Status | Confirmed |
Seminar Series | SEM-INFOR |
Subjects | hep-th,math,math-ph,math.AG,math.CO,math.KT,math.MP,math.QA |
Date | Wednesday 10 May 2017 |
Time | 11:00 |
Institute | LPTHE |
Seminar Room | Bibliothèque |
Speaker's Last Name | Zinn-Justin |
Speaker's First Name | Paul |
Speaker's Email Address | |
Speaker's Institution | University of Melbourne |
Title | Schubert calculus and quantum integrability (1/3) |
Abstract | Schubert calculus is a branch of enumerative geometry, which deals with configurations of linear subspaces of a vector space. Translated into the modern language, it amounts to certain calculations in the cohomology ring of Grassmannians and flag varieties. A practical problem is to give a combinatorial rule for the structure constants of that ring. A few years ago, I observed that there was a hidden quantum integrability in the case of Grassmannians (for which the combinatorial rule is the so-called Littlewood--Richardson rule). In a somewhat unrelated development, there has been a growing body of work (including my own) showing the deep connection between cohomology theories (ordinary cohomology, K-theory, elliptic cohomology) and quantum integrable systems. In particular Maulik and Okounkov introduced a nice framework for this connection. It is natural to try to reinterpret my observation above in this language. After introducing these various concepts, I shall present recent work with A. Knutson in this direction. In particular, this provides completely new rules for the calculation of structure constants of the equivariant cohomology or K-theory of d-step flag varieties for d smaller or equal to 4, thus moving several "steps" closer to the completion of the program of Schubert calculus. |
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