# Mathematical Sciences Research Institute

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# Seminar

Gauge Theory (Semi)-Virtual Seminar: Stability and Neck Pinches in Lagrangian Mean Curvature Flow December 12, 2022 (11:30 AM PST - 12:30 PM PST)
Parent Program: Analytic and Geometric Aspects of Gauge Theory MSRI: Online/Virtual, Baker Board Room
Speaker(s) Jason Lotay (University of Oxford)
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Video

#### Gauge Theory (Semi)-Virtual Seminar: Stability And Neck Pinches In Lagrangian Mean Curvature Flow

Abstract/Media

To participate in this seminar, please register HERE.

The famous relation between stability of holomorphic vector bundles and existence of Hermitian Yang-Mills connections can be demonstrated using Yang-Mills flow.  Motivated by this theory and Mirror Symmetry, Thomas-Yau conjectured a stability condition for Lagrangian mean curvature flow which detects when the flow wants to break up the Lagrangian.  When such break up occurs in the flow it is expected to be a singularity called a neck pinch.  I will report on joint work with F. Schulze and G. Szekelyhidi which shows that, for Lagrangian surfaces, Thomas-Yau stability does indeed rule out neck pinch singularities breaking up the Lagrangian along the flow.