Global equivariant homotopy theory II

• Applicant: Professor Dr. Stefan Schwede
• Subject Area: Mathematics
• Term: from 2015 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 269311553

Homotopy theory is an area of pure mathematics that investigates those aspects of geometric objects that are invariant under continuous deformations. Homotopy theory lies at the interface between the world of continuous and smooth objects (geometry and analysis) and the discrete world (algebra and combinatorics). Characteristic for equivariant homotopy theory is the additional presence of symmetries that must be preserved by all deformations. Typical questions are the classification of geometric objects of a certain kind with specified symmetry, or of the maps between them.This project is devoted to the study of equivariant phenomena that exist simultaneously and compatibly for all symmetries, i.e., aspects that exhibit "universal" or "global" symmetry. We want to investigate various fundamental questions about global homotopy theory of compact Lie groups and develop the necessary formal framework.

• DFG Programme: Priority Programmes
• Subproject of: SPP 1786: Homotopy Theory and Algebraic Geometry