The public website can be found there. Here is a short description of the planned content of each four-hour slot, following the order of the planned program. Each four-hour slot shall contains two one-hour lectures, with the remaining times being shared between tea break and tutorials (tutorials play an important role for participants, as well as for lecturers who can adjust the level of difficulty accordingly).
Lectures notes are mandatory for a CIMPA School. We shall print them before the school to make them available to participants during the school. They shall be light - at most five pages for each slot (references excluded) - in order to have no more than 100 pages for the whole school. They aim to provide a written copy of the main terms of each lecture (in particular to ease language comprehension) and references that can be consulted after the school. They do not aim to explain all what you not had time to do during the two-hour lecture!
To write down your notes, please download the main file and the template. Complete the template and make a separated bibtex file "isfahan.bib" for the bibliography. Check that it compiles. Then send me the modified template and the bibliography. I shall randomly upadte a complete pdf. Let us fix the deadline june 25 to send your notes, in order to have time to edit the proceeding before the school. But do not hesitate to send preliminary versions: you will still be able to update them, and this allows to have a better idea of the final result.
- Sage (T. Monteil)
- general introduction
- survival guide:
- how to get help
- object orientation
- for non programmers : python crash course
- basic tools (symbolic functions, graphics, polynomials, matrices, number theory,...)
- Parent, element, coercion. How does Sage represent real (complex) numbers ? Which representation is best for my problem ?
- Some problem solving techniques (backtracking, linear programming, Markov chains, ...)
- exercises related to the other lectures please add your suggestions and details here!
- Groebner bases (easy : shipped within sage)
- Combinatorics on words (easy : shipped within sage, some deep modifications could be done during Sage days 66 at Liege)
- Cut and projection tilings (already exists in Python but not in Sage <- where ?)
- computing the dimension of a polynomial system of equation (related to the lecture "Cut and projection 2")
- Flips on tilings and arctic circle phenomenon (Thomas should program it until then)
- Examples of 1D subshift entropy computation? (easy : automata and eigenvalues are shipped within sage)
- Coupling from the past (some work needs to be done depending on the size of the Markov chain)
- Rauzy fractal, dual substitution (easy : e_one_star is shipped within sage and produces very nice pictures)
- Cellular automata : tons of Python softs (some can be easily installed with
sage -pip install
command), Benjamin Hellouin wrote a Sage module but did not let it enter Sage (yet?).
- Core of a matrix in the non primitive case (contraction du cone positif).
- Figure diffraction d'un pavage substitutif simple ??
- Complexity of a substitutive tiling. Example of the chair tiling.
- Books that could be of interest for students during or after the school
- Aperiodic Order, Vol. 1, A Mathematical Invitation, Michael Baake, Uwe Grimm (TF)
- Quasicrystals and Geometry, Marjorie Senechal (TF)
- Finite Markov Chains and Algorithmic Applications, Olle Häggström (TF)
- Substitutions in dynamics, arithmetics and combinatorics, N. Pytheas Fogg (TF)
- Topological and symbolic dynamics, Petr Kurka (TF)
- Markov Chains and Mixing Times. David A. Levin, Yuval Peres, Elizabeth L. Wilmer.
- Tilings and Patterns, Branko Grunbaum, Geoffrey C. Shephard (out of print?)
- An Introduction to Symbolic Dynamics and Coding, Douglas Lind, Brian Marcus
- Automatic sequences, Jean-Paul Allouche and Jeffrey Shallit
- Miles of Tiles, Charles Radin
- Theory of Recursive Functions and Effective Computability, Hartley Rogers
- Substitution dynamical systems—spectral analysis, Martine Queffelec