Computation in geometric topology

11–15 December 2017

Organisers: Nathan DunfieldLink opens in a new window, Stephan TillmannLink opens in a new window, Saul SchleimerLink opens in a new window

Registration is now closed. Please contact the MRC directly if you wish to attend.

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Computer experiments and calculations have had a profound influence on many areas covered by this Symposium. In 3-manifold theory the program SnapPea has been widely used to explore the landscape of 3-manifolds, including the behaviour of invariants such as the Chern-Simons invariant and volume. In Teichmüller dynamics computation plays an important role in understanding $SL(2,\Bbb{R})$ -orbit closures in strata, starting with McMullen's work in genus two. In the study of mapping class group actions on representation varieties, computer experiments informed Tian Yang's proof of Goldman's conjecture for the four-times punctured sphere.

Different subjects naturally develop computer tools specific to problems in their own area. Since solutions to these problems are very often of interest to researchers in related areas, this raises the problem of communication between these tools. A principal goal of this workshop is to further the process of developing interfaces between existing computational tools. As just one example, Ben Burton has recently constructed an interface between his program Regina and SnapPea to extend the census of cusped hyperbolic three-manifolds; Regina should also be capable of producing monodromy data for surface bundles, which would then feed into the various software packages devoted to the mapping class group.

In general the workshop will bring together, from all areas of the Symposium, researchers who have worked extensively with computers, researchers with problems which might be amenable to computer assistance, and researchers who are primarily interested in the practical and theoretical computer problems arising from work done in these areas. The emphasis will be on communication among these different groups, discussing theoretical questions of computability and complexity as well as more concrete practical computational tools.

Speakers

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