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SUMMARY:Filip Živanović (Simons Center for Geometry and Physics at Stony
  Brook)
DTSTART:20231212T160000Z
DTEND:20231212T170000Z
DTSTAMP:20260423T022742Z
UID:Geolis/136
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Geolis/136/"
 >Filtrations on cohomology from Floer theory of contracting $\\mathbb C^*$
 -actions</a>\nby Filip Živanović (Simons Center for Geometry and Physics
  at Stony Brook) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nWe st
 udy open symplectic manifolds with pseudoholomorphic $\\mathbb C^*$-action
 s whose $S^1$-part is Hamiltonian\, and construct their associated symplec
 tic cohomology. From this construction\, we obtain a filtration on quantum
 /ordinary cohomology that depends on the choice of the $\\mathbb C^*$-acti
 on. One should think about this filtration as a Floer-theoretic analogue o
 f the Atiyah-Bott filtration. We construct filtration functional on the Fl
 oer chain complex\, allowing us to compute the aforementioned filtration v
 ia Morse-Bott spectral sequence that converges to symplectic cohomology\, 
 which is readily computable in examples. We compare our filtration with kn
 own ones from algebraic geometry/representation theory literature. Time-al
 lowing\, I may present the $S^1$-equivariant picture as well. This is join
 t work with Alexander Ritter.\n
LOCATION:https://researchseminars.org/talk/Geolis/136/
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