# HEGL Community Seminar SoSe22

## Location

The Seminar takes place in Seminar Raum C (Mathematikon) or online via Zoom. Contact us or join the HEGL Mailing List to get the Zoom coordinates.

## Schedule

### 04.07.2022 – Counting Pairs of Saddle Connections

Speaker: Sam Fairchild (MPI)
Time: 14:15
Abstract: A translation surface is a collection of polygons in the plane with parallel sides identified by translation to form a Riemann surface with a singular Euclidean structure. A saddle connection is a special type of geodesic, and the set of saddle connections form discrete subsets of the Euclidean plane. Studying the set of saddle connections is a long standing problem in the field of translation surfaces. I will discuss problems and results related to counting pairs of saddle connections. This talk will include some computer experiments, number theory, dynamics, and geometry. No previous knowledge of translation surfaces or counting problems is necessary.

### 30.05.2022 – Jayadev Athreya (Washington)

Time: 14:15 (on Zoom)

### 16.05.2022 – $$C^1$$ Isometric Embedding of the Hyperbolic Plane

Speaker: Mélanie Theillière (Luxembourg)
Time: 14:15
Abstract: In this talk, we will construct explicitly a $$C^1$$ isometric embedding of the Poincaré disk. And we will see propreties of the limit set (which can be seen as its limit edge) of such a construction. In particular, the Hausdorff dimension of the limit set of the surface built with the explicit parameters of the first part is $$1$$.

### 02.05.2022 – Dynamics, Finite Fields, and Character Varieties:  A Geometry Lab Project Working!

Speaker: Sean Lawton (George Mason)
Time: 15:00 (on Zoom)
Abstract: In 2014, the Mason Experimental Geometry Lab (MEGL) was founded at George Mason University (GMU). During Fall and Spring of that year, MEGL obtained funding, space, equipment, and participants. In Summer 2015, the first research  (and outreach) projects began. One of the first projects explored dynamics on the finite field points of certain algebraic varieties. This project continued every semester and summer until Fall 2018. In addition to interesting conjectures with substantial data to support them and 1000’s of lines of code generating said data, the project created awesome visualizations (images and 3D prints), a GMU-College of Science research award, an undergraduate honors thesis, a PhD thesis, a community of mathematicians (11 student participants, most in PhD programs or in professional scientific positions), and many fond memories. This talk is about that story.