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UID:7996@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20151005T140000
DTEND;TZID=Europe/Paris:20151005T150000
DTSTAMP:20241120T205623Z
URL:https://www.i2m.univ-amu.fr/evenements/an-affine-quantum-cohomology-ri
 ng-for-flag-manifolds-and-the-periodic-toda-lattice/
SUMMARY:Liviu Maré (...): An affine quantum cohomology ring for flag manif
 olds and the periodic Toda lattice
DESCRIPTION:Liviu Maré: I will talk about the quantum cohomology ring of f
 ull affine Kac-Moody flag manifolds\, which are the affine analogues of re
 gular coadjoint orbits of compact Lie groups. Such rings have been investi
 gated in papers by Guest and Otofuji (2001) and by myself (2004). However\
 , the rigorous foundations are still to be established. The main focus of 
 the talk will be on results that Leonardo Mihalcea and myself have obtaine
 d recently in this context. First\, we proved a quantum Chevalley formula\
 , which describes the quantum multiplication by degree-two classes. Even t
 hough these classes do not generate the entire cohomology ring\, our formu
 la can be used to define a new (associative) ring\, whose ideal of relatio
 ns is determined by the integrals of motion of a certain integrable system
  of Toda lattice type.\n\n\n
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 020/01/Liviu_Mare.jpg
CATEGORIES:Séminaire,Dynamique et Topologie
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