**SMS scnews item created by Stephan Tillmann at Wed 25 Mar 2015 0956**

Type: Seminar

Distribution: World

Expiry: 24 Jun 2015

**Calendar1: 26 Mar 2015 1200-1300**

**CalLoc1: Carslaw 535A**

Auth: tillmann@p710.pc (assumed)

### Geometry & Topology

# Deformations of the peripherial map for knot complements

### Peter Samuelson (Toronto)

========
Thursday 26 March 2015 from 12:00–13:00 in Carslaw 535A

Please join us for lunch at the Grandstand after the talk!

**Abstract:** Deformations of the peripherial map for knot complements
Abstract: The space \(Rep(M)\) of representations of the fundamental group
\(\pi_1(M)\) of a 3-manifold M into \(SL_2(\mathbb{C})\) has played an important role
in the study of 3-manifolds. If \(M = S^3 \setminus K\) is the complement of a
knot in the 3-sphere, then there is a map \(Rep(M) \to Rep(T^2)\) given by
restricting representations to the boundary. There is a natural
deformation \(X(s,t)\) of the space \(Rep(T^2)\) depending on two complex
parameters which comes from a "double affine Hecke algebra." We will
discuss some background and then describe a conjecture that the map
\(Rep(M) \to Rep(T^2)\) has a canonical deformation to a map \(Rep(M) \to X(s,t)\). (This is joint work with Yuri Berest.)