 4th April (place: UCD Ag. 1.01 ) 3:00pm

Speaker: S. Gardiner
Title: Analytic content and the isoperimetric inequality

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

Speaker: A. McCluskey (NUIG)
Title: A framework for the notion of betweenness

Tuesday 18th April (place: UCD Ag. 1.01 ) 3:00pm

Speaker: J. Buckley (IMS Madrid; KCL)
Title: On the number of nodal domains of toral eigenfunctions

Tuesday 18th April (place: UCD Ag. 1.01 ) 4:15pm

Speaker: A. T\"ornquist (Copenhagen)
Title: Fraisse theory: The Poulsen simplex and other examples

Tuesday 25th April, 2017 (place: UCD Ag 1.01 ) 4.15pm

Speaker: M. Golitsyna
Title: Sequences of real-rooted polynomials that converge in three points and the Laguerre-Polya class

Tuesday 2nd May, 2017 (place: UCD Ag 1.01 ) 4.15pm

Speaker: R. Smith
Title: Approximation of norms in preduals of Lorentz spaces

Tuesday 9th May, 2017 (place: UCD Ag 1.01 ) 4.15pm

Speaker: C. Gilmore
Title: Growth rates of frequently hypercyclic harmonic functions

Abstract The notion of frequent hypercyclicity stems from ergodic theory and has been an active area of research since it was introduced by Bayart and Grivaux (2004). Many natural continuous linear operators are frequently hypercyclic, for instance the differentiation operator on the space of entire functions. We will begin by recalling some basic examples and the pertinent notions of frequent hypercyclicity. We then consider the partial differentiation operator acting on the space of harmonic functions on $R^n$. Our primary goal is to identify sharp growth rates, in terms of the $L^2$-norm, of harmonic functions that are frequently hypercyclic vectors for the basic partial differentiation operator. This answers a question posed by Blasco et al. (2010). This is joint work with Eero Saksman and Hans-Olav Tylli.