[ SCOPE
 PROGRAM
 ABSTRACTS
 WHERE
 REGISTRATION/HOTELS
 PARTICIPANTS
 SUPPORT
 ORGANIZERS
 POSTER
 RELATED EVENTS
]
SCOPE
The aim of this meeting, the fifth one after similar meetings in 2000,
2004,
2008, and 2012, is to bring together
people interested in complex approximation theory mainly from France and Belgium,
but also from other european countries.
Subjects covered by the 2016 meeting include : orthogonal polynomials,
rational approximation, numerical aspects of approximation,
approximation by radial basis functions, low rank Tensor
approximation in high dimensions, asymptotic analysis
and RiemannHilbert problems, random matrices,
quadrature formulas,....
PROGRAM
(*) Posters presented by: Paraskevi Roupa (U. Athens),
Matteo Briani (U. Anvers), Olivier Sète (U. Oxford), Konstantin Usevich
(U. Grenoble), Benjamin Fahs (UC Louvain), Thomas Hélart (U. Lille).
TITLES AND ABSTRACTS

Annie Cuyt (U. Antwerp, Belgium):
Sparse Interpolation
Abstract.

Sylvain Chevillard (INRIA Sophia Antipolis):
An inverse magnetization problem in geosciences
Abstract.
When rocks are heated (typically when they are formed, or after subsequent alteration), they can become magnetized by the ambient magnetic field. This remanent magnetization is used to study important processes in Earth sciences, since it provides records of past variations of the geodynamo. It has been used, e.g., to study motion of tectonic plates and geomagnetic reversals.
This magnetization itself produces a weak magnetic field. SQUID microscopes are sensitive instruments, able to measure the field produced by thin slabs of magnetized rocks. More precisely, it can measure the vertical component of the magnetic field on a plane slightly above the sample, with a good spatial resolution.
The problem of recovering the magnetization distribution from the measurements provided by a SQUID microscope is severely illposed. However, an interesting quantity, namely the total net moment of the magnetization can, in theory, be recovered. This is already an important information for geoscientists, and not easy to measure with usual magnetometers.
We will present some properties of the magnetizationtofield map and of the corresponding adjoint operator. We formulate a bounded extremal problem whose solution is a function phi such that the integral of phi against the measured field should provide one with a good approximation of the desired net moment. If time permits, we will also present an alternate method based on asymptotic formulas, which is accurate when the measurements are made on a fairly large square.

Tom Claeys (UC Louvain la Neuve, Belgium):
Thinned random matrix eigenvalues and conditional probabilities
Abstract. Randomly incomplete, or thinned, spectra of random matrices were introduced by Bohigas and Pato. On one hand, one can study statistical properties of the incomplete spectrum. On the other hand, it is natural to investigate what the incomplete spectrum tells us about the complete spectrum. For instance, conditioning on a gap in the incomplete spectrum, what can we say about the complete spectrum? I will present identities in terms of orthogonal polynomials on the unit circle and Toeplitz determinants, and I will discuss asymptotic results as the size gets large.
The talk will be based on joint work with Christophe Charlier.

Albert Cohen (U. Paris VI):
Algorithms for high dimensional interpolation
Abstract. There exists many classical methods for interpolating a function of one or several variables
Practically all of these methods however face difficulties when considering functions of a large number of
variable. We shall discuss and compare two approaches that can handle high dimensional data, the first
based on Gaussian processes and the second based on sparse polynomial expansions. Both approach
give rise to adaptive greedy algorithms in which the interpolation points are chosen in a sequencial manner,
and which are still not well understood from a theoretical point of view.

Stefano de Marchi (U. Padova, Italy):
Polynomial approximation on Lissajous curves on the dcube
Abstract.
We present our recent studies on Lissajous curves in the dcube
that generate algebraic cubature formulas on a special family of rank1 Chebyshev lattices. These formulas
are used to construct hyperinterpolation polynomials via a single 1dimensional Fast Chebyshev
Transform (computed by the Chebfun package). In the case d = 2, 3
we are able to compute discrete extremal sets of Fekete and Leja type
for polynomial interpolation as well. Applications arise in the framework of Lissajous sampling
for MPI (Magnetic Particle Imaging). Joint work with L. Bos and M. Vianello.

Alfredo Deano (U. Kent, England)
Semiclassical Laguerre polynomials: asymptotics and applications
Abstract. Semiclassical Laguerre polynomials, orthogonal with respect to the weight function $x^{\lambda} \exp(x^2+tx)$ on $[0,\infty)$, appear in connection with
solutions of the Painlevé IV differential equation, and also in random matrix theory, as a deformation of the LUE ensemble. In this talk we will consider
their asymptotic behaviour as the degree tends to infinity, uniformly with respect to the other parameters, $t$ and $\lambda$. This analysis complements
previous results on the structure of the recurrence coefficients and on their large $t$ asymptotics given by Clarkson and Jordaan (2013) and Clarkson,
Jordaan and Kelil (2015).
This is joint work with Nicholas Simm (Mathematics Institute, University of Warwick, UK).

Antonio Duran (U. Sevilla, Spain):
Beyond the classics: Krall and exceptional orthogonal polynomials
Abstract. Krall and exceptional polynomials are two of the more important extensions of the classical families of Hermite, Laguerre and Jacobi. On the one hand, Krall or bispectral polynomials are orthogonal polynomials which are also eigenfunctions of a differential operator of order bigger than two. The first examples were introduced by H. Krall in 1940, and since the eighties a lot of effort has been devoted to this issue. If we consider difference operators, the first examples of Krall discrete polynomials were introduced by the author in 2012 using certain Christoffel transforms of the classical discrete weights. The first part of this talk will be devoted to show how these Krall discrete polynomials can be constructed. On the other hand, exceptional polynomials are orthogonal polynomials which are also eigenfunctions of a second order differential operator, but they differ from the classical polynomials in that their degree sequence contains a finite number of gaps. In mathematical physics, these functions allow to write exact solutions to rational extensions of classical quantum potentials. Taking into account the above definitions, it is scarcely surprising that no connection has been yet found between bispectral and exceptional polynomials. However, at the discrete level (difference operators), something very exciting happens: Duality interchanges Krall discrete and exceptional discrete polynomials. The second part of this talk will be devoted to explore some of the consequences of this unexpected connection.

Dries Stivigny (KU Leuven, Belgium):
Smallest eigenvalue distribution for products of random matrices.
Abstract. We study the distribution of the smallest eigenvalues for certain classes of
positivedefinite Hermitian random matrices, in the limit where the size of
the matrices becomes large. The limiting distributions that we will study
can be expressed as Fredholm determinants of certain integral operators, and
generalize in a natural way the extensively studied hard edge Bessel kernel
determinant. We will express the logarithmic derivative of those Fredholm
determinants identically in terms of a 2x2 RiemannHilbert problem, and
use this representation to obtain the socalled large gap asymptotics.
This is joint work with Tom Claeys and Manuela Girotti.
LOCATION OF THE WORKSHOP
The workshop takes place at
the Université de Lille 1, Salle de Réunion, Bâtiment M2 (first floor), Cité
Scientifique, Villeneuve d'Ascq, in the north of France. This lecture hall is
located in the main building M2 of the department of mathematics. Some useful links
REGISTRATION AND ACCOMODATION
There is no inscription fee, but registration before April 30 is mandatory, please use the following form.
The update of the list of participants
will be done manually on a regular basis. There will be a poster session.
Please let us know as soon as possible and before April 30
if you want to present a poster.
Most of the speakers will be at Hotel CALM in downtown Lille. There is also a hotel on the campus near the department of Mathematics called ASCOTEL. See this link for a complete list of hotels in Lille.
SOCIAL EVENTS
On Thursday May 19 in the evening we intend to go to some restaurant for those participants who arrive on time in Lille. Please tell us if you are interested to join us.
Some other events for those staying more time in Lille:
 Official website of the Lille tourism and convention bureau.
 Roubaix  La Piscine  Musée d'Art et d'Industrie de Roubaix André Diligent: an artdeco museum in a former swimming pool. Special exibition "BraïtouSala (18851972), l’élégance d’un monde en péril."
 Palais des Beaux Arts de Lille:
biggest french general art museum in the north of Paris, situated
downtown Lille at the place de la république (metro république). Special
exposition ZEP (bande dessinée). Special exposition "Les Belles du Nord".
 Villeneuve d'Ascq  Modern Art Museum, situated in the northwest of Villeneuve d'Ascq. Special exposition Amedeo Modigliani.
 Opera de Lille: L'ORFEO.
SUPPORT FOR THE WORKSHOP
We kindly acknowledge support from the
Laboratoire Paul Painlevé UMR 8524 (Université Lille 1  CNRS)


Laboratoire de Mathématiques Pures et Appliquées
Joseph Liouville (Université Littoral  CNRS)


Fédération de Recherche Mathématique du Nord Pas de Calais


LABEX CEMPI 

SMAISIGMA  interest group of the french mathematical society of applied mathematics


ORGANIZERS
Ana C. Matos (Laboratoire Painlevé, Lille),
Abderrahman Bouhamidi (LMPA, Calais),
Karl Deckers (Laboratoire Painlevé, Lille),
Bernd Beckermann (Laboratoire Painlevé, Lille).
RELATED EVENTS
Conference on Random matrices, free probability and determinantal processes, May 24, 2016, Lille
International Workshop SIGMA'2016, colloque organisé
par la SMAISIGMA
du 31 Octobre au 4 novembre 2016 au CIRM (Luminy).
BB (bbecker@math.univlille1.fr), Mai 10, 2016
Thanks to Stefano de Marchi for the logo.