Higher linear topoi and curved noncommutative spaces. University of Antwerp
Broadly, this project can be summarized as looking for connections between noncommutative algebraic geometry (NCAG) and higher category theory.NCAG is the modern understanding, and a drastic abstract generalization, of classical geometry. To known geometrical spaces, one can associate commutative (i.e. x*y = y*x) algebraic structures. However, in algebra, noncommutative structures are just as common. The idea of NCAG is to study new ``geometric ...