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.
07.02.2022 – Student Presentations
24.01.2022 – Rémi Coulon (CNRS)
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!
The Holiday Special is sadly canceled due to the rise of covid infections.
06.12.2021 – Algebraic Number Starscapes
Speaker: Kate Stange (Colorado Boulder)
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)
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)
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)