Introduction

The primary goal of this school is to provide students with a comprehensive understanding of modern algebraic and geometric methods, as well as their practical applications. The introductory courses will establish a solid foundation in recent developments such as combinatorial algebra, tropical combinatorics, and statistical models like graphical models. The more advanced lectures will focus on applied areas, such as dynamical systems, and explore their connections to algebra and geometry. The use of symmetries and other approaches to reduce complexity for high-dimensional phenomena will also be discussed. To further enhance their skills, participants will have access to training sessions and group discussions to delve deeper into the material and exchange ideas with peers.

To tackle cutting-edge challenges in science, it is essential to use up-to-date methods, particularly when dealing with high-dimensional data in fields such as data analysis or machine learning. This CIMPA school will address recent developments in algebra and geometry, with a strong emphasis on their practical applications. Chemical reaction networks, dynamical systems, and optimization are just a few examples of fields where sophisticated tools from algebraic statistics, combinatorics, toric geometry, and tropical geometry have proven successful in recent years. These approaches will be explored in depth during the school, equipping participants with the knowledge and skills needed to tackle modern scientific challenges.