Ricerc@Sapienza

The project is a continuation of previous ones with the same title and Principal Investigator. In this project the group of participants has expanded, so as to include all the structured staff of the Mathematics Department Guido Castelnuovo with algebraic research interests. The unification of previous smaller projects aims to improve mutual collaboration, to pool existing international collaborations, to create new ones and to carry out scientific events and support initiatives for young researchers more effectively. Unification is justified and motivated by the fact that many research topics fall into the comprehensive name of Representation Theory and have remarkable interest and applications in Mathematical Physics.

Diverse topics will be covered, all central to basic mathematical research and relevant to the fields of algebra, algebraic and complex geometry, topology, combinatorics (both algebraic and enumerative) and theoretical computer science. They range from representation theory of various kind of infinite-dimensional Lie algebras (affine algebras, vertex algebras, Lie superalgebras, Lie pseudoalgebras, cluster algebras) to more analytical and topological topics in the study of algebraic groups and complex geometry. Algebraic, combinatorial and theoretical computer science aspects will be covered, treated mainly via algebraic techniques. In detail, the topics studied, consistent with those of the previous editions of this and other projects, of which they are a refinement and deepening, will be the following:

- Unitarity in vertex operator algebras
- W-algebras and completely integrable Hamiltonian systems
- Lie pseudoalgebras
- Cluster algebras through Lie theory
- Spherical varieties
- Actions of complex algebraic and Lie groups
- Calibrations on manifolds
- Double quasi-symmetric functions
- PI Theory and related topics
- Integral geometry on trees
- Counting functions of languages