Speakers
Courses and invited speakers
 Wolfgang Arendt
 Universität Ulm

Vectorvalued holomorphic functions and oneparameter semigroups
 Eva Gallardo Gutierrez
 Universidad Complutense de Madrid

An introduction to Rota's universal operators: properties, old and new examples and future issues
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Eva Gallardo Gutierrez
An introduction to Rota's universal operators: properties, old and new examples and future issues
The Invariant Subspace Problem for (separable) Hilbert spaces is a longstanding question and the use of universal operators in the sense of Rota has been one tool for studying the problem. Recall that a Hilbert space operator is called universal (in the sense of Rota) every operator on a separable Hilbert space is similar to a multiple of the restriction of
the universal operator to one of its invariant subspaces. In this series of lectures, we will
focus on Rota’s universal operators, studying their main properties and exhibiting some
old and recent examples. Special attention will be given to the closed subalgebra, not
always the zero algebra, of compact operators in the commutant of some of the Rota’s
universal operators exhibited. Consequences and questions related will be also addressed.
 John McCarthy
 Washington University in St. Louis

Noncommutative function theory and noncommutative spectral theory
 Jonathan Partington
 University of Leeds

Truncated Toeplitz operators and their spectral theory
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Jonathan Partington
Truncated Toeplitz operators and their spectral theory
Truncated Toeplitz operators and their asymmetric versions
are considered in the context of reflexive Hardy spaces on the halfplane.
They are shown to be equivalent by extension to Toeplitz operators with
particular 2by2 matrix symbols. From this, various results on their spectral
properties can be proved.
Joint work with Cristina Câmara (Lisbon)
 Marco Peloso
 Università Statale di Milano

(Ir)Regularity of the Bergman projection on domains in C^n and related problems in one complex variable
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Marco Peloso
(Ir)Regularity of the Bergman projection on domains in C^n and related problems in one complex variable
In this talk I will present some recent results on the (ir)regularity
of the Bergman projection on some domains in C^2, called worm domains.
Such analysis is done by a reduction to weighted Bergman projections in
one complex variables. I will illustrate some of the problems that arise in
this context, some solved, many still open.
 Alexei Poltoratski
 University Texas A&M

Spectral Problems and Krein  de Branges theory
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Alexei Poltoratski
Spectral Problems and Krein  de Branges theory
We discuss some of the recent applications of the Krein  de Branges theory of Hilbert spaces of entire functions to spectral problems for differential operators and canonical systems.
 Stefan Richter
 University of Tennessee in Knoxville

Weak products, Hankel operators, and invariant subspaces
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 Richard Rochberg
 Washington University in St. Louis

A distance function on reproducing kernel Hilbert spaces
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Richard Rochberg
A distance function on reproducing kernel Hilbert spaces
If H, a space of functions on a set X, is a Hilbert space with reproducing kernel, then there is an induced metric δ defined on X. If H is the Hardy space, but only in that case, then δ is the classical pseudohyperbolic metric. In general δ describes the scale on which functions in, or related to, H can vary. For instance any multiplier of H is automatically a Lipschitz function in this metric. The infinitesimal version of this metric is the curvature invariant of CowenDouglas theory.
In these talks I will introduce the metric and develop its basic properties. I will then discuss places where the metric is a useful tool in studying H. Those include descriptions of interpolating sequences, the search for analytic structure in the spectrum of the multiplier algebra of H, and the study of the possibility of isometric embeddings in complex balls.
Proposed talks
 Corentin Avicou
 Université Claude Bernard Lyon 1

Semigroups of composition operators on the Hardy space view abstract
Corentin Avicou
Semigroups of composition operators on the Hardy space
Composition operators on the Hardy space $H^2(mathbb D)$ have been deeply studied over the past decades. Yet, compute the norm of such operators is still hard. Keeping this in mind, we will introduce an appraoch to this question using semigroups. We will see that the generator of such a semigroup has a very specific expression and we will give a condition for such an operator to generate a semigroup of composition operators on $H^2(mathbb D)$. We will deal with the analyticity and compactness of this semigroups.
 Davide Barbieri
 Universidad Autonoma de Madrid

Modular characterization of reproducing systems in spaces invariant under unitary actions of discrete groups view abstract
Davide Barbieri
Modular characterization of reproducing systems in spaces invariant under unitary actions of discrete groups
The notions of frames and Riesz bases, together with their reproducing formulas, can be extended to socalled L^2Hilbert modules. These are modules over a von Neumann algebra, endowed with an inner product which takes values in a space of measurable unbounded operators having finite absolute trace. The developed theory allows in particular to characterize ordinary reproducing systems in Hilbert spaces possessing general discrete groups invariances. More precisely, given a unitary representation P of a discrete group on a separable Hilbert space H, any closed subspace of H that is invariant under P can be obtained as closed span of orbits of a countable family of generators. By constructing an appropriate class of isometries from H to an L^2Hilbert module over the group von Neumann algebra, one can prove that such a family of orbits forms a frame (Riesz basis) in H if and only if the isometric image of the generators forms a frame (Riesz basis) in the corresponding module. Special cases are the characterizations of reproducing systems in shiftinvariant spaces obtained by De Boor, DeVore, Ron and Shen in the 90's with integer translations over L^2(R), and later extensions to discrete abelian groups. When the group is not abelian, Pontryagin duality is not available, but a natural replacement for the character group is the group von Neumann algebra. Its predual, that is isomorphic to the socalled Fourier algebra, is actually the target space of the considered L^2modular inner products, which generalize the standard tool of shiftinvariant spaces theory known as bracket map.
This is a joint work with E. Hernández, J. Parcet and V. Paternostro
 Hassan Jolany
 university of lille1

conical Kahler ricci flow on C^n view abstract
Hassan Jolany
conical Kahler ricci flow on C^n
We consider the canonical measure of singular subspaces of C^n along kahler ricci flow. We extend parabolic Schwartz lemma along conical ricci flow.
 Karmouni Mohammed
 University SIDI MOHAMMED BEN ABDELLAH

On algebric and analytic core view abstract
Karmouni Mohammed
On algebric and analytic core
 Alessandro Monguzzi
 Free researcher

Hardy spaces and the Szego projection on nonsmooth worm domains view abstract
Alessandro Monguzzi
Hardy spaces and the Szego projection on nonsmooth worm domains
In this talk I will define Hardy spaces on nonsmooth worm domains and study the associated Szego projection operator. Worm domains are domains in C^2 of primary importance since they are source of counterexamples to many classical conjectures.
 KarlMikael Perfekt
 Norwegian University of Science and Technology NTNU

On weak factorizations of and integration operators on Hardy spaces of Dirichlet series view abstract
KarlMikael Perfekt
On weak factorizations of and integration operators on Hardy spaces of Dirichlet series
To be announced.
 Giulia Sarfatti
 University of Bologna

Quaternionic Hankel operators view abstract
Giulia Sarfatti
Quaternionic Hankel operators
In this talk we introduce Hankel operators in the quaternionic
setting. We show that bounded Hankel operators on the Hardy space of
slice regular functions of a quateronic variable can be characterized
in terms of quaternionic BMO functions and of Carleson measures. As a
consequence of our characterisation result we get an analog of
Fefferman Theorem.
We conclude showing how Hankel theory can be exploited to measure the
L^{infty} distance of an L^{infty} quaternionic function from the
space of bounded slice regular functions.
 Riikka Schroderus
 University of Helsinki

The spectra of linear fractional composition operators on weighted Hardy spaces view abstract
Riikka Schroderus
The spectra of linear fractional composition operators on weighted Hardy spaces
 Aron Wennman
 KTH Royal Institute of Technology

A Critical Topology for Carleman Sobolev Classes view abstract
Aron Wennman
A Critical Topology for Carleman Sobolev Classes
Microscopic behavior of 2D Coulomb gas near singular points
 Nina Zorboska
 University of Manitoba

Hyperbolic distortion, finite Blaschke products and uniform local univalence view abstract
Nina Zorboska
Hyperbolic distortion, finite Blaschke products and uniform local univalence
The local hyperbolic distortion of an analytic selfmap of the unit disk describes the geometric behaviour of the map. It is also closely related to the characterization of the properties of composition operators acting on some spaces of analytic functions.
In my talk I will mention few results on the connections between the boundary regularity of an analytic selfmap of the unit disk and the boundary limits of its hyperbolic distortion, and the connections to uniform local univalence. In particular, I will give a characterization of the class of finite Blaschke products via the boundary behaviour of a weighted hyperbolic distortion.