Functor Calculus and Operads (11w5058)


Michael Ching (University of Georgia)

Nick Kuhn (University of Virginia)

(Kansas State University)


The Banff International Research Station will host the "Functor Calculus and Operads (*HALF)" workshop from March 13th to March 18th, 2011.

In Topology, one is studying geometric objects by means of algebraic invariants, with the goal of using these to classify fundamental types of geometric structure such as knots and higher dimensional surfaces. Such invariants need to be computable, which in practice means that if a `global' object is built out of `local' pieces, there is some process that allows one to attempt to calculate the global invariant from the local invariants. Often these invariants are left unchanged by `homotopies', i.e. deformations.

The Calculus of Functors is a relatively new systematic method of stratifying such invariants by a hierarchy of invariants that satisfy certain `polynomial' local--to--global behavior. This has some compelling similarity to how polynomials are used in ordinary calculus to approximate functions. The workshop will focus on the emerging perspective that Functor Calculus has deep connections with other, more studied parts of homotopy theory and related parts of algebra. Featured will be the theory of Operads, the study of deformations of algebraic operations like multiplication.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).