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Sergey Cherkis: Lectures

January 11, 2018
TITLE: Octonionic Monopoles and another look at the Twistor Transform

ABSTRACT: An octonionic monopole is a solution of an octonionic generalization of the Bogomolny equation. Conjecturally, it is dual to a solution of the Haydys-Witten equation and plays central role in using seven-dimentional gauge theory to provide invariants of knot and coassociative cycles in G_2 holonomy manifolds.

Motivated by the search for a model octopole solution, we present a twistorial view of the bow construction of instantons on the multi-Taub-NUT space. We emphasize its quaternionic formulation and its relation to the complex Ward construction, posing a question of similar octonionic-quaternionic relations for the octopole.