Colloquium: Tuesday Jan. 28, 2025. Speaker: Liat Kessler (Oranim). Title: “From symplectic deformation to isotopy, equivariantly”.
Speaker: Liat Kessler (Oranim)
Place: Room 614, Education and Sciences Building, University of Haifa
Date and Time: January 28, 2025, 14:00-15:00
Title: From symplectic deformation to isotopy, equivariantly
Abstract: We study symplectic blowups in four-manifolds in the presence of a group action. An (equivariant) symplectic blowup at a point amounts to removing the interior of an embedded ball centered at the point and collapsing the boundary along the Hopf fibration. We ask whether the blowup is determined by the radius r of the ball and the fixed point component F of the center. This is equivalent to asking whether the space of equivariant symplectic embeddings of a ball of radius r centered at F is path-connected.
In the non-equivariant setting, the question was answered by McDuff, applying inflation to turn a symplectic deformation, that is, a path of symplectic forms, between blowup forms into a symplectic isotopy, in which the forms are cohomologous. However, McDuff’s key step of applying Taubes’ “Seiberg-Witten equals Gromov” does not hold in the equivariant setting. In the talk, I will explain how we bypass this step and prove uniqueness of equivariant symplectic blowups. Our approach combines holomorphic and combinatorial methods.
The talk is based on joint work with Pranav Chakravarthy, River Chiang, and Martin Pinsonnault.
Zoom link: https://us02web.zoom.us/j/87282501214?pwd=gnoO4TOG9LKBQJrfQ89Od7nUkoy0S3.1
Meeting ID: 872 8250 1214