Winter 2022 Student Projects

HEGL Praktika

Signing Up for HEGL Praktika

To sign up for a HEGL Praktikum, email the Praktikum mentor(s) and sign up on Muesli. The HEGL Praktika Module is listed as a Module for Mathematics and Informatics students. Physics students should check with the Physics Dekanat if they can sign up for the HEGL Praktikum.

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 transversal 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.

Mathematics of Gerrymandering

Mentor: Diaaeldin Taha
Team members: Open for 3 members
Description: TBA
Prerequisites: Some knowledge of probability theory and basic programming skills are needed.

SFB Funded Projects

TBA

HEGL Student Seminars

TBA