2006 IRAN

(Version française de la page)

Scientific reports Michel Jambu (French, pdf)
Mehrdad Shahshahani (pdf)

 

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CIMPA-UNESCO-IRAN School

Recent Topics in Geometric Analysis

Objectives :
The interaction of Analysis and Differential Geometry has led to some of the most striking achievements of mathematics during the last few decades.
Analytic approaches to problems in Riemannian, pseudo-Riemannian or complex geometry and topology has given rise to very powerful tools in analysis.  The development of pseudo differential operators motivated by the index theorem, the existence of solutions to the Monge-Ampère equation and the Calabi conjecture, the Yamabe problem, Eells-Sampson theory and various rigidity results obtained via harmonic maps, the Ricci flow and Perelman’s program for the proof of the Poincaré conjecture are illustrative of the depth and breadth of this field.

The main objectives of the school are:

  1. To provide an introduction to some current problems in Geometric Analysis for young researchers and postgraduate students and present recent advances and perspectives in these topics for more specialized researchers
  2. To promote exchanges and collaborations between mathematicians from Iran and those from neighboring countries and to encourage the establishment of professional relationships and collaborative research between mathematicians from the region and experts from Europe.  
Particular attention will be given to graduate and postgraduate students from the region. This event will give them the opportunity to be introduced to some current fields of research and to set up contacts with experts from Europe and elsewhere.

Coordinators:
Ahmad EL SOUFI (University of Tours, France).
Mehrdad SHAHSHAHANI (IPM –Tehran, Iran)

Organizing Committee:
Ahmad El Soufi (University of Tours, France), Alireza Ranjbar-Motlagh (Sharif University, Tehran, Iran), Mehrdad Shahshahani (IPM-Tehran, Iran).

Scientific Committee:
Gérard Besson (CNRS and University of Grenoble I, France), Gilles Carron (University of Nantes, France), Bruno Colbois (University of Neuchatel, Switzerland), Thierry Coulhon (University of Cergy-Pontoise, France), Régis Monneau (ENPC, France), Frank Pacard (University of Paris XII, France), Tristan Rivière (ETH-Zürich, Switzerland).

Working languages:
English

Date and location :
May 20 – June 2, 2006, IPM – Tehran, Iran

Scientific programme: (Abstracts) (Schedule)

  • Gilles Carron, University of Nantes, France
    Lectures (I-III): Cohomology and Square Integrable Harmonic Forms an Non-Compact Manifolds

  • Bruno Colbois, University of Neuchâtel, Switzerland
    Lectures (I-IV): The Spectrum of the Hodge-De Rham Laplacian

  • Thierry Coulhon, University of Cergy-Pontoise, France
    Lectures (I-III): Heat Kernels and the Riesz Transform

  • Amir Daneshgar, Sharif University of Technology, Iran
    Spectral Geometry in Discrete Case. Some Results, Applications and Speculations

  • Eaman Eftekhary, Harvard University, USA
    -Lecture 1: Heegaard Floer Homology and its Applications
    - Lecture 2: Gluing Formulas in Heegaard Floer Homology
    - Lecture 3: Gromov-Witten Invariants and Counting Holomorphic Curves in Calabi-Yau Threefolds

  • Ahmad El Soufi, University of Tours, France
    Lecture (I-IV): Spectral Geometry

  • Michel Jambu, University of Nice and CIMPA, France
    Hypergeometric Integrals

  • Peter Markowich, University of Vienna, Austria
    TBA

  • Hossein Movasati, Ochanomizu University, Japan
    Lecture (I-III): Hodge Structures, Polarization, and the Period Mapping

  • Alisher Muminov, Institute of Applied Physics, Uzbekistan
    A Classical Model of Spin 1 Massless Particle

  • Frank Pacard, University of Paris XII, France
    - Lectures (I-II-V): The Singular Yamabe Problem
    - Lectures (III -IV): Singularly Perturbed Elliptic Equations

  • Alireza Ranjbar-Motlagh, Sharif University of Technology, Iran
    Lectures (I-II): Isoperimetric Inequalities, Sobolev Constants and Heat Kernels

  • Mehrdad Shahshahani, IPM, Iran
    Griffiths Uniformization and the Braid Group

  • Ashot Shahverdyan, Joint Institute for Nuclear Research, Armenia
    TBA

  • Zafar Turakulov, Institute of Nuclear Physics, Uzbekistan
    - Lecture 1: Singular Curves on Manifolds of Dimensions Two and Three
    - Lecture 2: Bare Singularities in General Relativity
    - Lecture 3: Geometric Analysis and Separability of Maxwell Equations

Prerequisites :
For most of courses, the prerequisites consist in an introduction to differential Geometry and elliptic PDE theory. Participants in the School are expected to be mainly research students (M. Phil. and Ph.D. candidates), post-doctoral students and researchers from Iran and neighbouring countries wishing to become initiated or to improve their knowledge in Geometric Analysis.

 Local web site : http://www.ipm.ac.ir/ga2006

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