Iran, Islamic Rep.

The interaction of Analysis and Differential Geometry has led to some of the most striking achievements of mathematics during the last few decades. Analytic approaches to problems in Riemannian, pseudo-Riemannian or complex geometry and topology has given rise to very powerful tools in analysis.

The school will present different aspects of computational methods in commutative algebras and algebraic geometry and their applications in various branches of mathematics, to introduce students and young researchers who can apply these methods in their work. Furthermore this will create an opportunity to establish a network of mathematicians from the region for collaboration on joint research projects with possibility of connections with leading experts on the subject.

The overall aim is to spread Modern Representation Theory of Finite Dimensional Algebras, and its fascinating links to major mathematical subjects, to young mathematicians from developing countries.

This is a 10-days school of mathematics & theoretical computer science for students from Iran and neighbor countries. It is devoted to mathematical aspects of tilings in the various contexts where they appear, with an effort to achieve coherence of the program:

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 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.

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.

One of the fascinating bridges between  classical  mechanics  and quantum physics  is expressed  in the fact that the length spectrum  and the Laplace  spectrum  of a closed Riemannian  manifold determine  each other (at least generically). The main goal of this school  is to introduce  graduate  students  and young  researchers to basic facts on these two spectra, and to the above correspondence.

The main theme of the proposed school are graph algebras, which are objects of growing interest that lie at the boundary between algebra and analysis among other mathematical fields. Despite being introduced only about a decade ago, Leavitt path algebras, as algebraic counterpart of graph C ∗ -algebras, have arisen in a variety of different contexts as diverse as symbolic dynamics, noncommutative geometry, representation theory, and number theory.

One of the fascinating bridges between  classical  mechanics  and quantum physics  is expressed  in the fact that the length spectrum  and the Laplace  spectrum  of a closed Riemannian  manifold determine  each other (at least generically). The main goal of this school  is to introduce  graduate  students  and young  researchers to basic facts on these two spectra, and to the above correspondence.