MATH-518 / 5 credits

Teacher: Richter Florian Karl

Language: English


Summary

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

Content

Keywords

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

Learning Prerequisites

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

Assessment methods

oral exam

Supervision

Office hours Yes
Assistants Yes
Forum Yes

Resources

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.

Ressources en bibliothèque

Notes/Handbook

Lecture notes will be provided

Moodle Link

In the programs

  • Semester: Spring
  • Exam form: Oral (summer session)
  • Subject examined: Ergodic theory & its applications to number theory
  • Lecture: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Semester: Spring
  • Exam form: Oral (summer session)
  • Subject examined: Ergodic theory & its applications to number theory
  • Lecture: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Semester: Spring
  • Exam form: Oral (summer session)
  • Subject examined: Ergodic theory & its applications to number theory
  • Lecture: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks

Reference week

 MoTuWeThFr
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     

Friday, 8h - 10h: Lecture MAA110

Friday, 10h - 12h: Exercise, TP MAA110