Pakistan

<div class="tex2jax_process">The main theme of this CIMPA School is Topological Data Analysis (TDA), an emerging field at the intersection of topology and data science that uses tools from Algebraic Topology to understand the “shape” of data. This school will provide participants with both foundational and advanced topics in TDA, along with an introduction to its integration with Machine learning techniques.

<div class="tex2jax_process">The school will present three active domains which are recent developments with origin in symbolic dynamics: progresses in the theory of tilings, questions of diophantine approximation and proofs of transcendance for some number with explicit expansions in a given base, and generalisations of the classical notion of substitution; the unifying theme will be to show how symbolic dynamics can be applied to obtain results in very different contexts.

The aim of this School is to introduce the students to the theory of configuration spaces, some classical and new results in this field, and to the many applications of these in real life.

This is also meant to open to the PhD students new important areas of research in geometry and topology.

Local analytic geometry is concerned with germs of zero sets of analytic functions, that is, the study of such sets in the neighbourhood of a point.

The school intends to introduce PhD students and young researchers to local analytic geometry and to enable them to receive the required knowledge for doing significant research in this area of mathematics.

The school intends to introduce PhD students and young researchers to combinatorial commutative and computational algebra and to enable them to receive the required knowledge for doing significant research in this area of mathematics.

In this school, we will discuss 6 different themes from Combinatorial Commutative Algebra. The idea of Combinatorial Commutative Algebra is to relate combinatorial objects, like simplicial complexes, graphs, hypergraphs or polytopes to algebraic objects like monomial, binomomial ideals and toric rings. The field benefits from the interplay between properties of combinatorial objects and the corresponding properties of the algebraic object. The binomial edge ideals as well as edge ideals of graphs and their powers as well as their symbolic powers will be considered.

The school will provide an introduction to both basic and more advanced topics in the moderntheory of dynamical system and ergodic theory. It will be aimed mostly at Masters level students and thus assume a reasonable general mathematical background but no previous specialised knowledge in the topics covered in the courses. The scientific content of the various courses will be tightly coordinated in order to provide the students with the possibility of a real concrete learning experience which can become the foundation for further study.

The central topic of the school is the mutual interaction of algebra, combinatorics and geometry. Objects of research in algebraic geometry are affine as well as projective varieties and their associated invariants which can be studied using methods from algebra and combinatorics. Toric and tropical varieties are instances where such kind of approaches were and still are very successful. In discrete geometry cones, graphs, hyperplane arrangements and matroids are examples of research subjects which naturally play prominent roles in algebra and discrete mathematics.

In this school we intend to focus on different concepts Combinatorics and its applications. The school will provide an introduction to both basic and more advanced topics. The scientific content of the various courses will be tightly coordinated in order to provide students with a possibility of the real concrete learning experience which further can become a foundation for the further study. We expect audience from Master, Phd and young faculty who are currently working or planning to work in this interesting area of Mathematics.

The school will provide an introduction to both basic and more advanced topics in the moderntheory of dynamical system and ergodic theory. It will be aimed mostly at Masters level students and thus assume a reasonable general mathematical background but no previous specialised knowledge in the topics covered in the courses. The scientific content of the various courses will be tightly coordinated in order to provide the students with the possibility of a real concrete learning experience which can become the foundation for further study.