The purpose of the school is to offer a global view of mathematical and computer science methods used for modelisation of biological problems. We also want to exhibit research problems which need new theoretical tools to be solved.
This CIMPA Summer School is intended for pregraduate and postgraduate students interested in Inverse Problems and related areas where these problems naturally arise as is the case of Control Theory, Optimal Design, Acoustics, Geophysics, Engineering, Biology, Medicine, etc. The different courses cover some of the current research areas in Inverse Problems with different fucuses presented by selected lecturers who are active researchers on these areas.
In this research school topics related to minimal surfaces, overdetermined problems and, more generally, geometric analysis will be studied. The main objective is to present to students and young researchers how tools from differential geometry and analysis of partial differential equations can be combined to obtain interesting, new results in both fields.
The workshop is on geometric methods in dynamics. We want to explain how simple geometric ideas can be used to obtain deep results in dynamics, such as the precise count of geodesics on surfaces of negative curvature, the count of periodic orbits of Hamiltonian systems on tori, and the existence of periodic orbits of a prescribed energy of classical mechanical systems.
The aim of the project is to study the role of certain algebraic objects, as Lie algebras, Hopf algebras, pre-Lie algebras, in the recent developement in quantum field theory, in the theory of pseudo-differential operators and in probability theory. More precisely, the lecture will cover the following subjects:
In recent years, toric geometry has experienced a rapid growth with a wealth of new results and connections with other areas of mathematics like arithmetic geometry and number theory, dynamical systems, non Archimedean and tropical geometry, mirror symmetry and birational geometry, This adds to the more classical connections to combinatorics, computer algebra and singularity theory among others, and applications to areas of science like mathematical biology and chemistry.
The objectives of the school are to introduce the participants to mathematical tools, in particular arithmetic, algebraic and geometric ones used in certain recent developments in algebraic Coding Theory , Cryptography and related areas. These directions are in full development and represent an extremely rich research area open to the applications.
The Escuela Latinoamericana de Geometría Algebraica (ELGA) series of schools quickly became a major event for algebraic geometry in Latin America working as meeting point for the whole community due in part to the novelty of having some of the best researchers in our eld lecturing in Latin Americaf
