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Arnold's dream: In search for higher-order helicity invariants

4:00 pm Thursday, October 14, 2010
Shea Vela-Vick ( Columbia University)

Arnold dreamed of a hierarchy of helicity invariants which could provide lower bounds for the L2-energy of a vector field under appropriate deformations. Ordinary helicity is a field analogue of the standard linking number between curves, and this correspondence quickly leads to an integral expression for helicity. The general expectation is that higher-order helicity invariants should be obtained as field generalizations of higher order linking invariants, of which Milnor's triple-linking number is the first in line. In this talk, I'll survey some of the history behind helicity invariant and show how one can use configuration space techniques to obtain a geometrically natural integral expression for the Milnor triple-linking number.

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