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Statut |
Confirmé |
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Série |
SEM-INFOR |
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Domaines |
hep-th,math,math-ph,math.AG,math.CO,math.KT,math.MP,math.QA |
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Date |
Mercredi 24 Mai 2017 |
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Heure |
14:00 |
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Institut |
LPTHE |
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Salle |
Bibliothèque |
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Nom de l'orateur |
Zinn-Justin |
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Prenom de l'orateur |
Paul |
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Addresse email de l'orateur |
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Institution de l'orateur |
University of Melbourne |
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Titre |
Schubert calculus and quantum integrability (3/3) |
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Résumé |
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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Numéro de preprint arXiv |
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