HEGL Community Seminar SoSe23

The Seminar usually takes place bi-weekly on Monday at 14:15 in Seminar Raum C (Mathematikon).

Schedule

08.05.2023

Speaker: Martin Traizet (Université de Tours)

Title: On the area of Lawson surfaces in the 3-sphere
Time: 14:15

Abstract: Lawson has constructed highly symmetric minimal surfaces of arbitrary genus \(g\) in the 3-sphere \({\mathbb S}^3\). I will explain how to construct these surfaces by an integrable system method — the DPW method. As a byproduct of the construction, we obtain accurate estimations of their area. In particular, the expansion of the area in term of \(1/g\) involves \(\zeta(3)\), where \(\zeta\) is Riemann zeta function. I will explain the path from minimal surfaces in \({\mathbb S}^3\) to values of \(\zeta\) and multi-zetas.
Joint work with L. Heller, S. Heller and S. Charlton.

22.05.2023

Speaker: Olga Paris-Romaskevich (CNRS/Aix-Marseille Université)

Title: Movement of light : tiling billiards and films.
Time: 14:15

Abstract: Introduced by Diana Davis and her collaborators, tiling billiards are the class of dynamical systems that model the propagation of the refracted light in a heterogeneous material. To every tiling of a plane is associated a billiard. There are very few tilings for which corresponding billiards are well understood.
I will give an introduction to this domain with a focus on the simplest example — billiards in periodic triangular tilings. We will see that their dynamics is reduced to that of a family of interval exchange transformations (with flips!) and can be understood via renormalization. Lately, my motivation to study such billiards was reinforced by the discovery of their connection to a topological question from the eighties : how do foliations defined by the restriction of a constant 1-form on a level surface of a 3-periodic function ?
The talk is based on collaborations with Pascal Hubert, Paul Mercat, Ivan Dynnikov and Alexandra Skripchenko, as well as on my personal work.

Movie suggestions: In recent years, I started making movies about mathematics, here are the links to the projects I have been involved into, the first two directly related to the subject of the talk (and we will see the first one together during the talk):

1. Refraction tilings (no words, only math and music)
by Ofir David

Short movie inspired by research on triangle tiling billiards

2. Je voudrais vous parler de mathématiques (in French, with English or Russian subtitles)
by Coralie Gourdon & Olga Paris-Romaskevich

Short movie inspired by Keane’s theorem on 2-interval exchange transformations with flips (or a « cake problem ») made in 48 hours for Pariscience film 2018 festival (coup de cœur of the jury prize)

3. Voyages au pays des maths/Mathewelten/Journey into Maths Country by Denis van Waerbaeke (in French and German, English subtitles for the first season)

Series of short mathematical movies. The first 5 movies of the second season are available (since one week!) in French and German : discover the Monty Hall paradox, Simpson paradox, non-euclidian geometries, plane tilings and graph theory videos, as well as ten videos from the first season.

I have participated as a scientific counselor in « A complex picnic » episode of season 1. In season 2, I was a scientific counselor for « Chaos » episode and wrote the scripts for the two episodes related to the work of Alicia Boole and Sophia Kowalevskaya, all three will appear this October on ARTE channel. Please share this link with your students : arte.tv/maths ! You can use these movies freely for pedagogical reasons but for any public projection please contact the distribution.

26.06.2023

Speaker: Philip Engel (University of Georgia)

Title: Weaving Quasicrystals
Time: 14:15

Abstract: I will begin by talking about joint mathematical work with Peter Smillie on tilings, quasicrystals, and moduli spaces of higher differentials. We will review the beautiful constructions of N. G. de Bruijn, who classified the Penrose tilings of the plane. Then, we will discuss how to generalize some parts of this work to build tilings of closed, flat surfaces.
For the second half of the talk, I will describe a joint art project with fiber artist Victoria Manganiello, on visualizing quasicrystals and higher dimensions. How are patterns made, converted into a format suitable for weaving, and then actually woven?

10.07.2023

Speaker: Érika Roldán (MPI Leipzig)
Website: https://www.erikaroldan.net/

Title: Topology and Geometry of Random Cubical Complexes
Time: 14:15

Abstract: In this talk, we will explore the expected topology (measured via homology) and local geometry of two different models of random subcomplexes of the regular cubical grid: percolation clusters, and the Eden Cell Growth model. We will also compare the expected topology that these average structures exhibit with the topology of the extremal structures that it is possible to obtain in the entire set of these cubical complexes. You can look at some of these random structures here (https://skfb.ly/6VINC) and start making some guesses about their topological behavior.