Semester | Mand. | Option | Filières |
MA2, MA4 | x | ||
MA2 | x |
Lecture | 2 weekly |
Exercises | 2 weekly |
Study plan | Semester | Mand. | Option | Filières |
Ingénierie Mathématiques 2021-22 | MA2 | x | ||
Ingénierie Mathématiques 2021-22 | MA4 | x | ||
Mathématiques 2021-22 | MA2 | x |
Cursus | Sem. | Type |
---|---|---|
Ing.-math | MA2, MA4 | Opt. |
Mathématicien | MA2 | Opt. |
In the broadest sense, ergodic theory is the study of group actions on measure spaces. Its history traces from Poincare's recurrence theorem in celestial mechanics and Boltzman's ergodic hypothesis in statistical physics to its mathematical proliferation in the 1930s through the ergodic theorems of von Neumann, Birkhoff, and Koopman. It has since grown into a hugely important research area with striking applications to other areas of mathematics, especially number theory and combinatorics. This course provides an introduction to the basics of ergodic theory. Among other things, this includes the theory of recurrence, the structure and convergence of ergodic averages, and the notion of entropy. We will motivate the main ideas and results through simple examples. Another focal point lies on the many groundbreaking applications of ergodic theory in number theory.
ergodic theory, dynamcial systems, measure-preserving transformation, entropy
Measure and integration
This course is aimed at master's or advanced bachelor's students. Since ergodic theory is largely based on the notions of measure theory, either some background in measure theory or the willingness to learn some of this material along the way is expected. I will provide a handout summarizing the prerequisites from measure theory that are needed for this course at the beginning of the semester.
in-person lectures, in-person exercise sessions with the teaching assistant
oral exam
Lecture notes will be provided
optionnel
optionnel
Cours
Lecture
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Exercices
Exercises
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Oral
Oral
Session été
Session summer
ETE
ETE
optionnel
optionnel
Cours
Lecture
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Exercices
Exercises
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Oral
Oral
Session été
Session summer
ETE
ETE
optionnel
optionnel
Cours
Lecture
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Exercices
Exercises
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Oral
Oral
Session été
Session summer
ETE
ETE
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