Advanced Lecture Course (2022/23): Topics in Algorithmic Dynamical Systems Theory
Synopsis
This graduate course is an overview of the algorithmic theory of
discrete linear dynamical systems, and will introduce some of the fundamental results and
techniques of the field. We will be covering the following topics:
- Discrete linear dynamical systems and linear recurrence
sequences: definitions and examples
- Decision problems: Kannan-Lipton Orbit Problem, Skolem Problem,
Positivity Problem, etc.
- Skolem-Mahler-Lech theorem
- Computations with algebraic numbers, separation bounds
- Baker theory (linear forms in logarithms)
- p-adic techniques
- Applications to Skolem and Positivity Problems at low orders
- Subspace theorem and S-unit techniques
- Applications to Ultimate Positivity
- Diophantine hardness
Organisation
The instructor is Joël Ouaknine and the teaching assistant is
Toghrul Karimov (toghs@mpi-sws.org).
There will be one lecture per week, Thursdays 2pm
to 3:30pm. Tutorials will be held following the lecture
(Thursdays 3:40pm to 4:10pm, allowing for a 10-minute break after the lecture).
Lectures and tutorials will take place in the MPI-SWS building (Campus
E1 5), Room 029, except for 24 Nov. and 8 Dec., where
both will take place in Room 005 of the MPI-SWS building.
Evaluation will be via an oral examination at
the end of the course. In order to attend the oral examination, at
least 50% of the coursework must have been completed.
This is an advanced course, worth 6 CP; it is restricted to graduate
students, or by special permission of the instructor.
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