# Luya Wang : Deformation inequivalent symplectic structures and Donaldsons four-six question

Studying symplectic structures up to deformation equivalences is a fundamental question in symplectic geometry. Donaldson asked: given two homeomorphic closed symplectic four-manifolds, are they diffeomorphic if and only if their stabilized symplectic six-manifolds, obtained by taking products with CP^1 with the standard symplectic form, are deformation equivalent? I will discuss joint work with Amanda Hirschi on showing how deformation inequivalent symplectic forms remain deformation inequivalent when stabilized, under certain algebraic conditions. This gives the first counterexamples to one direction of Donaldsonâ??s â??four-sixâ?ť question and the related Stabilizing Conjecture by Ruan. In the other direction, I will also discuss more supporting evidence via Gromov-Witten invariants.

**Category**: Geometry and Topology**Duration**: 01:04:09**Date**: October 7, 2024 at 3:10 PM**Views**: 0-
**Tags:**seminar, Geometry and Topology Seminar

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