# Mathematics Colloquia and Seminars

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### Stratifying On-Shell Cluster Varieties

**QMAP Seminar**

Speaker: | Jacob Bourjailly, Neils Bohr |

Related Webpage: | http://www-personal.umich.edu/~jbourj/ |

Location: | 2112 MSB |

Start time: | Fri, Oct 28 2016, 12:15PM |

There exists a deep correspondence between a class of physically important functions—called "on-shell functions"—and certain (cluster variety) subspaces of Grassmannian manifolds, endowed with a volume form that is left invariant under cluster coordinate transformations. These are called "on-shell varieties" (which may or may not include all cluster varieties). It is easy to prove that the number of on-shell varieties is finite, from which it follows that the same is true for on-shell functions. This is powerful and surprising for physics, because these on-shell functions encode

completeinformation about perturbative quantum field theory.In this talk, I describe the details of this correspondence and how it is constructed and give the broad physics motivations for obtaining a more systematic understanding of on-shell cluster varieties. I outline a general, brute-force strategy for classifying these spaces; and describe the results found by applying this strategy to the case of Gr(3,6).

Bring lunch