Positive Grassmannians: Applications to integrable systems and super Yang-Mills scattering amplitudes

July 27-31, 2015

Organizers : Marco Bertola (Concordia), Michael Gekhtman (Notre Dame), John Harnad (Concordia & CRM)

The discovery of cluster algebras by Fomin and Zelevinsky was in large part motivated by the study of the phenomenon of total positivity in reductive Lie groups. Grassmannians were among the first examples of varieties that support a natural cluster structure, that was arrived at in two ways: combinatarial, using Postnikov's work on parametrizing totally nonnegative cells in Grassmannians using directed planar networks, and geometric, that utilized properties of Grassmannians as Poisson homogeneous spaces.

A new setting in which totally positive Grassmannians have appeared recently is in the computation of scattering amplitudes in the planar limit of maximally extended supersymmetric Yang-Mills theory (SSYM). Using momentum space twistor transform methods, explicit integral representations of the leading term singularities were obtained as integrals over Grassmann manifolds, localized to submanifolds determined by the external momentum and helicity configurations.

Participants:

J. Bourjaily (Harvard), S. Franco (Durham), M. Glick (Minnesota), R Kedem (UI Urbana-Champaign), Y. Kodama (Ohio State), T. Lam (Michigan), A. Neitzke (UT Austin), V. Ovsienko (Reims), P. Pylyavskyy (Minnesota), K. Rietsch (King’s College London), M. Shapiro (Michigan State), F Soloviev (Fields Institute), S. Tabachnikov (Penn State), J. Trnka (Caltech), H Williams (Berkeley), L. Williams (Berkeley)