Sage Days 73 in Oaxaca, Mexico May 0407 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 0813. 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 started on wednesday 04 morning and ended on saturday 07. It took place at Punto Mexico Conectado @ Oaxaca in calzada Madero numero 101.
Schedule

Wednesday 4 May 
Thursday 5 May 
Friday 6 May 
Saturday 7 May 
09:00  10:00 
registro y instalación 
coding sprint 
coding sprint 
? 
10:00  11:00 
presentación de Sage 
coding sprint 
coding sprint 
? 
11:00  11:30 
té y café 
coffe break 
coffe break 
coffe break 
11:30  13:00 
actividades practicas 
coding sprint 
sharing code howto 
status report 
13:00  14:30 
lunch break 
lunch break 
lunch break 
lunch break 
14:30  15:30 
presentation / discussion 
coding sprint 
coding sprint 
FREE 
15:30  17:00 
tutorial: symbolic vs numeric 
coding sprint 
coding sprint 
FREE 
17:00  17:30 
coffe break 
coffe break 
coffe break 
FREE 
17:30  18:00 
Pat Hooper's demo 
Vincent's demo 
Charles's demo 
FREE 
18:00  19:00 
coding spring 
status report 
coding sprint 
FREE 
Talks
Presentación de Sage, (jupyter notebook Sage presentation.ipynb Sage presentation.pdf)
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 sagedevel. 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 Pat's demo: Demo 1 as a Sage Worksheet Demo 1 as a PDF Demo 2 as a Sage Worksheet Demo 2 as a PDF
the flatsurf package (demo, thursday 17:30  18:00, Vincent Delecroix)
computing Lyapunov exponents of the Teichmueller flow (demo, friday, 17:30  18:00, Charles Fougeron): CHARLES WORKHSEET TO COME
Projects
Teichmûller polynomials
people: Ferrán
 need traintracks automata with decorations. Then compute effectively dilatations in a given fibered face, Thurston norm, etc
Explore Thierry's Coulbois traintrack code
The algorithm that given the (decorated) traintrack 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
Pat and Vincent sageflatsurf
Vincent flatsurf
Charles code about Lyapunov exponents trac ticket #16102
 add more stuff
 Teichmueller flow for genus 1 quadratic differentials with Riemann theta functions
 More for infinite translation surfaces
 ThurstonVeech 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):
Given two complex structures on the pentagon, the first plot represents the graph of (half the logarithm of) the ratio of extremal lengths with respect to these structures, as a function on measured foliations. The next two plots are the derivative and second derivative respectively.
visualize the translation structure induced by a not so nice differential
people: Anja
Generating saddle connections in a given surface and study their statistics *efficiently*
people: Grace
Distribution of gap of saddle connection for a surface defined on a cubic field!
Computing quadratic differentials on tori
people: Charles
Using Weirstrass function one can find explicit formulas for quadratic differentials on tori
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
 not discrete
 has finite covolume
 has infinite covolume
 Affine interval exchange transformations: rotation number for affine circle homeos, generalized Rauzy induction, hyperbolicity, periodic points, ... (Charles)
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
Organizers
Participants
Thierry Monteil (might attend remotely)
Chris Swierczewski (might attend remotely)
Support
This workshop is supported by the ERC H2020 project OpenDreamKit and Punto Mexico Conectado @ Oaxaca.