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### Self-dual puzzles in Schubert calculus branching

**Algebra & Discrete Mathematics**

Speaker: | Iva Halacheva, Northeastern University |

Related Webpage: | https://sites.google.com/site/ivahalacheva3/ |

Location: | Zoom |

Start time: | Mon, Jun 1 2020, 1:10PM |

In classical Schubert calculus, Knutson and Tao’s puzzles are a combinatorial tool that gives a positive rule for expanding the product of two Schubert classes in equivariant cohomology of the (type A) Grassmannian. I will describe a positive rule that uses self-dual puzzles to compute the restriction of a Grassmannian (type A) Schubert class to the symplectic (type C) Grassmannian in equivariant cohomology. The proof uses the machinery of quantum integrable systems. I will also discuss a generalization in which the Grassmannians are upgraded to their cotangent bundles and Schubert classes—to Segre-Schwartz-MacPherson classes. The resulting construction involves Lagrangian correspondences and produces a generalized puzzle rule with a geometric interpretation. This is joint work with Allen Knutson and Paul Zinn-Justin.

Notes: https://www.math.ucdavis.edu/~egorskiy/AGADM/Halacheva_notes.pdf

Zoom link https://ucdavisdss.zoom.us/j/842986080, please contact Eugene Gorsky or José Simental Rodríguez for password.