This is a grant for participant support at the "Workshop on Equivariant, Chromatic, and Motivic Homotopy Theory" to be held at Northwestern University from Monday, March 25 to Friday, March 29, 2013. A remarkable number of the main results in homotopy theory of the past few years have been achieved by calculation, following on and benefiting from a period of building and implementing large theory, especially in derived algebraic geometry. The conference organizers hope to emphasize this point, highlighting the recent calculations and explaining what we have learned about basic homotopy theory. The largest success has been the solution of the Kervaire invariant problem and the attendant resurgence in interest in computational techniques in equivariant stable homotopy theory. Complementing this has been more progress in chromatic homotopy theory, both with large spectra, such as ring spectra coming from the theory of topological automorphic forms, and with small spectra, such as the K(2)-local sphere. There have also been new applications of old techniques, as the use of the Goodwillie calculus to study the EHP sequence and the use of Hochschild homology to make difficult calculations in algebraic K-theory.
Partly due to the shock provided by the solution of the Kervaire Invariant Problem, a great many young researchers have entered the field of algebraic topology, ranging from beginning graduate students to junior tenure-line faculty. This grant will be used entirely to support the participation of the members of this cohort in the conference. For those with established or emerging research programs the conference will provide a forum to publicize their work; for more junior researchers, the grant will support their attendance and work to integrate them into the wider community.
Further information can be found at the Workshop's website
www.math.northwestern.edu/~pgoerss/newemphasis/
This grant was used for participant support at a workshop in algebraic topology and homotopy theory held at Northwestern University March 25-29, 2013. The scientific focus of the meeting was on stable homotopy theory, especially recent advances and calculations in equivariant, chromatic, and motivic homotopy. This conference was part of an emphasis year in algebraic topology at Northwestern University. In nineteen talks over five days, the workshop highlighted the major advances of the past few years, especially the solution of the Kervaire invariant one problem and the renaissance in stable equivariant homotopy theory, recent advances in chromatic stable homotopy theory and the links to arithmetic algebraic geometry, computations in algebraic K-theory and topological cyclic homology (another link to equivariant stable homotopy theory), computations in K(2)-local homotopy theory and the stable homotopy groups of spheres, and calculations in motivic homotopy theory. The speaker list was a mixture of established leaders in the field, rising stars, assistant professors, researchers with postdoctoral appointments, and even one graduate student. One impetus for this conference was the observation that a remarkable number of the main results of the past few years have been achieved by calculation, following on and benefiting from a period of building and implementing large theory. The workshop emphasized concrete examples. There were 114 registered participants. The sole use of this grant was to fund travel and local expense for 52 graduate students, postdoctoral scholars, and other participants who do not routinely have access to travel support. Funding for most speakers and other researchers came primarily from Northwestern University. This kind of support in vital for building a vibrant community of research mathematicians and for optimizing the distribution of new ideas through the field, especially among research mathematicians beginning their careers.
