SMS scnews item created by Timothy Bywaters at Mon 31 Jul 2017 1438
Type: Seminar
Distribution: World
Expiry: 23 Aug 2017
Calendar1: 23 Aug 2017 1100-1200
CalLoc1: Carlsaw 352
CalTitle1: Gardam, Determining hyperbolic 3-manifold groups by their finite quotients
Calendar2: 23 Aug 2017 1400-1500
CalLoc2: Carslaw 375
CalTitle2: Elder, The structure of solutions to equations in free and virtually free groups
Auth: [email protected]
Group Actions Seminar: Gardam, Elder
The next Group Actions Seminar will be on Wednesday 23 August at the University of Sydney.
The schedule, titles and abstracts are below.
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11am - Noon, Carslaw 352
Speaker: Giles Gardam, The University of Oxford
Title: Determining hyperbolic 3-manifold groups by their finite quotients
Abstract: It is conjectured that if \(M\) and \(N\) are finite volume hyperbolic
3-manifolds, then \(M\) and \(N\) are isometric if and only if their fundamental groups
have the same finite quotients. The most general case in which the conjecture is known
to hold is when M is a punctured torus bundle over the circle, by work of Bridson,
Reid and Wilton. Distinguishing a single pair of hyperbolic 3-manifold groups by
naively enumerating finite quotients with a computer can take days. In this talk, I
will describe the relatively non-naive computational verification that the conjecture
holds when both \(M\) and \(N\) are chosen from the ~70,000 census manifolds included in
SnapPy, and the theory behind it.
Noon - 2pm Lunch
2-3pm, Carslaw 375
Speaker: Murray Elder , The University of Technology Sydney
Title: The structure of solutions to equations in free and virtually free groups
Abstract: I will describe work with Ciobanu and Diekert which expresses the full set of
solutions to an equation or system of equations over a free group, and over a virtually
free group, as an EDT0L language, and can be computed in PSPACE. EDT0L is a relatively
simple formal language class, so it is surprising that what seemed like a complicated
set has such an easy description. The new work with Diekert on virtually free groups
reduces equations to systems of twisted equations using Bass-Serre theory.
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