DAG-ARTS

This collaborative project focuses on derived algebraic geometry and its interactions with other fields, such as geometric representation theory, Donaldson-Thomas theory and singularities of schemes. Derived algebraic geometry is a rich and vibrant field that lies at the crossroad between algebraic geometry and homotopy theory. It was developed starting from 2000 thanks to the efforts of J. Lurie, B. Toën and G. Vezzosi, although one can date back several central ideas back to the work of Serre, Quillen and Illusie. Nowadays, derived geometry has become a widespread toolkit and found applications in a variety of subjects, ranging from symplectic geometry to p-adic Hodge theory. With this project we plan to push further the boundaries of derived geometry and to develop new applications to other subjects: we will study variations of cohomological Hall algebras, categorifications of Donaldson-Thomas invariants as well as derived foliations in positive characteristic and their applications to the theory of singularities of schemes.