SMS scnews item created by Alexander Kerschl at Sun 5 Aug 2018 2251
Type: Seminar
Distribution: World
Expiry: 14 Oct 2018
Calendar1: 6 Aug 2018 1700-1800
CalLoc1: Carslaw 535A
CalTitle1: Representation Varieties for SL(3,C): The Trefoil Knot
Auth: kerschar@202.76.184.146.dynamic.rev.eftel.com (aker8037) in SMS-WASM

# MaPSS: Maths Postgraduate Seminar Series: Dickson Annor -- Representation Varieties for SL(3,C): The Trefoil Knot

Hello all,

The next MaPSS talk of this semester will be at 17:00 on Mon 6th August in Carslaw 535.
Feel free to come, as it is a great opportunity to meet fellow postgrads, listen to
an interesting talk, and of course get free food!

**************************************************************************************

Speaker: Dickson Annor

Title: Representation Varieties for SL(3,C): The Trefoil Knot

Abstract: Following the foundational work of Thurston, Culler and Shalen, the
varieties of representations and characters of 3-manifold groups into SL(2,C) have
been extensively studied, as both reflect geometric and topological properties of
3-manifolds. However, much less is known about the representations of 3-manifold
groups into other Lie groups, notably SL(n,C) with n >= 3.

In this talk, we will study representation varieties of the trefoil knot group into
SL(3,C). Let G be the fundamental group of the complement of the trefoil knot in
S^3. This has presentation G = <x,y | x^2 = y^3> = <s,t | sts = tst>. In particular,
we will determine all representations up to conjugacy, using results of Fricke for
SL(2,C) and Lawton for SL(3,C).

**************************************************************************************

See you there!

Details can also be found on the schoolâ€™s new Postgraduate Society website:
http://www.maths.usyd.edu.au/u/MaPS/mapss.html

Cheers,
Alex


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