Geometry and physics: Where are we going? (English) Zbl 0865.53063

Atiyah, Michael

Andersen, Jørgen Ellegaard (ed.) et al., Geometry and physics. Proceedings of the conference at Aarhus University, Aarhus, Denmark, 1995. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 184, 1-7 (1997).

Summary: The aim of this talk is to give an overview of the interaction between geometry and physics. The talk will be in three parts: first a historical survey, then a look at several areas in mathematics which have benefited recently from interaction with physics, and finally a survey of some of the current challenges.
For the entire collection see [Zbl 0855.00020].

MSC:

53Z05	Applications of differential geometry to physics
81Txx	Quantum field theory; related classical field theories
53-02	Research exposition (monographs, survey articles) pertaining to differential geometry
57N13	Topology of the Euclidean \(4\)-space, \(4\)-manifolds (MSC2010)
53C07	Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills)

Keywords:

elliptic cohomology; quantum cohomology; mirror manifolds; moduli spaces; Jones-Witten theory; Seiberg-Witten invariants; Yang-Mills theory; topological field theory