IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar
Intersection Rigidity of Fixed Point Loci of Anti-Symplectic Involutions
The Arnold-Givental conjecture asserts that given a symplectic manifold with an anti-symplectic involution, if the image of the fixed-point locus under a Hamiltonian diffeomorphism intersect the fixed-point locus transversely, them the number of intersection points is bounded from below by the $F_2$ Betti number of fixed-point locus. I will explain a proof of this conjecture, which builds on translating the problem into an equivariant Hamiltonian orbit counting problem following an idea of Lu and our earlier work on integral Hamiltonian Floer theory. This is a joint work with Shelukhin, Wang, and Xu.
Date & Time
October 30, 2026 | 9:15am – 10:45am
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10/30/2026 09:15
10/30/2026 10:45
IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar
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Topic: Intersection Rigidity of Fixed Point Loci of Anti-Symplectic Involutions
Speakers: Shaoyun Bai, Massachusetts Institute of Technology
More: https://www.ias.edu/math/events/iasprincetonmontrealparistel-aviv-symplectic-geometry-zoominar-42
The Arnold-Givental conjecture asserts that given a symplectic
manifold with an anti-symplectic involution, if the image of the
fixed-point locus under a Hamiltonian diffeomorphism intersect the
fixed-point locus transversely, them the number of intersection points
is bounded from below by the $F_2$ Betti number of fixed-point locus.
I will explain a proof of this conjecture, which builds on translating
the problem into an equivariant Hamiltonian orbit counting problem
following an idea of Lu and our earlier work on integral Hamiltonian
Floer theory. This is a joint work with Shelukhin, Wang, and Xu.
Remote Access
a7a99c3d46944b65a08073518d638c23
Location
Remote AccessSpeakers
Shaoyun Bai, Massachusetts Institute of Technology