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Kathryn Hess: A calculus for knot theory

Tid: On 2015-11-04 kl 15.15

Föreläsare: Kathryn Hess, EPFL, Schweiz

Plats: lecture hall FD5 at Albanova


14.00-15.00 Pre-colloquium by Kaj Börjesson (room FB55 at Albanova)
15:15-16:15 Colloquium lecture by Kathryn Hess (lecture hall FD5 at Albanova, not the usual one)
16:15-17:00 SMC social get together with refreshments


A mathematical knot consists of an embedding of the circle in 3-space. Knot theory - the mathematical study of knots - has been an active, important field of research for well over 100 years. When studying knots, instead of considering one knot at a time, it can be very fruitful to analyze all at once the entire space of knots, i.e., the set of all knots, together with a notion of when two knots are "close" to each other.

The space of knots is an example of what is known as a space of embeddings. I will start by reviewing the classical theory of spaces of embeddings, including famous results of Hirsch, Smale, and Gromov, and explain the analogy between these results and the theory of linear functions. I will then describe how Goodwillie and Weiss extended this analogy, establishing a "calculus" for spaces of embeddings. In particular their theory enables us to construct "polynomial approximations" to spaces of embeddings, together with "converging Taylor series" under nice conditions. To conclude I will sketch briefly a couple of recent applications of the Goodwillie-Weiss calculus, in work of Arone and Turchin and of Dwyer and myself.


Kathryn Hess: A calculus for knot theory (audio only; MP3)

Kathryn Hess: A calculus for knot theory (video and audio; MP4)

Title Date
Dmitry Khavinson: "Between two truths of the real domain, the easiest and shortest path quite often passes through the complex domain." P. Painleve, 1900. A variation on the theme of analytic continua Dec 12, 2015
Kathryn Hess: A calculus for knot theory Nov 06, 2015
Gregory F. Lawler: Self-avoiding motion Oct 09, 2015
Claudio Procesi: Analytic and combinatorial aspects of the Non Linear Schroedinger equation (NLS) on a torus May 27, 2015
Alexander Razborov: Continuous Combinatorics Mar 18, 2015
Christiane Tretter: Operator theory and applications: a successful interplay Feb 04, 2015