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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	?	?	?
10:00 - 11:00	presentación de Sage	?	?	?
11:00 - 11:30	té y café	coffe break	coffe break	coffe break
11:30 - 13:00	actividades practicas	?	?	?
13:00 - 14:30	lunch break	lunch break	lunch break	lunch break
14:30 - 15:30	presentation / discussion	?	?	FREE
15:30 - 17:00	tutorial: symbolic vs numeric	?	?	FREE
17:00 - 17:30	coffe break	coffe break	coffe break	FREE
17:30 - 18:00	demo	?	?	FREE
18:00 - 19:00	coding spring	?	?	FREE

Talks

(tutorial, wednesday 15:30 - 17:00, Vincent Delecroix) symbolic vs numerics in Sage.
- 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. We will also spend some time on how to perform numerical computations in Sage: root finding, integration, solving ordinary differential equations.
(tutorial / presentation) Pat Hooper: Flatsurf
(tutorial / presentation) Vincent Delecroix: the flatsurf package (warning: distinct from the above!)
(tutorial) development howtos: git, the Sage trac server, mailing lists (sage-devel, sage-support, pari-users, etc) and forums (ask sagemath).
? (tutorial) number types in Sage: integers, rationals, number fields, symbolic, floating point, intervals, balls
? (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

Computing Teichmueller maps between translation surfaces (Maxime)
merge the two flatsurf projects https://github.com/videlec/sage-flatsurf and http://www.labri.fr/perso/vdelecro/flatsurf.html (Pat, Vincent)
visualize the translation structure induced by a 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 (Grace)
Affine interval exchange transformations: rotation number for affine circle homeos, generalized Rauzy induction, hyperbolicity, periodic points, ... (Charles)
Teichmueller flow for genus 1 quadratic differentials (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

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.

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-This is a Sage workshop prior to the conference [[http://www.birs.ca/events/2016/5-day-workshops/16w5010|Flat Surfaces and Dynamics of Moduli Space]]to be held in Oaxaca May 08-13. The aim is to:
+[[http://sagemath.org|Sage]] is an open source software for mathematics. This is the webpage for the Sage workshop prior to the conference [[http://www.birs.ca/events/2016/5-day-workshops/16w5010|Flat Surfaces and Dynamics of Moduli Space]] to be held in Oaxaca May 08-13. The aim is to:
 Line 5:
-- introduce Sage to people from Oaxaca or assisting to the conference
+ * introduce Sage to people from Oaxaca or assisting to the conference
 Line 7:
-- program and code presentations about surface dynamics
+ * have program and code presentations about geometry and dynamics of surfaces
 Line 9:
-- make a list of challenging computational question
+ * help people to implement their own projects
 Line 11:
-It is intended to be a small workshop (10 to 15 people).
+The workshop will start wednesday 04 morning and ends saturday 07 after lunch. It will take place at [[http://www.pmc.gob.mx/|Punto Mexico Conectado @ Oaxaca]] in [[https://www.google.com.mx/maps/place/Punto+M%C3%A9xico+Conectado+Oaxaca/@17.0630565,-96.7325754,19z/data=!4m2!3m1!1s0x85c722148d9070eb:0x431c6d96d211d5b5|calzada Madero numero 101]].

== Previsional schedule ==

||<5%>                    ||<15% #FFFFAA:> Wednesday 4 May ||<15%  #FFFFAA:> Thursday 5 May ||<15%  #FFFFAA:> Friday 6 May ||<15%  #FFFFAA:> Saturday 7 May ||
||<#FFFFAA> 09:00 - 10:00 || registro y instalación        || ?                             || ?                           || ?                             ||
||<#FFFFAA> 10:00 - 11:00 || presentación de Sage          || ?                             || ?                           || ?                             ||
||<#F0F0FF> 11:00 - 11:30 ||<#F0F0FF> té y café            ||<#F0F0FF> coffe break          ||<#F0F0FF> coffe break        ||<#F0F0FF> coffe break          ||
||<#FFFFAA> 11:30 - 13:00 || actividades practicas         || ?                             || ?                           || ?                             ||
||<#CCCCFF> 13:00 - 14:30 ||<#CCCCFF> lunch break          ||<#CCCCFF> lunch break          ||<#CCCCFF> lunch break        ||<#CCCCFF> lunch break          ||
||<#FFFFAA> 14:30 - 15:30 || presentation / discussion     || ?                             || ?                           || FREE                          ||
||<#FFFFAA> 15:30 - 17:00 || tutorial: symbolic vs numeric || ?                             || ?                           || FREE                          ||
||<#F0F0FF> 17:00 - 17:30 ||<#F0F0FF> coffe break          ||<#F0F0FF> coffe break          ||<#F0F0FF> coffe break        || FREE                          ||
||<#FFFFAA> 17:30 - 18:00 || demo                          || ?                             || ?                           || FREE                          ||
||<#FFFFAA> 18:00 - 19:00 || coding spring                 || ?                             || ?                           || FREE                          ||

== Talks ==

 * (tutorial, wednesday 15:30 - 17:00, Vincent Delecroix) '''symbolic vs numerics in Sage'''.
   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. We will also spend some time on how to perform numerical computations in Sage: root finding, integration, solving ordinary differential equations.

 * (tutorial / presentation) Pat Hooper: [[https://github.com/videlec/sage-flatsurf|Flatsurf]]

 * (tutorial / presentation) Vincent Delecroix: [[http://www.labri.fr/perso/vdelecro/flatsurf.html|the flatsurf package]] (warning: distinct from the above!)


 * (tutorial) development howtos: [[https://en.wikipedia.org/wiki/Git_%28software%29|git]], the [[http://trac.sagemath.org/|Sage trac server]], mailing lists ([[https://groups.google.com/forum/#!forum/sage-devel|sage-devel]], [[https://groups.google.com/forum/#!forum/sage-support|sage-support]], [[http://pari.math.u-bordeaux.fr/lists-index.html|pari-users]], etc) and forums ([[http://ask.sagemath.org/|ask sagemath]]).

 * ? (tutorial) number types in Sage: integers, rationals, number fields, symbolic, floating point, intervals, balls

 * ? (tutorial) SL2Z and triangle group code in Sage

 * ? (tutorial) graphs and digraphs in Sage ([[http://doc.sagemath.org/html/en/reference/graphs/index.html|Sage graph stuff]] and possibly [[http://www.tcs.hut.fi/Software/bliss/|bliss software]], [[http://pallini.di.uniroma1.it/|nauty and Traces]], [[http://igraph.org/redirect.html|igraph]], ...)

== Projects ==

 * Computing Teichmueller maps between translation surfaces (Maxime)

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

 * visualize the translation structure induced by a 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 (Grace)

 * Affine interval exchange transformations: rotation number for affine circle homeos, generalized Rauzy induction, hyperbolicity, periodic points, ... (Charles)

 * Teichmueller flow for genus 1 quadratic differentials (Charles)

 * ... ''add your own project'' ...

== Existing programs about translation surfaces ==

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

 * various [[http://math.rice.edu/~rm51/|programs by Ronen Mukamel]] (Delaunay triangulations, Teichmueller curves especially in genus 2)

 * Vincent Delecroix [[http://www.labri.fr/perso/vdelecro/flatsurf.html|flatsurf package]] (mostly interval exchanges and square tiled surfaces, but a bit of topology)

 * Vincent Delecroix and Pat Hooper [[https://github.com/videlec/sage-flatsurf|drawing program]]

 * Charles Fougeron code for Lyapunov exponents of strata coverings (see [[http://trac.sagemath.org/ticket/16102|trac ticket #16102]])

 * Chris Swierczewski [[https://github.com/abelfunctions/abelfunctions|Riemann surfaces package]]

 * [[http://www.math.udel.edu/~driscoll/SC/|Schwarz-Christoffel Toolbox in Matlab]]
-Line 17:
+Line 89:
+== Preliminary list of participants (to be confirmed) ==

 * [[http://www.labri.fr/perso/vdelecro/|Vincent Delecroix]]
 * [[https://www.math.toronto.edu/cms/fortier-bourque-maxime/|Maxime Fortier-Bourque]]
 * [[https://webusers.imj-prg.fr/~charles.fougeron/|Charles Fougeron]]
 * [[http://wphooper.com/|Pat Hooper]]
 * [[http://www.math.u-psud.fr/~lelievre/|Samuel Lelièvre]]
 * [[http://monteil.perso.math.cnrs.fr/|Thierry Monteil]] (might attend remotely)
 * --([[https://sites.google.com/site/yulanqing/|Yulan Qing]])--
 * [[http://www.math.toronto.edu/~rafi/|Kasra Rafi]]
 * [[http://www.math.kit.edu/iag3/~randecker/|Anja Randecker]]
 * [[http://www.cswiercz.info/|Chris Swierczewski]] (might attend remotely)
 * [[http://www.matmor.unam.mx/~ferran/|Ferrán Valdez]]
 * [[http://www.math.uiuc.edu/~work2/|Grace Work]]

== Support ==

This workshop is supported by the ERC H2020 project [[http://opendreamkit.org/|OpenDreamKit]] and [[http://www.pmc.gob.mx/|Punto Mexico Conectado @ Oaxaca]].

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