Representation Theory and Applications
The project is a continuation of previous ones with the same title and PI. The research team has expanded in different directions: besides including most of the department faculty with algebraic research interests, the new team hosts colleagues with more analytical background along with researchers from the applied sciences department. The unification of previous smaller projects aims at improving mutual collaboration, pooling existing international collaborations and creating new ones, as well as carrying out scientific events and support initiatives for young researchers more effectively.
Diverse topics will be covered, all central to basic mathematical research. The central bulk is representation theory of various kind of infinite-dimensional Lie algebras, but extends to cover more analytical and topological topics in the study of algebraic groups and complex geometry. Algebraic, analytical, combinatorial and theoretical computer science aspects will be covered, treated with algebraic techniques. In detail, the topics studied, consistent with those of the previous editions of the project are the following:
1. Vertex algebras and related topics
a. Unitarity in minimal W-algebras
b. Unitary tensor structures of module categories
c. Lax-type operators and affine W-algebras
d. Collapsing levels for affine W-algebras
2. Algebraic and topological Quantum Field Theory, integrable systems
a. Projective representations and anomalous QFTs
b. Classical and quantum W-algebras and applications to integrable systems
3. Combinatorial, cluster, geometric and PI algebras
a. PI theory and related topics
b. Categorification of cluster algebras
c. Braids and ties algebras
d. Combinatorial Hopf algebras
4. Algebraic groups, harmonic analysis
a. Spherical varieties
b. Symmetric spaces and conjugacy classes of Kac-Moody groups
c. Harmonic analysis on semi-homogeneous trees
d. Algebraic groups and quantum automata
Participants:
PAPI, PAOLO
DI TRANI, SABINO
BRAVI, Paolo
CASADIO TARABUSI, Enrico
CERULLI IRELLI, GIOVANNI
CILIBERTI, AZZURRA
D'ALESSANDRO, Flavio
DE CONCINI, CORRADO
DE SOLE, ALBERTO
FIORENZA, DOMENICO
MALVENUTO, Claudia
PASCUCCI, ELENA
PEZZINI, Guido
PINZARI, Claudia
PROCESI, Claudio
SPINELLI, ERNESTO
VALERI, DANIELE