Interactions of Elliptic Cohomology with Other Subjects

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AbstractAward: DMS-0504539Principal Investigator: Nora GanterThe project investigates the interaction of elliptic cohomologywith other areas of mathematics and physics, with a focus onequivariant phenomena and power operations. Subjects treatedrange from orbifold models in string theory over representationand character theory in 2-categories to generalized Moonshine andstable homotopy theory. Hopkins-Kuhn-Ravenel character theoryarose in the context of homotopy theory and exposes many formalsimilarities between the above fields. The goal of the projectis to better understand the mechanisms underlying theseobservations. Power operations in elliptic cohomology werealready linked to product formulas in string theory and to thetwisted Hecke operators of generalized Moonshine. This projectwill further pursue these connections, aiming to clarify thelinks between the literature in these three subjects.In less technical terms: Elliptic cohomology is a rich mix ofareas of mathematics and physics, which on the surface do notappear to have much to do with each other. Especially in thepresence of an action by a group of symmetries, one can observemany analogies between seemingly unrelated research areas. Withcollaborators from various fields of mathematics, this projectseeks to find an explanation for the deeper mechanisms underlyingthese phenomena.