MATH-518 / 5 crédits

Enseignant: Richter Florian Karl

Langue: Anglais

## Summary

This is an introductory course in ergodic theory, providing a comprehensive overlook over the main aspects and applications of this field.

## Keywords

ergodic theory, dynamcial systems, measure-preserving transformation, entropy

## Recommended courses

Measure and integration

## Important concepts to start the course

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.

## Learning Outcomes

By the end of the course, the student must be able to:

• Apply tools and techniques from ergodic theory in number theory and combinatorics
• Prove results in ergodic theory
• Formalize dynamcial ideas and concepts such as ergodicity, entropy, chaos, determinism, etc.
• Interpret examples of dynamical systems

## Transversal skills

• Use a work methodology appropriate to the task.
• Continue to work through difficulties or initial failure to find optimal solutions.
• Demonstrate a capacity for creativity.
• Demonstrate the capacity for critical thinking

## Teaching methods

in-person lectures, in-person exercise sessions with the teaching assistant

oral exam

## Supervision

 Office hours Yes Assistants Yes Forum Yes

## Bibliography

• M. Einsiedler, T. Ward, Ergodic Theory with a view towards Number Theory, Springer-Verlag London, 2011.
• P. Walters, An Introduction to Ergodic Theory, Graduate Texts in Mathematics, Springer New York, 1982.

## Notes/Handbook

Lecture notes will be provided

## Dans les plans d'études

• Semestre: Printemps
• Forme de l'examen: Oral (session d'été)
• Matière examinée: Ergodic theory & its applications to number theory
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines
• Semestre: Printemps
• Forme de l'examen: Oral (session d'été)
• Matière examinée: Ergodic theory & its applications to number theory
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines
• Semestre: Printemps
• Forme de l'examen: Oral (session d'été)
• Matière examinée: Ergodic theory & its applications to number theory
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines

## Semaine de référence

 Lu Ma Me Je Ve 8-9 MAA110 9-10 10-11 MAA110 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 20-21 21-22

Vendredi, 8h - 10h: Cours MAA110

Vendredi, 10h - 12h: Exercice, TP MAA110