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Invariants of Random Knots

Mathematical Physics & Probability

Speaker: Joel Hass, UC Davis
Location: 1147 MSB
Start time: Wed, Feb 25 2015, 4:10PM

Random curves in space and how they are knotted give an insight into the behavior 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 Evan-Zohar, Linial and Nowik, we have found explicit formulas for the distributions of the linking number of a two component link. We also find formulas for the moments of two finite type invariants of knots, the Casson invariant and for a coefficient of the Jones polynomial.