Abstract (pdf file 58kb, updated 03/03/23)                                      “***” indicates an online lecture.

Wednesday 8th March

Title: Cartan calculus in string topology

By:    Takahito Naito

         (Nippon institute of technology)

Abstract:

The classical Cartan calculus for differential geometry consists of three types of derivations on the de Rham complex: the Lie derivative, the interior product and the exterior derivative. It is well known that these operations satisfy a relation called Cartan (magic) formula. In this talk, I investegate a homotopy Cartan calculi in the sense of Fiorenza and Kowalzig on the free loop spaces. Roughly speaking, a homotopy Cartan calculus is a Cartan calculus which satisfies Cartan formula up to homotopy. I introduce a homotopy Cartan calculus on the Hochschild chain complex of the de Rham complex and give a geometric description of the calculus. Moreover, I also show that the description can be described by using the loop product and bracket in string topology. A part of this talk is based on joint work with K. Kuribayashi, S. Wakatsuki and T. Yamaguchi.

Title: Diffeological vector spaces ***

By:    Enxin Wu

         (Shantou University)

Abstract:

I will present some old and new results related to diffeological vector spaces, focusing on the aspects of smooth homological algebra together with its connections

to analysis, algebra, geometry and topology.