Differential Geometry Seminar

Organizers：

Jialong Deng, Akito Futaki

Speaker：

Thomas Schick (Goettingen)

Time：

Tues., 15:30-16:30, Dec. 17, 2024

Venue：

Jingzhai 105（静斋 105）

Title：

Equivariant T-duality

Abstract：

T-duality is a a concept inspired by certain aspects of string theory (the T stand for ``target space''). The physics predicts that one can pass from a torus bundle over a base space, equipped with some background B-field to a ``dual'' torus bundle with dual background B-field without changing the physical content of the theory. Strominger-Yau-Zaslow even propose that mirror symmetry is a special case of T-duality. To understand the mathematical underpinnings of this duality, the concept of topological T-duality has been introduced. We present the fundamental ideas of this concept: what are the objects we put in duality? what is the precise meaning of ``being dual''? Among the most striking mathematical consequences, we present the T-duality isomorphism between twisted K-theory of the two dual spaces. The last part of the talk will present new developments which concern the investigation of additional symmetries, encoded in the action of a compact group G. We discuss the meaning of ``equivariant T-duality'' and we show that one obtains a T-duality isomorphism in the full Atiyah-Segal equivariant K-theory.