What is Ergodic Theory
Dynamical systems are ubiquitous mathematical objects used to describe how structures or processes evolve, whether over time or through the repeated application of a rule. The study of the long-term statistical behavior of dynamical systems is known as ergodic theory.
Ergodic theory emerged in the early twentieth century in response to foundational questions in physics, particularly in statistical mechanics and thermodynamics. Since then, it has grown into a central area of modern mathematics, influencing both pure and applied fields and providing powerful tools for understanding chaotic phenomena across a wide variety of settings.
Whenever we ask:
What is the expected behavior over long times or large scales?
ergodic theory provides the framework to address this question.
Our Research
Because of its broad scope and flexibility, ergodic theory has become an important tool in many areas of mathematics and related disciplines. Our team investigates applications of ergodic theory across a diverse range of topics, tackling problems at the forefront of contemporary mathematical research.
These include applications to:
- Ramsey Theory
- Arithmetic Combinatorics
- Analytic and Multiplicative Number Theory
- Symbolic and Topological Dynamics
- Computer Science
- Geometric Measure Theory and Metric Number Theory
To learn more about these directions and ongoing work, we invite you to explore the research projects of the members of the Chair of Ergodic Theory: https://www.epfl.ch/labs/erg/members/