Type: Seminar

Distribution: World

Expiry: 23 Aug 2017

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

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