English

For more than forty years, string theory has been able to impact in the development of several fields of mathematics. K- theory, algebraic and differential geometry, topology, infinite dimensional analysis, representation theory and derived categories, to mention a few, have been profoundly influenced by “stringy” ideas such as mirror symmetry, conformal field theory, D-branes and quantum cohomology. The main goal of this CIMPA Research School is to provide an introduction to many of these mathematical subjects as well as some background on string theory. The courses will not only provide the basic material but also some of the current research trends in the respective fields. The school is specially addressed to graduate and undergraduate students, both in mathematics and physics, but also to young researchers attracted by possible interactions with the topics previously described. 

The school is organized around two thematic axes: Hopf algebras and tensor categories. The school is intended to introduce Ph.D. students and young researchers on both areas, to explain how they are interrelated, and also to present applications and new lines of research.

The courses on Hopf algebras aim to present the basics of this theory, the most relevant techniques and the classification program of finite-dimensional Hopf algebras. The theory of Nichols algebras will be presented, and how it fits into the classification program.

The courses on tensor categories aim to present basic notions of tensor categories, some new developments in the classification of such objects, and how these algebraic objects appear as symmetries of diverse structures of mathematical physics and computing science. The courses will survey an introduction, some techniques applied in their classification and also how the theory of Hopf algebras can be a powerful tool in this context.

This school aims to offer an intensive teaching session to graduate students and young researchers. That concerns key topics in Algebraic Geometry and Number Theory. Indeed many classical results and methods in these areas are used in flourishing domains of applied mathematics. We selected the following six courses:

•  Algebraic number theory and class field theory.
• Tate module and abelian varieties.
• Quantitative and algorithmic recent results in real algebraic geometry.
• Advanced topics in semi-algebraic geometry.
• Counting points on algebraic varieties.
• Fundamental groups in Algebraic and Arithmetic Geometry.

These fundamental courses describe all theoretical elements needed for the applications in cryptography and robot kinematics which will be developed at the end of the school.

Beyond lectures, we are also planning sessions devoted to solving exercises and to computer experiments with Pari/GP and Sage.

We expect that at the end of the school every participant will be able to select a suitable hyperelliptic curve for constructing some cryptosystems based on the discrete logarithm problem in its Jacobian. 

The aim of this school is to provide courses for graduate students and young researchers. These courses will focus on Control Theory (and, in particular, Geometric Control and Control of Partial Differential Equations) and also Information Theory. In addition, applications of Control and Information Theory as well as their interactions with other fields such as Economy and Physics will be studied. The scientific contents of the school can be decomposed in two parts. The first part is made of 3 courses (of 6 hours each) in Information Theory and one course in Geometric Control. The second part consists of 3 courses in Control of Partial Differential Equations and a course in Geometric Control Theory. Besides lectures, we consider some sessions for research presentations, which will present applications of the theories presented in the courses and interactions with other disciplines. 

The notion of a group describes symmetry in mathematics. In recent decades, certain quantum mathematical objects have appeared whose symmetries are better described by group-like objects called tensor categories. Examples of areas of mathematics where tensor categories play a key role include subfactors, quantum groups, Hopf algebras, quantum topology and topological quantum computation. The aim of this is school is to introduce graduate students to tensor category theory and their applications to Topological Quantum Field theory, Subfactor theory and Hopf algebras. We will bring together a wide variety of senior experts, postdocs, and graduate students from mathematics and physics. This mix of people will provide young researchers an opportunity to interact with experts, develop connections, and increase their exposure. 

This school is about a smooth transition from classical graph theory to modern approaches. At first extension of coloring results to homomorphisms of digraphs are presented. Next lectures would be on algorithmic graph theory with classic approaches such as LexBFS ordering being combined with modern ideas. Mixing algorithms with applications, there will be lectures on distributed algorithms. School will conclude by lectures on how to use power of randomness, which is a rather new modern and powerful method.

The school aims at presenting some of the current approaches in PDE modelling and mathematical analysis of biological phenomena or related domains. It aims at allowing the researchers and the students of Master’s degree level and talented undergraduate students to acquire a basic training in that field and to have an overview of what is the current research status of these types of problems.

This school will cover a wide class of models and applications including dynamics of intracellular and extracellular phenomena, neuronal networks, pattern formation, chemotaxis, and their implications in developmental biology, epidemiology and neurosciences. The main mathematical methods will concern the study of evolutionary partial differential equations, such as their large time behaviour, their links with microscopic or stochastic models, as well as numerical methods to approximate their solutions. 

Application of Dynamical Systems to Biology is nowadays an important challenge. The goal of this school is, on the one hand to present the basic tools in Dynamical Systems to solve ODE's, and, on the second hand, to present how these tools can be used in Biology. The school will comprise two series of lectures. One theoretical one and one for applied mathematics. A large part will be devoted to exercises sessions.

The theoretical part will focus both on Symbolic Dynamics and Geometric Dynamics (mainly uniformly hyperbolic dynamical systems). The applied part will make connections between the theoretical's one by using the tools presented in the theoretical courses to study the logistic family, population evolutions or emergence of epilepsy crises. 

The primary objective of this summer school is to provide an opportunity for mathematicians and biologists in Nepal and neighboring countries to explore mathematical skills that can be applied to address issues of real-life biological systems. The summer school aims to introduce students, junior faculty members, and young researchers to the important theories and appli- cations of Mathematical Biology.

The program of the school includes six major topics of mathematical biology : Discrete and Continuous Population Dynamics (N. Vaidya), Biological Data and Model Parameters (G. Jeremie), Mathematical Epidemiology (R. Smith?), Within-host Modeling (L. Rong), Evolu- tion and Genetics (L. Wahl), and Ion Transport in Biological Tissues (H. Huang). Participants will also get opportunities to work in group projects aiming to address real-life biological questions. 

Representation theory is a central branch of modern mathematics that studies realizations of abstract non-linear structures using classical linear and/or combinatorial concrete structures like matrices, linear operators and quivers. It is a very active and dynamic area, both heavily influenced by important applications to algebra, combinatorics, geometry, topology, analysis, category theory, number theory, mathematical physics and other branches of mathematics and physics.

The aim of this school is to introduce some of the currently most active research topics of the subject mainly to Iranian algebra community and also to neighboring countries. The emphasis will be on background from and connections to more classical theory. Some of the central topics that will be discussed during the School by well-known experts are: support varieties and connection to group representations, triangulated categories, categorical and combinatorial aspects of recent generalizations of tilting theory, and model theoretical aspects of representation theory.