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13th
European Intensive Course on Complex Analysis and applications to partial differential equations |
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Departamento de Matemática,
Universidade de Coimbra, Portugal
Departamento de Matemática,
Universidade de Aveiro, Portugal
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| Goal of the Course | |||||||||||||||||||||||||||||||||
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This intensive course follows the twelve held at the Universities of Coimbra and Aveiro from 1995 to 2006 (1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006) 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 23rd of June 2007. |
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| Title: ORTHOGONAL POLYNOMIALS OF SEVERAL VARIABLES | |||||||||||||||||||||||||||||||||
| Summary: While orthogonal polynomials in one variable already have numerous and varied applications in many fields of science, the theory of orthogonal polynomials in two and more variables is applied insufficiently widely. The study of orthogonal polynomials of several variables goes back to C. Hermite ( 1865). Later on, books of P.Appell (1881), P. Appell & K. de Feriet (1926) and papers of D. Jackson (1938) and T. Koornwinder (1975) introduced a considerable number of results on this theory. With the intention of making this seminar useful to a wide audience, we shall introduce standard matrix notation in order to present general properties of orthogonal polynomials of several variables and specially of two variables over a domain with arbitrary weight. Following mainly the monographs of P.K. Suetin (1988) and Ch.F. Dunkl & Y. Xu (2001), a systematic exposition and detailed discussion of many important results, examples and applications on the theory of orthogonal polynomials in two (continuous and discrete) variables is given. | |||||||||||||||||||||||||||||||||
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| Title: BASIC CLIFFORD ALGEBRA AND CLIFFORD ANALYSIS | |||||||||||||||||||||||||||||||||
| Summary: Abstract and practical definitions of Clifford Algebras Cl_{p,q,r}=R_{p,q,r}. Rotation in a euclidean plane, in a 3-dimensional euclidean space: C=R_{2,0,0}^+ and H=R_{3,0,0}^+ and in 4-dimensional spaces. The Dirac equation and spinors. Monogenic, hypermonogenic, Clifford holomorphic and Clifford analytical functions in R_{0,n,0}. Translation of Clifford Analysis from R_{0,n,0} to R_{n+1,0,0}. | |||||||||||||||||||||||||||||||||
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| Title: CONJUGATE HARMONICITY IN EUCLIDEAN SPACE | |||||||||||||||||||||||||||||||||
Summary:
1. The real Clifford algebra R0,m+1 2. Monogenic functions versus self-conjugate differential forms 3. Conjugate harmonicity, harmonic primitives and monogenic primitives of mono- genic functions. 4. Monogenic r-forms versus harmonic r-forms 5. Bases for the space of monogenic homogeneous vector-(or para-)vector valued polynomials 6. Cauchy transforms and conjugate harmonicitymore |
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| Title: L-HOLOMORPHIC FUNCTIONS IN ELASTICITY FLUID DYNAMICS | |||||||||||||||||||||||||||||||||
Summary:
1. Lecture: About the notion of holomorphy
2. Lecture: Quaternionic operator calculus - Hodge type decompositions
3. Lecture: Fluid flow problems
4. Lecture: problems in Elasticity
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| Title: CLIFFORD ANALYSIS METHODS FOR TIME EVOLUTION EQUATIONS | |||||||||||||||||||||||||||||||||
Summary:
1. Heat equation and related topics
2. Scattering
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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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REGISTRATION FORM (please copy into email)
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| Rafael Hernández Heredero, Universidad Politécnica de Madrid | |||||||||||||||||||||||||||||||||
| Odete Ribeiro, Departamento de Matemática, Instituto Politécnico de Viseu | |||||||||||||||||||||||||||||||||
| Márcio Sacramento, Departamento de Matemática, Instituto Politécnico de Viseu | |||||||||||||||||||||||||||||||||
| Ulises Fidalgo Prieto, Universidade de Aveiro | |||||||||||||||||||||||||||||||||
| Luis Garza, Universidad Carlos III de Madrid | |||||||||||||||||||||||||||||||||
| Norman Gürlebeck, Friedrich Schiller UniversityJena, Germany | |||||||||||||||||||||||||||||||||
| Luís Cotrim , Instituto Politécnico de Leiria | |||||||||||||||||||||||||||||||||
| Anabela Monteiro Paiva, Universidade da Beira Interior | |||||||||||||||||||||||||||||||||
| Maria da Neves Vieiro Rebocho, Univ. Beira Interior/Univ. Coimbra | |||||||||||||||||||||||||||||||||
| Ana Isabel Gonçalves Mendes, Instituto Politécnico de Leiria | |||||||||||||||||||||||||||||||||
| Herbert Dueñas Ruiz, Universidad Carlos III de Madrid | |||||||||||||||||||||||||||||||||
| Judit Mínguez Ceniceros, Universidad de La Rioja | |||||||||||||||||||||||||||||||||
| Sven Ebert, University of Freiberg | |||||||||||||||||||||||||||||||||
| Frank Dierich, University of Freiberg | |||||||||||||||||||||||||||||||||
| Matti Schneider, University of Freiberg | |||||||||||||||||||||||||||||||||
| André Schlichting, University of Freiberg | |||||||||||||||||||||||||||||||||
| Juliane Mueller , University of Freiberg | |||||||||||||||||||||||||||||||||
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| With support from CMUC (Centro de Matemática da Universidade de Coimbra), UI&D "Matemática e Aplicações" da Universidade de Aveiro, and the Socrates programme |
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