Event Type:

M.Sc. Presentation

Date/Time:

Monday, June 8, 2020 - 01:00 to 03:00

Location:

Zoom

Abstract:

A translation surface $(X,\omega)$ is a collection of polygons in $\mathbb{R}^2$ together with a set of side-pairing identifications such that identified sides are parallel, equal length and of opposite orientation. There is a natural action of $\text{GL}_2\mathbb{R}$ on the set of all translation surfaces. The subgroup of orientation-preserving elements of the stabilizer of $(X,\omega)$ under this action is called the Veech group, denoted $\text{SL}(X,\omega)$. We present an implementation into SageMath of Edwards's algorithm for computing the Veech group of a compact translation surface $(X,\omega)$. In general, the algorithm returns every element of $\text{SL}(X,\omega)$ whose Frobenius norm is bounded above by a given constant. If the Veech group is a lattice, the algorithm returns a finite set of generators for $\text{SL}(X,\omega)$ in finite time.

If you are interested in attending this presentation, please send an email to Nikki Sullivan - nikki.sullivan@oregonstate.edu - to request Zoom log in details.