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SUMMARY:Equivariant formality of the little disks operad - Joana Cirici (U
 niversitat de Barcelona)
DTSTART:20250619T091500Z
DTEND:20250619T101500Z
UID:TALK230701@talks.cam.ac.uk
DESCRIPTION:I will show that the little n-disks operad is SO(n)- and O(n)-
 equivariantly formal over the rationals. Equivalently\, the oriented and u
 noriented framed little disks operads are rationally formal as infinity-op
 erads. The approach to prove these results relies on a &ldquo\;purity impl
 ies formality&rdquo\; technique. Specifically\, we consider the action of 
 the Grothendieck&ndash\;Teichm&uuml\;ller group on the rationalized little
  disks operad\, constructed using the additivity theorem. This induces an 
 action on the rationalized Borel construction\, with special purity proper
 ties.&nbsp\;\nAs a consequence of our method\, we also establish rational 
 formality for algebraic group actions on smooth complex projective varieti
 es\, using Galois action on &eacute\;tale cohomology as input.&nbsp\;\nThi
 s is joint work with Pedro Boavida de Brito and Geoffroy Horel.
LOCATION:Seminar Room 1\, Newton Institute
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