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Invariants of Random Knots

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Random curves in space and how they are knotted give an insight into the behaviour of “typical” knots and links. They have been studied by biologists and physicists in the context of the structure of random polymers. There have been many results obtained via computational experiment, but few explicit computations. In work with Hass, Linial and Nowik, we study random knots based on petal projections, developped by Adams et al. (20120. We have found explicit formulas for the distribution of the linking number of a two component link. We also find formulas for the moments of two finite invariants of knots, the Casson invariant and another coefficient of the Jones polynomial. No background in Knot Theory will be supposed. All the terms above will be explained.

Joint work with Joel Hass, Nati Linial and Tahl Nowik.

This talk is part of the Probability series.

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