On the interaction of normal square-tiled surfaces and group theory

Abstract: A translation surface is obtained by taking finitely many polygons in the Euclidean plane and gluing them along their edges by translations. If we restrict to gluing unit squares, we obtain a square-tiled surface, also known as origami. In the first part of the talk, I explain some motivations for studying translation surfaces. I especially aim to point out why it is natural to study square-tiled surfaces in some of these contexts. In the second part of the talk, we consider certain square-tiled surfaces with maximal symmetry group in more detail. More precisely, we examine their types of singularities and their Veech groups using group theoretic methods. This is partially joint work with Johannes Flake.

algebraic geometry

Audience: researchers in the discipline

American Graduate Student Algebraic Geometry Seminar

Series comments: The American Graduate Student Algebraic Geometry Seminar (AGSAGS) is a virtual seminar by and for algebraic geometry graduate students.

The goal of this seminar is for graduate students to share their research through online talks and to provide an algebraic geometry graduate networking system. Grad students, postdocs, and professors are welcome to attend.

Seminars will be held on Mondays at 4 p.m. Eastern on Zoom. We hope this time is convenient for graduate students in the Americas, hence the name AGSAGS. Prior registration is required and interested participants should register here: sites.google.com/view/agsags/registration. In addition to graduate talks, there will be occasional social events.