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.