A-twisted quantum mechanics, topological descent and A_infty structure

For the student seminar of this week we will have a couple of short talks by Andres and Dang.

Abstract: This talk will give a conceptual introduction to twisted supersymmetric quantum mechanics and its role as the simplest setting in which topological descent and higher algebraic structures naturally appear. After reviewing the twisting procedure and the resulting cohomological description of observables, we will explain how topological descent produces a hierarchy of multilinear operations on local operators, organizing them into an A_infty-algebra. These operations encode the higher homotopies arising from BRST symmetry and provide a universal algebraic model for topological defects and boundary conditions. If time permits we sketch an idea of how these higher structures arise in higher dimensional field theories.