7th ISAAC Congress
7th ISAAC Congress
V.2. Stochastic Analysis
Organisers: D. Crisan (London), T. Lyons (Oxford)
Stochastic analysis aims to provide mathematical tools to describe and model high-dimensional random systems that arise in the study of stochastic differential equations and stochastic partial differential equations, infinite dimensional stochastic geometry, random media and interacting particle systems, super-processes, stochastic filtering, mathematical finance, etc. It has emerged as a core area of late 20th century mathematics and is currently undergoing quite rapid scientific development. The section will provide a forum for researchers working on the different aspects of stochastic analysis to present their findings, and to interact with people working in the wider area of analysis.
V.3. coercivity and functional inequalities
Organisers: D. Bakry (Toulouse), B. Zegarlinski (London)
The session intend to present an overview of a recent progress in coercive and functional isoperimetric inqualities and their applications to study long time behaviour of (sub-)elliptic problems, variety of probabilistic problems, analysis on groups as well as other related areas.
V. Applied Analysis
V.1. Inverse Problems
Organisers: Y. Kurylev (London), M. Yamamoto (Tokyo)
Inverse problems is a multidisciplinary subject having its firm origin in application of mathematics to such problems as search for oil, gas and other mineral resources, medical imaging, process monitoring in micro-biological, chemical and other industries, non-destructive testing of materials, to mention just few. Its mathematical underpinning stretches from discrete mathematics, to geometry, to computational methods with, however, the principal background being in analysis. In particular, the use of analytic methods makes it possible to address such issues of IP as their strongly non-linear nature and severe ill-posdnesss.
In recent years, these relations have made it possible to solve a number of long-standing inverse problems, including those with data on a part of the boundary, with significantly reduced requirements on regularity and the number of measurements, etc. These were based on the advancing and employing such topics in analysis as Carleman estimates for PDE's, harmonic and quasi-conformal analysis, global and geometric analysis, microlocal calculus and stochastic/probabilistic methods. In this section we intend to represent those progress by inviting the leading people in the area to give relevant talks.
V.4. Dynamical Systems
Organisers: J. Lamb, S. Luzzatto (both London)
Dynamical Systems aims to provide the mathematical tools to describe and model deterministic systems that arise in the study of ordinary Differential Equations and in the iteration of maps on smooth manifolds. A variety of ideas and techniques from Analysis and other areas come together to provide existence and classification results regarding the dynamical properties of systems from geometrical, topological, probabilistic points of view.
This section will provide a forum for high level researchers working mainly in Bifurcation Theory and Ergodic Theory to present their recent research and to discuss open problems and technical issues.
V.5. Functional Differential and difference equations
Organisers: L. Berezansky (Beer-Sheva), J. Diblik (Brno), A. Zafer (Ankara)
Scope of the session: Qualitative theory of functional differential and difference equations: stability, boundedness, oscillation, asymptotic behaviour, positive solutions, dynamic equations on time scales, applications to population dynamics.
V.6. Biomathematics
Organisers: R. Gilbert (Delaware)