Knots, three-manifolds and instantons - Peter Kronheimer & Tomasz Mrowka - ICM2018

Plenary Lecture 11
Knots, three-manifolds and instantons
Peter Kronheimer & Tomasz Mrowka
Abstract: Over the past four decades, input from geometry and analysis has been central to progress in the field of low-dimensional topology. This talk will focus on one aspect of these developments, namely the use of Yang-Mills theory, or gauge theory. These techniques were pioneered by Simon Donaldson in his work on 4-manifolds beginning in 1982, but the past ten years have seen new applications of gauge theory, and new interactions with more recent threads in the subject, particularly in 3-dimensional topology and knot theory. In our exploration of this subject, a recurring question will be, “How can we detect knottedness?” Many mathematical techniques have found application to this question, but gauge theory in particular has provided its own collection of answers, both directly and through its connection with other tools. Beyond classical knots, we will also take a look at the nearby but less-explored world of spatial graphs.
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