## Braids in Algebra, Geometry and Topology

07 Oct 2016, by Sponsored events in22 – 26 May 2017

ICMS, Edinburgh

Braids are a classical object of study in mathematics and physics. One often first thinks of a braid geometrically, in the sense of “plaits”, with a natural group structure. Braids also describe the configuration space of points in a disk or plane; this in turn can be viewed as the space of roots of polynomials over the complex numbers. Hence braids play a prominent role in a wide variety of disciplines including knot theory and low-dimensional topology, number theory, algebraic geometry, geometric group theory, algebraic topology, and mathematical physics. Braid groups also play a huge role in many applied areas such as cryptography, robotics, fluid dynamics, and molecular biology.

The purpose of this workshop is to celebrate the breadth of the topic, with an eye on identifying common problems that admit multiple phrasings and multiple approaches. We will foster collaborations who may use algebro-geometric techniques to solve a problem in braid groups, for example, but we will also promote the use of braids as a common currency through which, say, a problem in algebraic geometry could be solved using techniques from one of the other fields listed above. Our aim is to ensure that a variety of viewpoints on the subject remains a shared experience for practitioners in a variety of fields, at all career stages.

**Organisers:**

Tara Brendle, University of Glasgow

Jordan Ellenberg, University of Wisconsin

Andrew Putman, University of Notre Dame

Andrew Ranicki, University of Edinburgh