The proposal focuses on problems in Combinatorial Algebra related to The Burnside Problem and to Lie algebras of finite growth. The three main problems are (i) the version of the restricted Burnside problem with periodic primitive elements, (ii) tau-property of Golod - Shafarevich groups and (iii) classification of conformal algebras of Gelfand-Kirillov dimension one.
These problems are motivated by deep applications in Geometry, Topology and Mathematical Physics.
