India

The aim of the School is to introduce mathematicians from developing countries to some fundamental techniques and recent developments in Commutative Algebra and to promote the collaboration between mathematicians of different developing and developed countries.

Security is now a primary objective in computer systems and networks, providing privacy, integrity, authentication, digital signature, etc. Security is also recognized as a part of mathematics, of analysis of complexity and of mathematical logic. Indeed formal frameworks used for programming languages and concurrency theory have been used to describe security protocols. India has already many specialists in security of computer systems; the school will contribute to train graduate students and researchers, in order to increase their mathematical approach to security.

The aim of the School is to bring together eminent scientists who are active in the domain of integrable discrete systems so that they can introduce young researchers working in India and other developing countries to this rapidly expanding domain.

The school is devoted to three classes of problem: the generalized Nash equilibrium problems, the bilevel problems and the Mathematical Programming with Equilibrium Constraints. They interact through their mathematical analysis as well as their applications.

Fourier theory has been a useful analytic tool in studying discrete structures. Some of the areas where this theory has been particulaly fruitful are additive combinatorics, eigen values of graphs and random walks on finite groups or in the study of Boolean functions used in computer sciences.

The development of Computational methods for partial differential equations (PDEs) is a key tool for the development of science and technology. For its development, it is important to have a deep understanding of the classical and new methodologies used in numerical methods. The summer school will provide an overview of some techniques that allow one to address the computational challenges encountered in different applications.

The scope of problems accessible for a numerical treatment has been constantly broadened over the last fifty years. In particular, there has been a lot of research activity in the recent decades aimed at the problems with multi-scale and multi-physics features. The dedicated numerical methods (model reduction, micro-macro models and model coupling, non standard FEM) stem from diverse techniques and ideas such as homogenization, asymptotic analysis, statistical physics, domain decomposition methods, etc.

Recent developments in non-commutative algebra include parallel theories of graph C*-algebras and Leavitt path algebras. In this research school, we mainly focus on theories of Leavitt path algebras and their connections with other areas of mathematics.

Geometric flows are burning topic now a days which involve the evolution of Riemannian metric along with some geometric concepts.

Numerical analysis, simulation and scientific computing for the solution of partial differential equations (PDEs) using FEM and related methods have been cornerstones of applied mathematics over the last fifty years. In fact, it is well known that the study of computational methods for PDEs is extremely crucial for the development of science and technology.