HEGL Praktika
* Mathematics and Informatics bachelor’s students can directly sign up for Praktika. However, physics students should confirm with their department before signing up.
HEGL Praktika
Penrose Tilings of Closed Surfaces
Mentor: Peter Smillie
Members: Open for 3 members
Registration: Sign up on Müsli
Description: Penrose tiles are the most famous examples of a set of tiles which can tile the plane, but cannot tile the plane periodically. Equivalently, there can be no Penrose tiling of a flat torus. However, it is sometimes possible to tile a flat surface of higher genus. In this project, we will work towards developing an atlas of which flat surfaces can be Penrose tiled and which cannot. The primary method is a version of the cut-and-project method developed by De Bruijn in 1981; an alternative method is a version of the combinatorial method of Hurwitz. If the project is successful, it should help understand some open problems.
Prerequisites: Basic familiarity with programming, for example in Python, is helpful.
Using Reinforcement Learning to Find Counterexamples in Mathematics
Mentor: Diaaeldin Taha
Members: Open for 3 members
Registration: Sign up on Müsli
Description: In a beautiful 2021 paper, Adam Wagner used reinforcement learning to find explicit constructions and counterexamples to several previously open conjectures in combinatorics. In this project, and following Wagner’s work, we will learn about reinforcement learning and how to set up some mathematical questions as problems that can be attacked with reinforcement learning.
Prerequisites: Basic programming knowledge, in Python in particular, will be helpful. Familiarity with deep learning is a plus.
Persistent Homology and Applications
Mentor: Alexandre Janaud
Members: Open for 3 members
Registration: Sign up on Müsli
Description: This project aims to introduce persistence homology and its applications. We will first discover the theoretical aspect and how to implement it, through the example of Ribbs complexes for cloud of points. We will then tackle a more complex application using real-world data.
Prerequisites: basic Python; notions of homology