|I will be giving a talk at the Geometry Seminar of the Institute of Mathematics at Gdansk University on the 19th March.|
Title: On the higher order tangent bundles of a supermanifold.
Abstract: In this talk I will introduce the notion of a supermanifold as a “manifold” with both commuting and anticommuting coordinates. After that I will discuss the notion of a curve on a supermanifold and how to construct their jets, this will lead to a kinematic definition of the higher order tangent bundles of a supermanifold. However, to formulate this properly we are lead to more abstract ideas that have their roots in algebraic geometry and in particular notion of internal Homs objects. I will not assume the audience to be experts in the theory of supermanifolds nor jets, only that they have some basic knowledge of standard differential geometry.