Winter 2022 Student Projects

HEGL Praktika

Physics-Based Graph Layout in Hyperbolic Space

Mentor: Zachary Greenberg
Team members: Open for 3 members
Description: In Euclidean space, a physics simulation has been successfully used to find graph layouts that show the symmetries of a given graph without being explicitly specified. Some graphs have hyperbolic symmetries that should be revealed via an analogous simulation on the Poincare disc. Time permitting, we can explore other geometries, including layout in 3d.
Prerequisites: Basic programming skills.

Physics-based layouts in Euclidean space.

Rolling Knots

Mentors: Anja Randecker and Maurice Reichert
Team members: Open for 3 members
Description: In the year 1980 M. H. Freedman conjectured that every generic smooth knot in 3-dimensional euclidean space has a tritangent plane, i.e. a plane tangent to 3 distinct points. Ten years later A. M. Amilibia, J. J. N. Ballesteros and H. R. Morton used trefoil knots to construct a family of counterexamples. Such a tritangentless knot has no stable position, when sitting on a plane or table, and is therefore able to roll in at least 2 directions like a wobbly chair. A. Eget, S. K. Lucas and L. Taalman further optimized the ability to roll on Mortons family of trefoil knots by reducing the height deviation of the center of mass.
In this project our goal is to understand the proof by Morton, find new families of tritangentless knots and optimize them with respect to smooth roll-ability. Finally, we also want to 3D print these objects.
Prerequisites: Some knowledge of projective geometry, basic topology, algebra and rudimentary complex analysis skill are needed, but can be learned during the project. Basic programming skills in Python or Matlab are useful for 3D printing and Visualization.

Geometric Deep Learning

Mentors: Diaaeldin Taha
Team members: Sharanya Achut
Description: TBA

Math and Data Science for Social Good

Mentor: Valentina Disarlo and Diaaeldin Taha
Team members: Saifeldin Mandour, Samer Sheich Essa
Description: TBA

Political Geometry

Mentor: Valentina Disarlo and Diaaeldin Taha
Team members: Ayşegül Peközsoy, Leonard Späth, Klaus Stier
Description: TBA
Prerequisites: Some knowledge of probability theory and basic programming skills are needed.

Continuous Cellular Automata

Mentor: Diaaeldin Taha
Team members: Adrian Becker
Description: TBA

Advanced Practicals

An Interactive Web-Based Animation Application for Graph Algorithms

Mentor: Diaaeldin Taha
Team members: Tillmann Fehrenbach
Description: This project aims to build an interactive, web-based tool for visualizing graph algorithms.

Independent Projects

Ricci Flow on Surfaces of Revolution

Mentor: Marek Kaluba
Team members: Mathias Häberle, Ricardo Waibel
Description: TBA

Developing Outreach Materials

Mentor: Anna Schilling
Team members: Alexandra Fuchs
Description: This project aims to develop materials for math outreach and communication. The activities involved vary from organizing workshops for high school students to organizing big public events such as the Millenium Prize MathFest event from last Semester.

Aperiodic Tilings of the Hyperbolic Plane

Mentor: Anna Schilling, Diaaeldin Taha
Team members: TBA
Description: TBA

SFB Funded Projects

Symplectic Billiards

Mentor: Peter Albers
Team members: Fabian Lander, Jannik Westermann
Description: This project aims to simulate symplectic billiards on non-convex polygons and to search for periodic orbits in particular.

Hyperbolic Billiards

Mentor: Diaaeldin Taha
Team members: Jannis Heising
Description: The project aims to study closed billiard trajectories in hyperbolic polygons.
GitHublink

Student Seminars Projects

Minimal Surfaces

Mentor: Peter Smillie
Seminar: Minimal Surfaces
Team members: TBA
Description: TBA

Root Systems and their Weyl Groups

Mentor: Marius Leonhardt
Seminar: Illustrating Mathematics
Team members: TBA
Description: TBA

Quasicrystals and the Cut-and-Project Method

Mentor: Diaaeldin Taha
Seminar: Illustrating Mathematics
Team members: TBA
Description: TBA

Poncelet’s Porism

Mentor: Diaaeldin Taha
Seminar: Illustrating Mathematics
Team members: TBA
Description: TBA

BOGY-Internships

Visualizing Random Walks in the Poincaré Disk

Mentors: Anna Schilling, Diaaeldin Taha
Team members: Paul Martin
Description: In this two-week internship, we will learn about the mathematics of random walks in the hyperbolic plane and simulate these dynamical systems.
Online app: link