## Brussels-London

geometry seminar

Day-long geometry seminars with three talks on a common theme

Next seminar Join mailing list

The seminar involves geometers from the Université libre de Bruxelles and the following London colleges:

University College, King's College, Queen Mary's College, and Imperial College.

#### Brussels-London XV

# Teichmüller theory and hyperbolic geometry

#### University College London, 21st September 2018

The talks will take place at University College London. The lectures will be in the Harrie Massey Lecture Theatre, in 25 Gordon Street. The breaks will be in room 502 of the Department of Mathematics, also in 25 Gordon Street. Directions and maps are available below.

Registration is free, but necessary so that we know how many people to expect. To register please send an email to Jason Lotay. Lunch will be provided for all registered attendees.

#### 11:00 Marc Lackenby

#### 14:00 Viveka Erlandsson

#### 15:30 Jean-Marc Schlenker

**Marc Lackenby.** The triangulation complexity of 3-manifolds.

The triangulation complexity of a closed orientable 3-manifold M is the minimal number of tetrahedra in any triangulation of M. It is a natural, but poorly understood, invariant. In my talk, I will explain how it may be computed, to within a bounded factor, for any hyperbolic 3-manifold that fibres over the circle with fibre a given closed orientable surface S. I will show that it is equal, up to a bounded factor, to the translation distance of the action of the monodromy on the mapping class group of S. I will also explain how the methods that we develop can be applied to lens spaces; we determine their triangulation complexity to within a universally bounded factor. All this is joint work with Jessica Purcell.

**Viveka Erlandsson.** Determining the shape of a billiard table from its bounces.

Consider a billiard table shaped as a Euclidean polygon with labeled sides. A ball moving around on the table determines a bi-infinite “bounce sequence” by recording the labels of the sides it bounces off. We call the set of all possible bounce sequences the “bounce spectrum” of the table. In this talk I will explain why the bounce spectrum essentially determines the shape of the table: with the exception of a very small family (right-angled tables), if two tables have the same bounce spectrum, then they have to be related by a Euclidean similarity. The main ingredient in proving this fact is a technical result about Liouville currents for flat cone metrics. This is joint work with Moon Duchin, Chris Leininger, and Chandrika Sadanand.

**Jean-Marc Schlenker.** The renormalized volume of quasifuchsian manifolds.

Quasifuchsian hyperbolic manifolds have infinite volume, but have a well-defined "renormalized" volume. We will explain a simple, differential-geometric definition of this quantity and explain how it relates to, and brings new insight on, the Weil-Petersson geometry of Teichmüller space.

#### Getting to UCL

The talks will take place at University College London, in the building which houses the Mathematics Departement, 25 Gordon Street. The The lectures will be in the Harrie Massey Lecture Theatre, on the ground floor of 25 Gordon Street. The breaks will be in room 502 of the Department of Mathematics, also in 25 Gordon Street.

A map showing how to get to the Harrie Massey Lecture Theatre, 25 Gordon Street is available here.

#### Registration

Registration is free, but necessary in order that we know how many people to cater for. In order to register for the seminar please send an email to Jason Lotay. Lunch will be provided for all registered attendees.

Register

#### Past seminars

Click on the seminar names to see the speakers, titles and abstracts.

#### Scientific committee

The organisers of the Brussels-London geometry seminar are Joel Fine (ULB), Jason Lotay (UCL) and Felix Schülze (UCL).

In addition to the organisers, the scientific committee includes:

- Mélanie Bertelson (Université libre de Bruxelles)
- Simone Gutt (Université libre de Bruxelles)
- Reto Müller (Queen Mary's College, London)
- Dmitri Panov (King's College, London)
- Bruno Premoselli (Université libre de Bruxelles)
- Michael Singer (University College, London)
- Guiseppe Tinaglia (King's College, London)

#### Funding

The seminar is supported by the London Mathematical Society, the ERC and the FNRS. Thanks to this support, there is funding to help graduate students and postdocs attend this seminar. If you are based in London, please contact Jason Lotay or Joel Fine.

#### Mailing list

To keep up-to-date with the seminar schedule, add your name to our mailing list.

Join mailing list