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UID:d36c6e6d9899c941ae71a1f2e1b1de8e
CATEGORIES:Symplectic Geometry Seminar
CREATED:20260428T143843
SUMMARY:Steenrod operations, operads, and Lagrangian realization
LOCATION:SEC 117
DESCRIPTION:Title: Steenrod operations, operads, and Lagrangian realization\nAbstract: 
 It is classically known that the fundamental class of an algebraic cycle in
  a smooth projective complex variety has vanishing odd Steenrod powers; thi
 s leads to the first counterexample to the integral Hodge conjecture by Ati
 yah and Hirzebruch. Motivated by mirror symmetry, one may ask what obstruct
 ions are there for a middle homology class of a closed symplectic manifold 
 to be realized by a rigid Lagrangian (i.e. supporting an object of the Fuka
 ya category). In this talk, I would like to share some ongoing (and far fro
 m complete) attempts at this question that see interesting links to Fukaya 
 category, E_2 operadic structures, and equivariant operations in Gromov-Wit
 ten theory. \n
X-ALT-DESC;FMTTYPE=text/html:<p>Title: Steenrod operations, operads, and Lagrangian realization</p><p>Ab
 stract: It is classically known that the fundamental class of an algebraic 
 cycle in a smooth projective complex variety has vanishing odd Steenrod pow
 ers; this leads to the first counterexample to the integral Hodge conjectur
 e by Atiyah and Hirzebruch. Motivated by mirror symmetry, one may ask what 
 obstructions are there for a middle homology class of a closed symplectic m
 anifold to be realized by a rigid Lagrangian (i.e. supporting an object of 
 the Fukaya category). In this talk, I would like to share some ongoing (and
  far from complete) attempts at this question that see interesting links to
  Fukaya category, E_2 operadic structures, and equivariant operations in Gr
 omov-Witten theory.&nbsp;</p>
CONTACT:Zihong Chen (Cambridge)
DTSTAMP:20260827T220127
DTSTART;TZID=America/New_York:20260501T101500
DTEND;TZID=America/New_York:20260501T111500
SEQUENCE:0
TRANSP:OPAQUE
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