Talk page
Title:
Gap and index estimates for Yang-Mills connections in 4-d
Speaker:
Abstract:
In this talk I want to discuss 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. I will present some recent work (joint with Kelleher and Streets) that attempts to address each question when the base manifold has positive scalar curvature. I will also mention some other geometric applications in 4-d.
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