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University of Glasgow, 9 December 2024
Timetable
The talks will be held in the Mathematics and Statistics Building, precisely in room 311b.
1.00 – 2.00 pm: Monika Kudlinska, Analogues of the Thurston norm in groups.
2.00 – 2.30 pm: Break.
2.30 – 3.30 pm: Oli Jones, Finiteness Properties of Outer Automorphisms Groups Of Large Type Artin Groups.
3.30 – 4.00 pm: Tea Break.
4.00 – 5.00 pm: Luke Jeffreys, SL(2,Z)-invariants of single-cylinder square-tiled surfaces.
5.30 pm: Dinner (restaurant to be confirmed).
Please complete the form by 02/12 if you plan to attend. We are planning to book a restaurant close to Hillhead subway station—from there, you can take the subway to the train station.
Please email either Riccardo Giannini or Philipp Bader for any questions.
Analogues of the Thurston norm in groups
Analogues of the Thurston norm in groups
The Thurston norm of a 3-manifold M measures the minimal topological complexity of surfaces dual to characters of M. In this talk, we will introduce a real-valued function on the first cohomology of an arbitrary group which generalises the Thurston norm. We will propose a strategy for proving that such a function defines a seminorm using the theory of L2-invariants. Finally, we will implement this strategy for some classes of right angled Artin groups using the recent calculations of L2-Betti numbers of Artin kernels due to Fisher-Hughes-Leary.
Finiteness Properties for Outer Automorphism Groups of Large Type Artin Groups
Finiteness Properties for Outer Automorphism Groups of Large Type Artin Groups
In this talk I will introduce a deformation space for connected large type Artin groups. Under mild hypotheses, the space depends only on the isomorphism type of the Artin group (not the presentation graph), and in these cases admits an action of the outer automorphism group. I will discuss how this action can be used to show the outer automorphism groups of such Artin groups are of Type VF (which in particular implies finitely presentability).
SL(2,Z)-invariants of single-cylinder square-tiled surfaces
Translation surfaces are surfaces obtained by identifying opposite sides of Euclidean polygons (think of gluing the sides of a square to get a torus). The space of translation surfaces carries a natural and well-studied action by SL(2,R). When all the polygons used to construct the surface are squares, we say that the surface is square-tiled. On the set of square-tiled surfaces, the action of SL(2,R) restricts to an action of SL(2,Z). The classification of SL(2,Z)-orbits of square-tiled surfaces has only been carried out in a few cases and is wide open in general. In this talk, in an attempt to understand their SL(2,Z)-orbits, I will discuss work calculating certain SL(2,Z)-invariants (monodromy and spin parity) of a family of (single-cylinder) square-tiled surfaces recently constructed by Aougab-Menasco-Nieland. I will also present some computational evidence suggesting a connection between monodromy groups of single-cylinder square-tiled surfaces and finite simple groups. This is joint work with Tarik Aougab, Adam Friedman-Brown, and Jiajie Ma.
Support
Some travel funding is available for attendees, and PhD students and postdocs will be prioritised. We’d appreciate it if those interested in travel funding contacted us before the meeting so that we can allocate it accordingly.
We expect to be able to partially cover the cost of dinner for postgraduate students and early-career researchers.
Seminar Information
The North British Geometric Group Theory Seminar is a collaborative seminar that has been running since 2003. The seminar involves geometric group theorists from Heriot–Watt, Glasgow, Newcastle, Durham, York, Leeds, Manchester, Nottingham, St Andrews, and Leicester, and meets three times a year.
We are very grateful for financial support from the London Mathematical Society and the Glasgow Mathematical Journal Learning and Research Support Fund.
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