Philippines

This school is intended for graduate students, young researchers, teachers and practitioners who are working on applied mathematics, numerical methods and mathematical finance. We hope that the School will strengthen collaboration between Southeast Asian and European mathematicians.
It is part of the Asia Link program IMAMIS (International Master in Applied Mathematics and Information Sciences) that has been worked out mostly by the Université de Nice Sophia-Antipolis (UNSA) and the University of the Philippines (UP).

Pseudo-random sequences are used in industry in various contexts like cryptography in computer security and simulation in numerical analysis. The aim of the schoool is to gather industrial and academic partners to make a survey and a synthesis of the diverse mathematical techniques (arithmetic, logic, combinatorial) employed in the various applications.

In the seventies, Philippe Delsarte in a seminal work developed a method in Algebraic Combinatorics that yields upper bounds for the cardinality of codes with given minimal distance as a solution of a linear program. This method, also called the Delsarte method, or polynomial method, was developed in the framework of Association Schemes , which is the most general framework dealing with finite metric spaces.This method also obtains bounds in more general situations, such as lower bounds for designs (combinatorial and spherical).

The school aims to teach students the tools necessary for the analysis of partial differential equations, their numerical approximation and applications to some natural phenomena. The courses include Sobolev spaces, variational theory of PDEs and numerical solution of PDEs. As applications, we will discuss fluid mechanics, the numerical modeling of waves, tsunamis and hurricanes. These natural phenomena are especially meaningful to those living in the Southeast Asian region.

The theory of algebraic curves over finite fields is a very active subject both from a theoretical and an applied point of view. The research school aims to cover theoretical, computational and applied aspects of the topic and thus will be useful to a broad range of students and young mathematicians interested in algebra and its applications.

The objective of the school is to present various results and techniques related to linear and nonlinear PDE, both in theoretical and applied domains, in a form that is accessible to beginning researchers as well to doctoral students in analysis.

Numeration is an active and developing field of study that encompasses different areas of mathematics and theoretical computer science. The goal of the research school is to introduce graduate students and young researchers to the fundamentals of the geometric, combinatorial, and dynamical aspects of numeration systems as well as to topics of current research. The basic courses of the research school will include lectures on beta expansions, canonical number systems, formal languages, substitutions, and others.

The school aims to introduce graduate students and young researchers to key topics in algebraic number theory and arithmetic geometry and their computational aspects. Modular forms and elliptic curves will be central, with a view towards Galois representations, complex multiplication and class field theory. Understanding of the abstract theory will be facilitated by an explicit and algorithmic approach, through an interactive approach where we will make use of freely available computer algebra systems.

In this school, we intend to introduce modern mathematical modelling tools which are useful to solve and analyse ecological, medical and environmental challenges. Our aim is to prepare students and staff members for concrete problems arising in mathematical modelling in ecosystems, more particularly environmental and ecological issues that can be applied in the context of South-East Asia. We will present theoretical and numerical lectures about deterministic and stochastic differential equations and their calibration.

The school aims to introduce graduate students and young researchers to modern algebra and its applications, with a focus on Leavitt path algebras, Shift algebras and some non-associative algebras, such as Lie algebras, Jordan algebras, Poisson algebras and their applications in other areas of mathematics, e.g. geometry, topology and analysis, and in theoretical physics. The courses will deal with a description of certain algebraic systems, their classification and connection with other algebraic systems.