📎Deformations and Cohomologies of Algebraic Structures

In this course, first, we introduce deformations and cohomologies of Lie algebras with
applications. Then we apply the same idea to other types of algebraic structures, such as
Rota-Baxter Lie algebras, difference Lie algebras, and embedding tensors. If time permits,
we will also talk about the global objects corresponding to these structures.

📎Bialgebras structures, Hopf algebras and quantum groups.

Bialgebras and Hopf algebras appeared first in Topology, since then applications and
their popularity as a topic of study have grown tremendously. They are used in
combinatorics, category theory, homological algebra, Lie groups, topology, functional
analysis, quantum theory, and Hopf-Galois theory. The aim of this course is to provide an
introduction to the structures of bialgebras, Hopf algebra and Quantum groups. We will
discuss the motivations and provide the basic definitions and tools. Moreover, we
summarize the relevant results and explore some of the applications.

📎Automorphisms, Derivations and Cohomology of Classical and Quantum Algebras

Polynomial algebras, differential operator algebras and enveloping algebras of Lie algebras, along with their quantum versions, are ubiquitous in almost all branches of
mathematics as well as quantum physics. Their structure, representation theory, combinatorics and geometric features are of pivotal importance and have shaped
fundamental trends in modern research, feeding on outstanding open problems, such as the Jacobian and Dixmier conjectures. The purpose of this course is to study these objects from the point of view of their symmetries, surveying recent methods which have been proven successful in the study of their automorphisms, derivations and Hochschild cohomology.

📎Bialgebras structures, Hopf algebras and quantum groups.

Bialgebras and Hopf algebras appeared first in Topology, since then applications and
their popularity as a topic of study have grown tremendously. They are used in
combinatorics, category theory, homological algebra, Lie groups, topology, functional
analysis, quantum theory, and Hopf-Galois theory. The aim of this course is to provide an
introduction to the structures of bialgebras, Hopf algebra and Quantum groups. We will
discuss the motivations and provide the basic definitions and tools. Moreover, we
summarize the relevant results and explore some of the applications.