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There are many approaches to the KP-hierarchy, ranging from the formal approach in terms of vertex algebras to the more geometric approach using spectral curves. The theory is well-understood in one space dimension, but little has been done in higher dimensions. By casting the geometric approach in terms of the Fourier-Mukai transform, one finds that the theory generalizes nicely, to produce solutions of equations of KP-type associated to varieties of any dimension.

Motohico Mulase is the host.