English

The school will address a selection of topics of importance in modern research in combinatorics, representation theory, higher structures via the prism of geometry, and their interrelation. Specific themes to be covered are geometric representation theory, quantum groups, the use of higher structures to study the geometry of various spaces, categorification, combinatorial aspects of geometry and cluster algebras.

Official language of the school: English

Two centuries after its origin, Complex Analysis remains a vi- brant and fruitful field of research. Its applications go well beyond the realm of Mathematics and range from Physics to Engineering. Current research in Complex Analysis blends techniques from a variety of Mathematical areas and thus requires a broad expertise. Following this philosophy, the school will expose students to a wide spectrum of fields interacting with Complex Analysis. Special emphasis will be put on Differential Geometry, Partial Differential Equations, Dynamical Systems and Algebraic Geometry.

The school is addressed to graduate students in Lebanon and abroad, and its program is spread over two weeks. The first week will serve as a preparation and will focus on introductory topics. The second week will present more advanced and modern developments. In addition to the mini courses, complementary activities will engage the students more directly with open problems, exercises, or career opportunities.

Official language of the school: English

Recent years have witnessed the emergence of powerful semantic tools for non-classical logics. These semantic methods draw from web of mathematical formalisms at the intersection of ordered and universal algebra, topology, and category theory, and together provide a flexible and unifying framework for the study of logic across a host of domains. LIACT serves as a broad introduction to this dynamic and quickly growing area of modern mathematical research, and places particular emphasis on this area's deep interactions with/and applications to computer science.

Official language of the school: English.

Differential equations are typically considered to be a subject of mathematical analysis or, more generally, "continuous mathematics". However, algebraic and discrete methods have been successfully applied to questions about differential equations such as, for example, finding symmetries or closed-form solutions. Recent years have witnessed significant development of constructive aspects of algebraic geometry and tropical algebra including deep theory and efficient algorithms. Exploring connections between these advances and problems about differential equations creates numerous opportunities for applying algebraic and tropical methods in the realm of differential equations. The goal of the school is to introduce the participants to selected constructive methods of algebraic geometry and tropical algebra, present existing applications of these methods to differential equations, and engage the participants into working on open problems in this area.

Official language of the school: English

Coding theory is a remarkable example of how various areas of mathematics can be used to solve problems in the storage and transfer of information. In this school, participants will be introduced to various techniques used in recent years to solve problems in coding theory. The aim is to motivate participants to do research in coding theory.

Participants will study coding theory in general including cyclic codes and Goppa codes. They will also explore, among others, combinatorial and algebraic properties of graphs and designs related to codes, permutation decoding of codes from graphs and designs, linear codes with complementary dual, evaluation codes in code-based cryptography, networks and network coding problems, rank metric codes and coding in distributed systems.

Official language of the school: English

The summer school aims at introducing students, junior faculty members, and young researchers to important theories and applications of data visualization, statistical and mathematical modeling, and various mathematical tools for model analysis.  There will be seven courses which will cover a variety of topics from data modeling to in-depth analysis and mathematical justifications for data-based decision making. The summer school will emphasize on preprocessing a wide variety of data sets, designing data driven hypotheses, developing statistical models to extract relevant inferences, developing data-driven mathematical models, and using modern methods from matrix algebra, knot theory and mathematical analysis to analyze mathematical models.

Official language of the school: English.

The School aims to introduce students to the mathematical and statistical underpinnings of some of the latest Data Science methods that seek to address the challenge of Big Data analysis. There will be an emphasis on matricial methods both in modelling and in numerical computations. The topics covered will include Randomized Numerical Linear Algebra, Deep Generative Models, Bayesian Nonparametric Models and their Asymptotic Properties, Modern Graphical Models and High- Dimensional Statistics Based on Random Matrix Theory.

The courses will start by introducing randomized numerical linear algebra, deep generative and modern graphical models, fundamental for problems of interest in machine learning and statistical data analysis. For all lectures there will be dedicated exercises with practical problems (in particular with R and/or Python) to be solved by the students under the experts’ guidance.

There will be also be seminars by workshop participants to showcase their works as well as invited talks by Data Science experts in South Africa to expose participants to real world problems being worked on by academics and industry practitioners.

Official language of the school: English

Although cryptography has a long history, it has developed during the 20th century into a modern science with the help of computer science and mathematical objects coming from algebra, number theory, geometry, combinatorics,...

The school will present modern aspects of cryptography based on number theory, algebra, and algebraic geometry. The courses will present various aspects of the subject: elementary and algebraic number theory, elliptic curves, lattices, computational aspects, and their use in cryptography. Training sessions will be devoted to PARI/GP or SageMath, two efficient computer algebra systems which are open-source and widely used by the community.

The school aims at promoting and developing these new research areas for teachers and researchers in Senegal, attracting new students and developing scientific collaborations with other countries, including co-directions of Ph.D. students.

Official languages of the school: English and French

Graph Theory lies on the interface between combinatorics and discrete mathematics. The domain has expanded considerably over the last decades with interactions invarious fields such as the study of social networks, algorithms, computer science, interprobabilities, discrete geometry, producing some spectacular results.

There will be 5 mini courses of 6 hours each and 2 mini courses of 3 hours each. The courses will first introduce basic tools and the, move on to more advanced concepts in graph theory such as algorithms and their applications to computer sciences, combinatorial optimization related to linear programming, scale-free graphs, spectral theory, the theory of infinite graphs. Applications will include models of the internet, social networks, small world phenomena, also discrete geometry and probability theory. 

Official language of the school: English

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. The main goal of this school is to build bridges between various disciplines of mathematics which have in common to apply algebraic and combinatorial methods in geometry. The lectures range from the foundations to recent results and applications of the relevant theory.

Official language of the school: English