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

Talks

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

• 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?)

  • git, the Sage trac server, mailing lists (sage-devel, sage-support, pari-users, etc) and forums (ask sagemath).

• ? (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, ...)

Projects

• Teichmûller polynomials: need train-tracks automata with decorations. Then compute effectively dilatations in a given fibered face, Thurston norm, etc (Ferrán)
• Compute properties of Coxeter or Artin groups (normal forms, ...)

• Explore Thierry's Coulbois train-track code

• Incidence relations for vector space over Z/2Z (done!)
• More for infinite translation surfaces (Pat)
• (easy) add Thurston-Veech construction into the flatsurf package
• visualize Teichmueller spaces: geodesics, balls, triangles, ... Needs computing Teichmueller maps, i.e. solving PDE (Maxime)

• merge the two flatsurf projects https://github.com/videlec/sage-flatsurf and http://www.labri.fr/perso/vdelecro/flatsurf.html (Pat, Vincent)

• nice 3d plots to make animations of geodesic in Teichmueller space
• visualize the translation structure induced by a not so nice differential (Anja)
• 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)
• add Lyapunov exponents computation in the flatsurf package (Charles, Vincent)
• Affine interval exchange transformations: rotation number for affine circle homeos, generalized Rauzy induction, hyperbolicity, periodic points, ... (Charles)
• Teichmueller flow for genus 1 quadratic differentials with Riemann theta functions (Charles)

• ... add your own project ...

Existing programs about translation surfaces

• Alex Eskin code (saddle connection exploration + decomposition in cylinders)

• various programs by Ronen Mukamel (Delaunay triangulations, Teichmueller curves especially in genus 2)

• Vincent Delecroix flatsurf package (mostly interval exchanges and square tiled surfaces, but a bit of topology)

• Vincent Delecroix and Pat Hooper drawing program

• Charles Fougeron code for Lyapunov exponents of strata coverings (see trac ticket #16102)

• Chris Swierczewski Riemann surfaces package

• Schwarz-Christoffel Toolbox in Matlab

Organizers

• Vincent Delecroix

• Ferrán Valdez

Preliminary list of participants (to be confirmed)

• Vincent Delecroix

• Maxime Fortier-Bourque

• Charles Fougeron

• Pat Hooper

• Samuel Lelièvre

• Thierry Monteil (might attend remotely)

• Yulan Qing

• Kasra Rafi

• Anja Randecker

• Chris Swierczewski (might attend remotely)

• Ferrán Valdez

• Grace Work

Support

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