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Gap and index estimates for Yang-Mills and harmonic map theory

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Monday, October 21, 2019
3:15 pm - 4:15 pm
Casey Lynn Kelleher
Geometry/topology Seminar

In this talk we want to discuss joint work with Streets and Gursky on two related questions about the variational structure of the Yang-Mills functional in dimension four. The first is the question of 'gap' estimates; i.e., determining an energy threshold below which any solution must be an instanton, hence a minimizer for the Y-M energy. The second question is about non-minimal solutions, and in this case the problem is to estimate the index of a solution. Time permitting, we will also discuss related joint work with Gursky on a gap estimate in harmonic map theory.