Bridging visualization and understanding in Geometry and Topology

Europe/Paris
Amphithéâtre Hermite (Institut Henri Poincaré)

Amphithéâtre Hermite

Institut Henri Poincaré

11 rue Pierre et Marie Curie 75005 Paris
Description

Illustration as a Mathematical Research Technique

Workshop 2: Bridging visualization and understanding in Geometry and Topology

February 16 to 20, 2026 - IHP, Paris

Summary

Geometry and topology are two areas of mathematics that are naturally fueled by illustrations. However, as W. Thurston once noted, "mathematicians usually have fewer and poorer figures in their papers and books than in their heads". The aim of this conference is to explore visualization techniques in geometry and topology. What are the challenges of producing rigorous and enlightening illustrations? How can they guide research and sharpen our understanding in this field? etc. In addition to research talks, the conference will provide opportunities for participants to engage in new research collaborations using illustration.

Registration is free but mandatory

Participants should register using the "Registration" link the the left menu. (The registration form is the same for the trimester and for the workshops.)

List of speakers:

One of the afternoons will be dedicated to technique sessions. Participants will be spread in small groups to experiment some illustration techniques. Session leaders are

 

The schedule can be found here

Organising Committee:

  • Aarons Abrams (University of Virginia)
  • Vincent Borrelli (Université Claude Bernard - Lyon 1)
  • Rémi Coulon (CNRS / Université de Dijon)
  • Francis Lazarus (CNRS / Université Grenoble Alpes)
    • 09:30 10:00
      Welcome Coffee/Remise des badges 30m
    • 10:00 11:00
      Plenary talk 1h

      TBA

    • 11:00 11:30
      Coffee break 30m
    • 11:30 12:30
      Plenary talk 1h

      TBA

    • 12:30 14:30
      Lunch break 2h
    • 14:30 15:30
      Plenary talk 1h

      TBA

    • 15:30 17:30
      Exhibition session 2h
    • 09:30 10:30
      Plenary talk 1h

      TBA

    • 10:30 11:00
      Coffee break 30m
    • 11:00 12:00
      Plenary talk 1h

      TBA

    • 12:00 12:10
      Group Photo 10m
    • 12:10 14:00
      Lunch break 1h 50m
    • 14:00 17:00
      Technique session 3h
      Orateur: Alison Martin
    • 14:00 17:00
      Technique session 3h
      Orateur: Chaim Goodman-Strauss
    • 14:00 17:00
      Technique session 3h
      Orateur: Edmund Harriss
    • 14:00 17:00
      Technique session 3h
      Orateur: Henry Segerman
    • 14:00 17:00
      Technique session 3h
      Orateur: Laura Taalman
    • 14:00 17:00
      Technique session 3h
      Orateur: Steve Trettel
    • 14:00 17:00
      Technique session - Drawing 3h

      En élargissant rectilinéairement une bande de Möbius, on peut engendrer une famille de surfaces réglées. Si cette procédure (homéomorphisme) est aisée à formuler, voir complètement et clairement ces surfaces, dans tous leurs détails, l'est beaucoup moins. Leur unilatéralité et le fait qu'elles présentent des auto-recoupements et des points singuliers intriguent et déroutent notre perception. Nous nous livrerons donc dans cet atelier à des essais de visualisation de ces surfaces par les moyens les plus simples du dessin (du papier et des crayons), sans l'aide d'un formalisme algébrique ni d'un outil de modélisation informatique.

      Orateur: Sylvie Pic
    • 14:00 17:00
      Technique session - Real-time visualization of dynamical systems 3h

      Solutions of differential equations can be animated with a particle system in Unity 3D game engine. You can drop a particle on a random position - its initial condition, say (x y z) at t=0 - and watch it move real-time in whichever direction the equations command. With modern graphic cards, you can do it with millions of colored particles at the same time. This is a way to highlight and explore the entire phase space. Parameters can be updated real-time without restarting the simulation, enabling fast and thorough explorations. This approach is not limited to real 3-dimensional PDEs as any number of dynamic variables can be computed each step.

      Implementation of the classic Lorenz attractor will be demonstrated and explained from scratch.

      Orateur: Alex Andrix
    • 09:30 10:30
      Plenary talk 1h

      TBA

    • 10:30 11:00
      Coffee break 30m
    • 11:00 12:00
      Plenary talk 1h

      TBA

    • 12:00 13:00
      Plenary talk 1h

      TBA

    • 09:30 10:30
      Plenary talk 1h

      TBA

    • 10:30 11:00
      Coffee break 30m
    • 11:00 12:00
      Plenary talk 1h

      TBA

    • 12:00 14:00
      Lunch break 2h
    • 14:00 16:00
      Problem session 2h
    • 16:00 17:00
      Plenary talk 1h

      TBA

    • 09:30 10:30
      Plenary talk 1h

      TBA

    • 10:30 11:00
      Coffee break 30m
    • 11:00 12:00
      Plenary talk 1h

      TBA

    • 12:00 14:00
      Lunch break 2h
    • 14:00 16:00
      Video session 2h