# 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

*Speaker:* E. Mihailescu (Romanian Academy)

*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.