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
07.02.2022 – Student Project Presentations
Time: 14:15 (in person)
Abstract: We will end the semester with a round of seven presentations of the HEGL student projects from the Winter Semester 2021/2022. Each group will present their project and results in approximately 5-minute presentations. The topics are:
- Symplectic billiards
- Hyperbolic billiards
- Ping Pong game in the Poincaré disk
- Delta-slim triangles in the Poincaré disk
- Escher inspired 3D prints of several tilings of the poincaré disk
- Visualizing sub Riemanniann billiards
- Planimeters and bicycle tires
24.01.2022 – First Person Exploration of Thurston’s Geometries
Speaker: Rémi Coulon (CNRS)
Time: 14:15 (in person)
Abstract: Thurston’s conjecture (proved by Perelman) states that any reasonable three-dimensional space can be decomposed into elementary “building blocks” each of which is modeled onto a specific geometry. There are eight such models. Some of them are familiar, like the Euclidean space or the hyperbolic space, others are wilder like Nil or Sol. To gain more insight on this topic, we develop a web app that simulates in real-time what an inhabitant would see in each of these geometries. In this talk, we will explain how this software was built and exploit it to illustrate some fun features of the Thurston geometries. This is joint work with Elisabetta A. Matsumoto, Henry Segerman, and Steve Trettel
10.01.2022 – Sam Fairchild (MPI) – POSTPONED
Sam Fairchild’s in-person talk is, unfortunately, postponed due to the current covid situation in Germany.
20.12.2021 – Holiday Special! – CANCELED
The Holiday Special is sadly canceled due to the rise of covid infections.
06.12.2021 – Algebraic Number Starscapes
Speaker: Kate Stange (Colorado Boulder)
Time: 14:00 (on Zoom)
Abstract: In the spirit of experimentation, at the Fall 2019 ICERM special semester on “Illustrating Mathematics,” I began drawing algebraic numbers in the complex plane. Edmund Harriss, Steve Trettel, and I sized the numbers by arithmetic complexity and found a wealth of pattern and structure. In this talk, I’ll take you on a visual tour and share some of the mathematical explanations we found for what can be quite stunning pictures (in the hands of a mathematician and artist like Edmund). The images also give some insight into the approximation of complex numbers by algebraic ones.
22.11.2021 – Regular 4-Polytopes, Quaternions, and Hopf Fibrations
Speaker: Jürgen Richter-Gebert (TU München)
Time: 14:15 (on Zoom)
Abstract: Platonic solids are very special objects that exhibit an extremely high degree of symmetry. Regular polytopes are their generalization to higher dimensions and admit (no surprise) even higher degrees of symmetry. Among all dimensions, dimension 2 and dimension 4 play a very special role since they carry algebraic structures that allow expressing geometric rotations as multiplications with ‘numbers’. For dimension 2 these are the complex numbers – in dimension 4 these are the quaternions. Bringing together regular 4-dimensional polytopes with quaternions opens a mathematical playground full of unexpected twists (literally) and surprises. Using interactive visualizations this talk aims to build up an intuition for this interplay. It will be shown how the elements of the rotation group of a dodecahedron translate into the faces of a 120-cell (the 4-dimensional analogue of the dodecahedron), and how subgroups and their cosets turn into systems of nested rings in 4D – a discrete version of the Hopf fibration.
08.11.2021 – Illustrating Billiards, Flat Surfaces, and Hyperbolic Geometry
Speaker: Samuel Lelievre (Orsay)
Time: 14:15 (in person)
Abstract: We showcase some mathematical illustrations pertaining to polygonal billiards, flat surfaces, and hyperbolic geometry which arises naturally when considering moduli of flat tori. An essential tool for me is programming with SageMath, which allows producing computer graphics, and layouts for laser-cut wood and mirrors, 3d-printed objects, and origamis from paper which is cut and pre-folded by a numerically commanded blade or laser. Mirror rooms are joint work with Alba Málaga. Periodic trajectories in regular polygons are joint work with Diana Davis. Isometric polyhedral embeddings of flat tori (and half-translation or translation surfaces, including some infinite-area ones) in euclidean space are joint work with Alba Málaga and Pierre Arnoux. Pseudosphere renderings are joint work with Alba Málaga.
25.10.2021 – Seminar Inauguration and Lab Visit
Speaker: Dia Taha (Heidelberg)
Time: 14:15 (hybrid)