2014

The Research School covers three topics in Graph Theory which are active fields of research and give the opportunity to present a wealth of open problems and existing techniques to attack them.

The school has as its main objective to provide different perspectives on singularity theory. These (usually complementary) include the theory of Poincaré­Hopf and characteristic classes, commutative algebra, real and complex algebraic geometry, holomorphic foliations and tropical geometry among others.

The goal is that students and young researchers increase and enrich their knowledge about several aspects of the theory of singularities, and have contact with experts on the subject.

The objective of our school is to propose courses from basic to advance level in Dynamical Systems, specially in Complex Dynamics and Ergodic Theory, to young mathematicians (from graduate level students to researchers) of Nepal and neighbouring countries.

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.

Linear Algebra and Operator Theory are powerful tools in the study of Quantum Mechanics. The main aim of this CIMPA research school is to introduce students, young researchers and all interested mathematicians having background in linear algebra and basic operator theory to the foundations of Quantum Mechanics and Quantum Information.

The aim of this CIMPA School is to train postgraduate (Master/PhD) students and postdocs in research activity in areas of Inverse Problem. The proposed topics include areas which are currently active and the School intends to initiate the participants in working together doing research lead by some active researchers in the area of Inverse Problem.

The objectives of the school are:

We wish to gather in this school Palestinian students interested in the study of Random Structures. Since the seventies this is a topic considered both in Theoretical Computer Science and in Probability. In particular, the analysis of the mean behaviour of algorithms and structures used in computer software and hardware rests on both approaches; as examples, the mean behaviour of trees or sort algorithms can be analyzed by these methods.

Real algebraic geometry has greatly expanded its horizon in the past few years, in great part due to the invention of new tools and the use of methods from other fields (complex algebraic geometry, tropical geometry, symplectic geometry, algebraic topology, combinatorics, etc.). The goal of this school is to present several of these aspects through 5 courses of 5 hours each. The school will end with a 3-day conference, destined to give the students the widest possible and most up-to-date vision on real algebraic geometry.

Algebraic number theory is a very active field of mathematics. We plan to introduce the subject and its application to cryptography. After given courses in elementary arithmetic, algebraic numbers and p-adic numbers, we will focus on the basics of elliptic curves and finite fields. Applications will also figure prominently in the program as it is shown by the presence of the following courses: Introduction to cryptography, Elliptic curves and cryptography.

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.