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A nice animation of a Teichmueller geodesic embedded in R3 (four time punctured sphere): KASRA GIF PICTURE TO COME!! A nice animation of a Teichmueller geodesic embedded in R3 (four time punctured sphere):

{{attachment:twist-small.gif}} {{attachment:P2

Sage Days 73 in Oaxaca, Mexico May 04-07 2016

Sage is an open source software for mathematics. This is the webpage for the Sage workshop prior to the conference Flat Surfaces and Dynamics of Moduli Space to be held in Oaxaca May 08-13. The aim is to:

  • introduce Sage to people from Oaxaca or assisting to the conference
  • have program and code presentations about geometry and dynamics of surfaces
  • help people to implement their own projects

The workshop will start wednesday 04 morning and ends saturday 07 after lunch. It will take place at Punto Mexico Conectado @ Oaxaca in calzada Madero numero 101.

Previsional schedule

Wednesday 4 May

Thursday 5 May

Friday 6 May

Saturday 7 May

09:00 - 10:00

registro y instalación

coding sprint

sharing Sage/Python code


10:00 - 11:00

presentación de Sage

coding sprint

type and classes in Python


11:00 - 11:30

té y café

coffe break

coffe break

coffe break

11:30 - 13:00

actividades practicas

coding sprint



13:00 - 14:30

lunch break

lunch break

lunch break

lunch break

14:30 - 15:30

presentation / discussion

coding sprint



15:30 - 17:00

tutorial: symbolic vs numeric

coding sprint



17:00 - 17:30

coffe break

coffe break

coffe break


17:30 - 18:00

Pat Hooper's demo

Vincent's demo

Charles's demo


18:00 - 19:00

coding spring

status report




  • Presentación de Sage, (jupyter notebook Sage presentation.ipynb)

    During the elaboration of the talk it appeared that many things differ between the jupyter and Sage notebook. It was reported on the mailing list sage-devel. Some of the problem are already fixed (see e.g. #20562)!

  • symbolic vs numerics in Sage (tutorial, wednesday 15:30 - 17:00, Vincent Delecroix)

    • There are many ways to deal with numbers within Sage (algebraic numbers, floating points, intervals, ...). We will present and illustrate pros and cons of all of them on some concrete problems: root finding, integration, solving ordinary differential equations. symbolic_vs_numeric.rst

  • Flatsurf (demo, ¿when?, Pat Hooper)

  • the flatsurf package (demo, ¿when?, Vincent Delecroix)

  • computing Lyapunov exponents of the Teichmueller flow (demo, ¿when?, Charles Fougeron)

  • developing tools (tutorial, ¿when?, ¿who?)

  • ? class howto ?
  • ? (tutorial) SL2Z and triangle group code in Sage
  • ? (tutorial) graphs and digraphs in Sage (Sage graph stuff and possibly bliss software, nauty and Traces, igraph, ...)


Teichmûller polynomials

people: Ferrán

  • need train-tracks automata with decorations. Then compute effectively dilatations in a given fibered face, Thurston norm, etc
  • Explore Thierry's Coulbois train-track code

The algorithm that given the (decorated) train-track algorithm produces the Teichmueller polynomial is ready!! Remains to produce automatically these graphs.

flatsurf Package(s)

people: Charles, Pat, Vincent

Build a nice Sage module for all translation surface related stuff. The aim is to

  • merge four distinct projects
  • add more stuff
    • Teichmueller flow for genus 1 quadratic differentials with Riemann theta functions
    • More for infinite translation surfaces
    • Thurston-Veech construction

visualize Teichmueller spaces

people: Maxime, Kasra

  • geodesics, balls, triangles, ... Needs computing Teichmueller maps, i.e. solving PDE
  • nice 3d plots to make animations of geodesic in Teichmueller space

A nice animation of a Teichmueller geodesic embedded in R3 (four time punctured sphere):

twist-small.gif P2A-small.gif

visualize the translation structure induced by a not so nice differential

people: Anja

flat_picture_of_z-quared-dz.png other_flat_picture_of_z-quared-dz.png

other projects

  • Compute properties of Coxeter or Artin groups (normal forms, ...)
  • Incidence relations for vector space over Z/2Z (done!)
  • Subgroups of SL(2,R) given from generators. Design an algorithm that given a finite set of matrices in SL(2,R) answers whether the group generated by these is
    1. not discrete
    2. has finite covolume
    3. has infinite covolume
    In case 2. and 3. the algorithm should also output a fundamental domain and generators in canonical forms. (Charles, Vincent)
  • Generating saddle connections in a given surface and study their statistics *efficiently* (Grace)
  • Affine interval exchange transformations: rotation number for affine circle homeos, generalized Rauzy induction, hyperbolicity, periodic points, ... (Charles)

Existing programs about translation surfaces




This workshop is supported by the ERC H2020 project OpenDreamKit and Punto Mexico Conectado @ Oaxaca.

days73 (last edited 2016-06-10 15:39:44 by wphooper)