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Summer School 2022 - Cohomology, Geometry and Explicit number theory (COGENT)
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Summer School 2022 - Cohomology, Geometry and Explicit number theory (COGENT)

Collection Summer School 2022 - Cohomology, Geometry and Explicit number theory (COGENT)

Organizer(s) Institut Fourier, CNRS, UGA
Date(s) 13/06/2022 - 30/06/2022
linked URL https://if-summer2022.sciencesconf.org/
00:00:00 / 00:00:00
51 55

Illustrating the mathematics of COGENT: A hyperbolic angle

By Herbert Gangl

One of the COGENT topics concerns symmetric spaces and relations to arithmetic. We obtain an example of this when we let a discrete group of isometries act on hyperbolic 3-space for which we can study a fundamental domain. It turns out that for the building blocks of such a fundamental domain one can often find hidden symmetries, giving rise to aesthetically pleasing by-products like highly symmetric polytopes and variants thereof. In this lecture series we will discuss a little bit of the background story and illustrate it by way of a couple of those new kinds of polyhedra, in 3D-printed form. We briefly outline the underlying process of how they were generated and, most importantly, give you a few pointers and examples of how you can rather quickly design a 3D-printed object yourself--on the spot!--using the free software package "OpenSCAD" (similar to Python). We should find time to print some of your designs during the summer school: There is a Fab Lab onsite which we are planning to pay a visit a day later, hopefully allowing us to see it already in the process of realising some of your creations--ideally the latter should reflect some of the beautiful structures that you have encountered in your own studies.

Information about the video

  • Date of recording 15/06/2022
  • Date of publication 03/12/2025
  • Institution Institut Fourier
  • Licence CC BY NC ND
  • Language English
  • Format MP4

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