The program addresses mostly problems related to the structure and applications of moduli spaces of various geometrical objects, and problems in representation theory and Lie theory and their ramifications.
There are four main research lines.
The first (moduli, "classical") is centered around moduli spaces of curves, abelian varieties, K3 surfaces and potentially higher-dimensional hyperkähler varieties, vector bundles. Another prominent part in this “classical” section will be played by fibrations, to be understood in a wide sense: Hitchin fibration, variation of Hodge structure, monodromy representation.
The second research line (moduli, "non-classical") addresses various aspects of deformation theory (mostly via the machinery of DGLA's), and derived algebraic geometry.
The third (Lie theory) deals with Lie and algebraic groups, Lie algebras and superalgebra, their infinite dimensional generalizations (vertex algebras, quantum groups), and on the connections with Physics (Hamiltonian systems, Conformal Field Theory).
The fourth line of research deals with the topology of braid groups and hyperplane arrangements: this line of research is somewhat at the intersection of the other three.
The training of young researchers is one of the most important aims of the project.