Uzbekistan

Topics of school include various aspects of the theory of non-associative algebras, their representations and applications, including Lie, Leibniz, Jordan and other classes of algebras.

This school aims at providing interested graduate students from Uzbekistan and other Central Asian countries with the basic notions and some recent ideas and techniques at an advanced stage of current research in a wide spectrum of themes from classical complex analysis, pluripotential theory, geometry of compact complex manifolds and holomorphic dynamics.

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 Tits-Kantor-Koecher construction, Jordan algebras, Rota-Baxter Lie algebras and some non-associative algebras, such as Lie algebras, Jordan algebras, automorphisms, derivations and cohomology of classical and quantum algebras and their applications in other areas of mathematics. The courses will deal with a description of certain algebraic systems, their classifi cation, and their connection with other algebraic systems.