Statut  Confirmé 
Série  SEMINFOR 
Domaines  hepth,math,mathph,math.AG,math.CO,math.KT,math.MP,math.QA 
Date  Mercredi 24 Mai 2017 
Heure  14:00 
Institut  LPTHE 
Salle  Bibliothèque 
Nom de l'orateur  ZinnJustin 
Prenom de l'orateur  Paul 
Addresse email de l'orateur  
Institution de l'orateur  University of Melbourne 
Titre  Schubert calculus and quantum integrability (3/3) 
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 socalled LittlewoodRichardson 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, Ktheory, 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 Ktheory of dstep 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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