# 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