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: timothyb@como.maths.usyd.edu.au

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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