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Singularity Formation of the Yang-Mills Flow

Connections for Women: Differential Geometry January 14, 2016 - January 15, 2016

January 15, 2016 (02:00 PM PST - 03:00 PM PST)
Speaker(s): Casey Kelleher (Princeton University)
Location: MSRI: Simons Auditorium
Tags/Keywords
  • differential geometry

  • Manifolds

  • curvature

  • geodesic flow

  • Yang-Mills equations

  • Hausdorff dimension

  • singularities

  • stratification

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video
No Consent
The speakers have declined to have their material posted on the web
Abstract

We explore the structure of the singularities of Yang-Mills flow in dimensions n ≥ 4. First we derive a description of the singular set in terms of concentration for a localized entropy quantity, which leads to an estimate of its Hausdorff dimension. We develop a theory of tangent measures for the flow at such singular points, which leads to a stratification of the singular set. By a refined blowup analysis we obtain Yang-Mills connections or solitons as blowup limits at any point in the singular set. This is joint work with Jeffrey Streets

Supplements
25482?type=thumb Kelleher_Notes 12.6 MB application/pdf Download