# 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

### 20.07.2022 – Final Project Presentations

Time: 13:00 (Seminar Raum C)
Abstract: Join us to learn about the HEGL Student Projects from the Summer 2022 Semester. There will be lightning talks on:

• Symplectic billiards
• Hyperbolic billiards
• Ray marching in translation surfaces
• Hyperbolic shooting game
• Moebius paint
• Mirrors
• Hopf Fibration

Pizza and refreshments will be presented in the Foyer after the talks. Note the unusual date and time.

### 18.07.2022 – Periodic billiards on regular polygons

Speaker: Diana Davis (Phillips Exeter Academy)
Time: 14:15 (Seminar Raum C)
Abstract: Imagine that you hit a ball in a regular polygon-shaped billiard table, and after bouncing around for a while, the ball comes back to where it started and then repeats its path. I’ve been studying these “periodic” paths for many years, and it turns out that they’re very beautiful, like mathematical art. I’ll show lots of pictures, and explain the underlying tree and group structures. This is joint work with Samuel Lelièvre.

### 04.07.2022 – Counting Pairs of Saddle Connections

Speaker: Sam Fairchild (MPI)
Time: 14:15 (Seminar Raum C)
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.

### 20.06.2022 – A tour of 3D printed mathematics: Tritangentless trefoils, ideal graph configurations, and chaotic attractors

Speaker: Laura Taalman & Steve Lucas (James Madison)
Time: 14:15 (on Zoom)
Abstract: In this talk, we’ll take a 3D-printed tour of a collection of mathematical objects we have made over the years. We’ll start with building tritangentless trefoils and show how to make them roll as easily as possible. We will then look at ways to construct collections of ideal graph configurations in three dimensions. Finally, we will show how to create 3D mesh models to accurately visualize a variety of chaotic orbits. Along the way, we will explore the technical and computational tools needed for creating 3D-printable mathematical models, including OpenSCAD, Mathematica, and MATLAB, and provide resources to help students and mathematicians who wish to create their own models.

### 15.06.2022 – Mid-Semester Presentations

Time: 13:00 (Seminar Raum A)
Organizers: Zachary Greenberg, Merik Niemeyer, Diaaeldin Taha
Abstract: Join us to learn about the HEGL Student Projects from the Summer 2022 Semester. There will be lightning talks on:

• Symplectic billiards
• Hyperbolic billiards
• Ray marching in translation surfaces
• Hyperbolic shooting game
• Moebius paint
• Mirrors
• Hopf Fibration

Pizza and refreshments will be presented in the Foyer after the talks. Note the unusual time and location.

### 30.05.2022 – What is Research in Mathematics

Time: 14:15 (on Zoom)
Abstract: What does it mean to create/discover new mathematics? How does one get involved in this process? We’ll discuss this via a couple of examples: no background needed, and there will be *lots* of pictures!

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

Speaker: Mélanie Theillière (Luxembourg)
Time: 14:15 (Seminar Raum C)
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.