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Laurant coefficients of renormalized potential energies

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If you have a question about this talk, please contact Mustapha Amrani.

Topological Dynamics in the Physical and Biological Sciences

Energy of a knot was originally defined as the integration of the renormalized potential of a certain kind. Here, the renormalization can be done as follows: Suppose we are interested in a singular integral $int_Omegaomega$, which blows up on a subset $X ubsetOmega$. Remove an $delta$-tubular neighbourhood of $X$ from $Omega$, consider the integral over the complement, expand it in a Laurant series of $delta$, and take the constant term. This idea gave rise to a M”obius invariant surface energy in the sense of Auckly and Sadun, and recently, to generalization of Riesz potential of compact domains. If we integrate this generalized Riesz potential over the domain, we may need another renormalization around the boundary, according to the order of the generalized Riesz potential.

In this talk I will give “baby cases” of the application of the above story to the study of knots or surfaces.

This talk is part of the Isaac Newton Institute Seminar Series series.

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