2024

The school aims at introducing the students to a few lines of research in number theory revolving around the concepts of lattices, heights and diophantine approximation. Part of the school is devoted to presenting the recent proof by Maryna Viazovska that the densest sphere packing in dimension 8 is the one given by the E_8 lattice. In 2022 she was awarded the Fields medal. To this end we introduce the students to lattices, sphere packings and modular forms.

The school aims to introduce graduate students and young researchers to modern algebra and its applications, with a focus on Leavitt path algebras, Shift algebras and some non-associative algebras, such as Lie algebras, Jordan algebras, Poisson algebras and their applications in other areas of mathematics, e.g. geometry, topology and analysis, and in theoretical physics. The courses will deal with a description of certain algebraic systems, their classification and connection with other algebraic systems.

Cutting-edge challenges in science require up-to-date methods, especially if high-dimensional data is involved in areas like data analysis or machine learning. The overriding topic of this CIMPA school is recent developments in algebra and geometry with a strong focus on applications. Chemical reaction networks, dynamical systems, and optimization are examples of fields where sophisticated tools from algebraic statistics, combinatorics, toric geometry, or tropical geometry have been applied successfully in the past years.