# Analysis Seminar Archive for 2013-14

**Tuesday 1st October, 2013 **
(place: UCD
Ag 1.01 )
4:00pm

*Speaker:* R. Smith

*Title:*Operators on C(K)-spaces and the `bishop' property

**Tuesday 8th October **
(place: TCD
WR20 )
2:30pm

*Speaker:* D. McConnell

*Title:*The Dauns-Hofmann theorem and tensor products of C*-algebras

**Tuesday 8th October **
(place: TCD
WR20 )
4:00pm

*Speaker:* R. Timoney

*Title:*Kadison-Singer solution by Marcus, Spielman and Srivastava

**Tuesday 15th October, 2013 **
(place: UCD
Ag 1.01 )
4:00pm

*Speaker:* M. Ghergu

*Title:*Stable solutions for Lane-Emden systems

**Tuesday 29th October, 2013 **
(place: UCD
Ag 1.01 )
4:00pm

*Speaker:* S. Gardiner

*Title:*Universal Taylor series and the Picard property

**Tuesday 5th November, 2013 **
(place: UCD
Ag 1.01 )
4:00pm

*Speaker:* R. Levene

*Title:*Distance formulae

**Tuesday 12th November **
(place: UCD
Ag. 1.01 )
3:00pm

*Speaker:* C. Boyd

*Title:*Geometry of the Marcinkiewick function space

**Tuesday 12th November **
(place: UCD
Ag. 1.01 )
4:15pm

*Speaker:* H. Render

*Title:*Remarks on the Khavinson-Shapiro conjecture

**Tuesday 19th November **
(place: UCD
Ag 1.01 )
4:00pm

*Speaker:* A. Brown

*Title:*TBA

**Tuesday 26th November, 2013 **
(place: TCD
WR20 )
4:00pm

*Speaker:* J. Boland

*Title:*Approximately hypercyclic operators

**Tuesday 3rd December **
(place: TCD
WR20 )
2:30pm

*Speaker:* N. Snigireva

*Title:*Deformation spaces for iterated function systems

**Tuesday 3rd December **
(place: TCD
WR20 )
4:00pm

*Speaker:* M. Mackey

*Title:*A random constant

**Tuesday 4th February, 2014 **
(place: TCD
WR20 )
4.00

*Speaker:* R. Timoney

*Title:*What are nc-holomorphic functions?

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

*Speaker:* R. Smith

*Title:*Towards a new theory
of boundaries of Banach spaces?

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

*Speaker:* V. Bible

*Title:*Smooth Renormings of
the Injective Tensor Product

**Tuesday 18th February, 2014 **
(place: TCD
WR20 )
4.00

*Speaker:* D. McConnell

*Title:*Sheaves of C*-algebras

**Tuesday 25th February **
(place: UCD
Ag. 1.01 )
3:00pm

*Speaker:* T. Carroll (UCC)

*Title:*Modelling the voltage drop in an on-chip power distribution network

**Tuesday 25th February **
(place: UCD
Ag. 1.01 )
4:15pm

*Speaker:* M. Ghergu

*Title:*Behavior around
singularities for elliptic systems

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

*Speaker:* J. Ratzkin (Cape Town \& UCC)

*Title:*Isoperimetric
inequalities for extremal Sobolev functions

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

*Speaker:* S. Gardiner

*Title:*Universal expansions for holomorphic functions on multiply connected domains

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

*Speaker:* N. Snigireva

*Title:*Deformations spaces for Iterated Function Systems: Part II

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

*Speaker:* P. Hoffmann (NUIM)

*Title:*A result on the
intersection of certain sets of operator tuples

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

*Speaker:* S. Power (Lancaster)

*Title:*The rigidity of infinite graphs and crystals

**Abstract**
Geometric rigidity theory has its origins in the theory of bar-joint
linkages and Cauchy's rigidity theorem for convex simplicial
polyhedra. A foundational result of G. Laman in 1970 characterises
those finite simple graphs whose generic realisations in $R^2$ give
rigid bar-joint frameworks. Rigidity theory is also relevant in the
condensed matter physics of crystals in connection with low energy
phonon modes (rigid unit modes or RUMs) and displacive phase
transitions. Here the bar-joint frameworks in mathematical models
are infinite and crystallographic. I will talk about recent work
with Derek Kitson. On the generic side, we obtain generalisations
of the Cauchy and Laman theorems for non-Euclidean norms and for
infinite graphs. On the crystallographic side we characterise almost
periodic rigidity in terms of the RUM spectrum (or Bohr spectrum)
of the crystal framework. Geometric rigidity theory is a wonderfully
hybrid research area and in fact there is no known 3D counterpart
to Laman's combinatorial characterisation. Infinite frameworks and
their rigidity operators in particular invite methods from harmonic
analysis and operator theory.

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

*Speaker:* R. Harte

*Title:*The love knot

**Tuesday 1st April **
(place: UCD
Ag. 1.01 )
3:00pm

*Speaker:* M. Barnsley (Canberra)

*Title:*The largest set defined by an iterated function system

**Abstract**
In this lecture I will describe recent, to me very exciting, work
concerning natural extensions of attractors of iterated function
systems. The results so far are largely joint work with Andrew
Vince and Krystoph Lesniak. My goal will be to explain the new
ideas, the motivation for them, and the shape of the final "big
picture". But next, here, I quote the abstract of one of a number
of recent papers on the topic, to give some flavour. (The lecture
itself will be less technical.) We define and exemplify the
continuations and the fast basin of an attractor of an IFS. Then
we extend the standard symbolic IFS theory, concerning the dynamics
of a contractive IFS on its attractor, to a symbolic description
of the dynamics of a invertible IFS on a set that contains the fast
basin of a point-fibred attractor. We use this description to define
the fractal manifold, a new topological invariant, associated with
a point-fibred attractor of an IFS. We establish relationships
between the fractal manifold, the fast basin, and the set of
continuations of an attractor of an IFS. We establish how sections
of projections, from code space to an attractor, can be extended
to yield sections of projections from code space to the f-manifold
and to the basin. We use these sections to construct transformations
between fractal manifolds and show how their projections extend
fractal transformations between attractors to corresponding
transformations between fast basins of attractors. We present
practical conditions that control the topological properties, such
as continuity, of these transformations. We show how a section of
a projection from code space to an attractor yields a unique address
for each point on the fractal manifold, and how the set of addresses
provides a tiling of the manifold that project to diverse tilings
of the basin. Many standard tilings, and schemes for describing
them, as well as an abundance of new tilings, result from this new
unified approach to fractal tiling. This work has implications to
coding theory and numeration systems.

**Tuesday 1st April **
(place: UCD
Ag. 1.01 )
4:15pm

*Speaker:* C. Boyd

*Title:*Real Extreme Points in Spaces of Complex Polynomials

**Tuesday 15th April 15 **
(place: TCD
WR20 )
2:30pm

*Speaker:* J. McCarthy (St Louis)

*Title:*Non-commutative function theory

**Abstract**
A holomorphic function (in d variables) can be thought of as a
generalized polynomial in d variables. These functions work very
well when applied to d-tuples of commuting matrices or operators.
An nc function in d variables can be thought of as a generalized
non-commutative polynomial in d variables. These functions can
naturally be applied to d-tuples of non-commuting matrices or
operators. We shall talk about how this is useful when studying
matrix varieties, that is sets of tuples of matrices like
$\lbrace (X,Y) : X^2 + 2XY + 3YX = 0 \rbrace$; and when automorphisms
of symmetric domains in $\mathbb C^d$ extend to nc automorphisms
of the corresponding nc-domains.

**Tuesday 15th April 15 **
(place: TCD
WR20 )
4:00pm

*Speaker:* P. Mellon

*Title:*Holomorphic dynamics on finite dimensional spaces

**Tuesday April 22 **
(place: UCD
Ag. 1.01 )
3:00pm

*Speaker:* R. Ryan (NUIG)

*Title:*Regular holomorphic functions

**Tuesday April 22 **
(place: UCD
Ag. 1.01 )
4:15pm

*Speaker:* Y.-F. Lin (QUB)

*Title:*Group C*-algebras and
examples on exponential Lie groups

**Tuesday May 13th, 2014 **
(place: UCD
Ag1.01 )
4.00

*Speaker:* M. Klimek (Uppsala)

*Title:*Stochastic methods in multidimensional complex analysis

**Abstract**
For many decades probabilistic methods have been used in real
potential theory and - to a lesser extent - in complex analysis
in one variable. In the theory of functions of several complex
variables the situation is markedly different and while a number
of significant results based on stochastic approach have been
obtained over the years, they remain relatively isolated. In the
talk, a possible explanation of this state of affairs will be
combined with a concise survey of the field and presentation of
some new results.

**Tuesday May 20th **
(place: TCD
WR20 )
4.00pm

*Speaker:* M. Chica Rivas (Granada)

*Title:*The Bishop-Phelps-Bollabas modulus of a Banach space

**Abstract**
We introduce the Bishop-Phelps-Bollobas modulus of a Banach space
which measure, for a given Banach space, what is the best possible
Bishop-Phelps- Bollobas theorem in this space. We show that there
is a common upper bound for these moduli for all Banach spaces and
we present an example showing that this bound is sharp. We prove
some important properties about these moduli and some important
consequences of them.

**Tuesday June 17 **
(place: UCD
Ag. 1.01 )
3:00pm

*Speaker:* W. Werner (M\"unster)

*Title:*Inductive limits of JB*-triple systems

**Tuesday June 17 **
(place: UCD
Ag. 1.01 )
4:15pm

*Speaker:* E. Pernecka (Prague)

*Title:*Approximation properties, decompositions and bases in Lipschitz-free spaces