Diagram Categories in Homotopy Theory
This CRG will study diagram categories in homotopy theory, focusing on functor calculus, equivariant
homotopy theory, and polyhedral products. These are active and important fields of research with
connections to each other and to other areas of mathematics. We have strong research groups in homotopy
theory within the PIMS network, and the CRG will strengthen connections among these groups, enhance
their impact in other areas of mathematics, provide training for junior mathematicians, and produce
world-class research outputs.
The planned activities include a summer school, several workshops and minischools, and an international
research conference. We also request funding for one Postdoctoral Fellow and a number of research visits.
Research Interests
The research areas related to this CRG include
- Algebraic topology
- Homotopy theory
- Homological algebra
- Cohomology operations
- Structured spectra arising from categorical structures
- K-theory
- Equivariant homotopy theory.
- Stable homotopy theory
- Functor calculus for manifolds
- Spaces of embeddings.
- Configuration spaces
- Polyhedral products
- Derived categories.
- Azumaya algebras.