Posted January 16, 20191:30 pm - 3:00 pm Lockett 233
Shea Vela-Vick, Louisiana State University
Arnold's dream: in search for higher-order helicity invariants
Abstract: Arnold dreamed of a hierarchy of helicity invariants which could provide lower bounds for the L_2-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.