Title: Entropy, Stability and Yang-Mills Flow
Speaker: Casey Kelleher, UC Irvine
Date: Monday, December 15, 2014
Time: 11:30am – 12:30pm
Place: Lecture Hall 102, Simons Center
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Abstract: (Joint work with Jeffrey Streets). Following the work of Colding and Minicozzi in the case of mean curvature flow, I will define a notion of entropy for connections over Euclidean n-space which has shrinking Yang-Mills solitons as critical points. This entropy is defined implicitly, making it difficult to work with analytically. I will discuss a characterization of entropy stability in terms of the spectrum of a certain linear operator associated to the soliton. This characterization leads furthermore to a gap theorem for solitons. These results point to a broader strategy of studying “generic singularities” of Yang-Mills flow, and I will discuss the differences in the strategy in dimension n=4 versus larger n.