# Sergey Cherkis : Octonions, Monopoles, and Knots

In 2011 Witten gave a formulation of the Khovanov homology of knots in terms of a system of nonlinear partial differential equations in five dimensions: the Haydys-Witten equations. We highlight the octonionic nature of these equations. This elucidates the importance of the underlying G2 structure and presents the Haydys-Witten equations as a dimensional reduction of the eight-dimensional Spin(7) instanton of Donaldson and Thomas. We conjecture that solutions of the Haydys-Witten equations are in one-to-one correspondence with octonionic monopoles with specific boundary conditions determined by the knot. Octonionic monopole equation also allows to define more general invariants associated to coassociative sumbanifolds in a G2 manifold.

**Category**: Probability**Duration**: 01:34:49**Date**: November 11, 2014 at 4:25 PM**Views**: 164-
**Tags:**seminar, Probability Seminar

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