--------------------------------------------------------------------------------------------------
Lunch: Before the talks, we will meet for a lunch at 12pm near the main entrance to the department - please e-mail Anna Felikson if you plan to join. The lunch will be in the Grey college, very close to the department, if you arrive between 12pm and 13pm you can join us there (see here for the map).
The construction of the Farey tessellation in the hyperbolic plane starts with a finitely generated group of symmetries of an ideal triangle and induces a remarkable fractal structure on the boundary of the hyperbolic plane, encoding every element by the continued fraction related to the structure of the tessellation. The problem of finding a generalisation of this construction to the higher dimensional hyperbolic spaces has remained open for many years. In this paper we make the first steps towards a generalisation in the three-dimensional case. We introduce conformal bryophylla, a class of subsets of the boundary of the hyperbolic 3-space which possess fractal properties similar to the Farey tessellation. We classify all conformal bryophylla and study the properties of their limiting sets. This is joint work with Oleg Karpenkov.
I shall sketch the proof of an embedding theorem for finitely presented groups that can be used to show that many properties of finitely generated, residually finite groups cannot be detected from a complete knowledge of their finite quotients -- for example, one cannot see if the group is virtually torsion-free, is 2-dimensional (or finite dimensional), contains Z^7, is virtually free-by-free, is left-orderable, or 2-free, ...
16:00-16:30 Tea
Given a surface, one might want to understand how "complex" the surface is, in terms of curves. More specifically, we may ask how many times two curves on this surface can intersect. Of course, longer curves might intersect more times. A way to make this precise is to define a quantity called KVol which, intuitively, measures how many times curves on our surface can intersect, modulo their length. We will give an overview of some cases for which this quantity has been calculated, with particular focus on Veech surfaces, a class of flat surfaces with a rich group of symmetries. This is joint work with Julien Boulanger.
Dinner: There will be a dinner at 6pm at Lebaneat restaurant. Please e-mail Anna Felikson if you plan to attend.
--------------------------------------------------------------------------------------------------
The MAGIC room MCS3070 is on the top floor of the Maths and Computer Science building, in the central corridor.
