Geometry through the Lens of dg Manifolds

Abstract: Differential graded (dg) manifolds, or $Q$-manifolds, provide a powerful framework for unifying diverse structures in modern geometry. By equipping a graded supermanifold with an odd homological vector field $Q$ (satisfying $Q^2 = 0$), we obtain a robust language capable of "taming" complex geometric problems. In this talk, I will demonstrate the versatility of the dg-framework by exploring its underlying geometry and its applications across several domains, specifically focusing on how it characterizes complex structures and foliations.

mathematical physicsalgebraic topologydifferential geometryrepresentation theorystatistics theory

Audience: researchers in the topic

( slides | video )

Prague-Hradec Kralove seminar Cohomology in algebra, geometry, physics and statistics

Series comments: Virtual coffee starts on Zoom already 15 minutes before the seminar.