12th
European Intensive Course on Complex Analysis
and
Applications
to Partial Differential Equations |
June 26 to July 7,
2006 |
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Goal
of the Course |
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Organizers |
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Schedule
of the course |
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List
of Participants |
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Financial
Support |
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Registration Form |
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Sponsors |
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Goal of the Course |
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This intensive course follows the
eleven held
at the Universities of Coimbra
and Aveiro from 1995 to 2005 (1995,
1996,
1997,
1998,
1999,
2000,
2001,
2002,
2003,
2004,
2005) and there are plans for intensive courses
in the following years. The
lecture
notes of some of the courses have been published in Coimbra and
others are in print.
This
intensive course will have a total of 40 hours of lectures and is at
postgraduate level. Lecturers will have time available to discuss with
the students. Successfully participating students will get a
certificate. This course is organized by the Universities of Coimbra and
Aveiro with the same goals as the ones organized under the Socrates/Erasmus
Intensive Program of Higher Education, and is opened to all young mathematicians interested in Complex
Analysis and its applications.
There
will be a
Workshop
on "Applications and Generalizations of Complex Analysis" on
the 1st of July 2006. |
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First Week
(Coimbra University) |
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June
26 |
June
27 |
June
28 |
June
29 |
June
30 |
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Opening
session
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9h30m-10h |
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Lopez Lagomasino |
10h-12h30m |
10h-12h30m |
10h-12h30m |
10h-12h30m |
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Irene
Falcão |
14h30m-17h |
14h30m-17h |
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14h30m-17h |
10h-12h30m |
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Second Week
(Aveiro University) |
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July
03
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July 04
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July 05
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July 06
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July 07
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Martínez Finkelshtein |
10h-12h30m |
10h-12h30m |
10h-12h30m |
10h-12h30m |
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Sebastian
Bock |
14h30m-17h |
14h30m-17h |
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14h30m-17h |
10h-12h30m |
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Title: The
Riemann-Hilbert technique for Polynomials Orthogonal on the Unit
Circle |
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Summary: The
Riemann-Hilbert method has proved to be extremely fruitful in the
analysis of the orthogonal polynomials. It has allowed to answer
many long standing questions in the theory, as well as has developed
as a natural tool for the solution of the so-called inverse
problems. Its application is especially elegant in the case of the
orthogonality on the unit circle. The main goal of this course is to
provide the main ingredient of this rapidly developing technique and
to illustrate its applications in the asymptotic analysis of these
polynomials. The course intends to be self-contained: only some
basic facts from the Complex Analysis and Operator Theory are
needed. |
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Title:
Multi-Orthogonal Polynomials. |
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Summary: Definition
of multiple orthogonal polynomials. Normality of
multi-indices. The $m+2$ terms recurrence relation satisfied
by multiple orthogonal polynomials. Interlacing property of
zeros.Spectral properties of the matrix associated with the
recurrence relation and its connection with the location of
zeros of multiple orthogonal polynomials. Nikishin systems
of measures. Ratio and n-th root asymptotic behavior of
Nikishin multiple orthogonal polynomials. Application to
vector rational approximation of Nikishin systems and to
simultaneous quadrature formulas. |
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Title:
Numerical conformal mappings and generalizations: part I |
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Summary:
One of the most important aspects of conformal mappings
is the persistence of solutions of Laplace's equation. This property is
very useful in physical problems involving Laplace's equation, such as
electrostatics, heat flow, fluid mechanics, etc. In fact, once the
equation has been solved on a particular domain, the solution is
immediately known on all domains which can be mapped onto the original via
a one-to-one analytic function. |
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There are several methods for solving conformal
mapping problems. In this course we will present two numerical methods: i)
the
Schwarz-Christoffel
formula for
the computation of conformal maps to polygonally bounded regions; ii) the
so-called Bergman kernel method (1921), based on
the reproducing property of the kernel function. |
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The construction of reproducing kernel functions is
not restricted to real 2-dimension. Indeed, the two complex variable case
has been already considered by Bergman himself. Moreover, results
concerning (and restricted to) the construction of Bergman kernel
functions in closed form for special domains in the framework of
hypercomplex function theory (which not supposes the consideration of
spaces corresponding to even real dimensions) can be found in
recent papers. (Constales and Krausshar, 2002, Vasilevski, 2000). They
suggest that BKM can also be extended to mapping problems in higher
dimensions, particularly 3-dimensional cases. We will present some recent
results (2006) concerning such a generalization. |
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Title:
Numerical conformal mappings and generalizations: part II |
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Summary: In this second part we will try
to close the gap between the theoretical background of the presented
numerical conformal mapping techniques and their practical
application. This part of the course is planned to be held as an
application-oriented and interactive seminar in the computer lab
using the computer algebra system Maple. |
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To motivate our work we start by studying
a well known practical example from fluid dynamics and show the
considerable advantages in solving physical problems by help of
conformal mappings. Afterwards we will use the theoretically
discussed techniques for the 2-dimensional complex case to evaluate
some selective mappings with respect to their conformal mapping
properties, the required computation expenditure and the obtained
approximation error. Finally some recent results in the
generalization of the complex BKM approach to the framework of
hypercomplex function theory will be presented and by help of an
appropriate and specially developed Maple software package utilized. |
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Living expenses can be partially covered for some
students if they do not have support from their own institution and if
there is enough money available. |
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| Name: |
| Affiliation: |
| I intend to participate in the Intensive Course: Yes/No |
| I intend to participate in the Workshop with a
communication ___ / without a communication __ |
| Tentative title: |
| I need an invitation letter: _____; for that purpose,
contact me via the e-mail:____________or by
fax:_______________________ |
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I need help with accommodation in Coimbra or Aveiro:_______ |
| Please send as soon as possible a short abstract of your
communication (in Latex, at most 10 lines) |
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Almeida, Elisabete Sousa. address. Instituto
Politecnico de Viseu, Viseu, Portugal. e.mail.
betty@mat.estv.ipv.pt. |
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Bock, Sebastian. address.
Bauhaus-Universität Weimar, Germany. e.mail.
bastian.bock@web.de. |
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Carvalho, José Manuel. address. Departamento de
Matemática da Faculdade de Ciências e Tecnologia da Universidade
Nova de Lisboa,
2829-516, Monte da Caparica.e.mail. jmprc@netcabo.pt. |
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Costas Santos, Roberto, Universidad Carlos III de
Madrid, Spain.
e.mail. rcostas@math.uc3m.es. |
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Cotrim,
Luís. address. Escola Superior de Tecnologia e Gestão do
I.P.L., Quinta do Seixo lote 1 - 4 Dto, 2410 Leiria, Portugal. e.mail.
lmsc@estg.ipleiria.pt. |
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Coutinho, Cláudia. address. Departamento
de Matemática da Universidade
de Aveiro, Portugal. e.mail. claudia.coutinho@mat.ua.pt. |
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Dueñas Ruiz, Herbert Alonso. address.
Universidad Carlos III de Madrid, Spain. e.mail. haduenasr@unal.edu.co. |
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Falcão, Irene. address.
Departamento de Matemática da Universidade do Minho, Campus de
Gualtar, 4710-057 Braga.e.mail. mif@math.uminho.pt. |
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Faustino, Nelson. address. Departamento
de Matemática da Universidade
de Aveiro, Portugal. e.mail. nfaust@mat.ua.pt. |
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Ferreira, Mílton. address. Departamento
de Matemática da Universidade
de Aveiro, Portugal. e.mail. mferreira@mat.ua.pt. |
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Garza Gaona, Luis Enrique. address. Universidad
Carlos III de Madrid, Spain. e.mail. luisgarzagaona@hotmail.com. |
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Jesus, Márcio Dinis do
Nascimento de. address. Instituto Politecnico de Viseu,
Escola Superior e Tecnologia de Viseu. e.mail.
mnasce@mat.estv.ipv.pt. |
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López Garcia, Abey. address. Universidad Carlos
III de Madrid, Spain.e.mail. abey.lopez@Vanderbilt.Edu. |
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López Lagomasino, Guillermo.
address. Departamento de Matemáticas, Universidad Carlos III de
Madrid, 28911 Leganés-Madrid, Spain. e.mail.
lago@math.uc3m.es. |
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Martinez-Finkelshtein,
Andrei. address. Dept. Estadistica y Matematica Aplicada, Universidad de Almeria, La Canada, 04120
Almeria, Spain. e-mail. andrei@ual.es. |
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Matos, José.
address. Departamento de Matemática do Instituto Superior
de Engenharia.
e.mail. jma@isep.ipp.pt. |
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Mendes, Ana Isabel. address.
Escola Superior de Tecnologia e Gestão do I.P.L., Quinta do Seixo
lote 1 - 4 Dto 2410 Leiria, Portugal. e.mail.
aimendes@estg.ipleiria.pt. |
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Paiva,
Anabela Monteiro. address. Departamento de
Matemática da
Universidade da Beira Interior, Av. Marquês D'Ávila e Bolama, 1, Covilhã.
e.mail. apaiva@noe.ubi.pt. |
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Pereira
de Sousa, Victor Luís. address. Instituto Politécnico
de Bragança, Escola Superior de Tecnologia e de Gestão de Bragança,
Ap. 134, 5301-857 Bragança, Portugal. e.mail. vitorsousa@ipb.pt. |
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Petronilho, José Carlos. address.
Departamento de Matemática da Universidade de Coimbra, Apartado
3008, 3000 Coimbra, Portugal. e.mail. josep@mat.uc.pt. |
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Prieto, Ulises Fidalgo. address. Departamento de Matemáticas,
Universidad Carlos III de Madrid, 28911 Leganés-Madrid, Espanha.
e.mail. ulisesfidalgoprieto@yahoo.es. |
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Rchid, Sidi. address. Departamento de
Matemática da Universidade
de Aveiro, Portugal. e.mail. . |
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Rebocho,
Maria das Neves. address. Universidade da Beira Interior,
Departamento de Matemática, Av. Marquês D'Ávila e Bolama, 1, Covilhã.
e.mail. mneves@noe.ubi.pt. |
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Ribeiro, Odete. address. Instituto Politecnico
de Viseu, Viseu, Portugal. e.mail.
odetecr@mat.estv.ipv.pt. |
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Rodrigues, Maria João.
address. Departamento de Matemática Aplicada da
Universidade do Porto.
e.mail. . |
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Vieira, Nelson Felipe Loureiro. address.
Departamento de Matemática da Universidade de Aveiro, Campus de
Santiago, 3810-193, Aveiro, Portugal. e.mail.
nvieira@mat.ua.pt. |
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With
support from
Centro
de Matemática da Universidade de Coimbra, UI&D "Matemática e
Aplicações" da Universidade de Aveiro, and the Socrates programme |
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