Participation in INI programmes is by invitation only. Anyone wishing to apply to participate in the associated workshop(s) should use the relevant workshop application form.
The last fifteen years have seen an upheaval in algebraic topology. Old problems have been solved using new methods, new methods led to new ideas, new ideas to new problems, and new problems to new theorems. The result has been a renaissance.
In retrospect, we can see that this fundamental change occurred as the mathematicians in the field confronted and solved an array of related problems. These included the task of making sense of Witten's insights on the elliptic genus, of finding a provable formulation of Mumford's conjecture, the related development of topological field theories, attempts to make rigorous Morava's program using the geometry of formal algebraic groups to organize stable homotopy theory, and the solution of the Kervaire invariant problem and subsequent reintegration of equivariant homotopy theory. In each case, there was enormous progress after the introduction and the study of higher homotopical structure.
This programme will highlight four related themes: the new algebraic topology of differentiable manifolds, derived representation theory and equivariant homotopy theory, the interplay between arithmetic geometry and stable homotopy theory, and the analysis of foundations in these new contexts "the homotopy theory of homotopy theory". The four areas are bound together by the use of higher structures, but they do have slightly different characters: some study objects, others are an analysis of methods. This interplay is intentional: objects inspire methods and methods make objects accessible. The intent is to develop the community of scholars from these diverse, but overlapping, areas of algebraic topology, both through a programme of long-term visitors and a sequence of workshops, one each for the various themes.