Higher Helicities, Geometric Linking Integrals, and Koschorke's Conjecture

speaker: Clayton Shonkwiler (Haverford College, USA)

abstract: The search for higher helicities, which ought to provide lower bounds on the field energy when the usual helicity vanishes, has been ongoing for more than twenty years. The analogy between helicity and the linking number suggests that geometric integral formulas for higher-order linking invariants may lead to higher helicities. I will present such an integral formula for Milnor's triple linking number and discuss the connections between this formula and a conjecture of Koschorke relating link-homotopy invariants of links and the homotopy invariants of associated maps to configuration space.

timetable:
Wed 18 May, 15:50 - 16:20, Aula Dini
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