## Analysis Research Group

The Analysis Research Group focuses on the theory of (partial) differential equations and in particular on the structures and properties of solutions to such equations. Differential equations are often motivated by concrete questions from physics, biology, and engineering.

In the natural sciences, such questions are often investigated through experiments and simulations. But due to the complexity of many situations, experiments and simulations often run up against their limits. This is where the theory of differential equations can be employed. Mathematical results about the existence and uniqueness of solutions and about the solutions’ qualitative and quantitative properties help us understand such complex phenomena.

Professor Gianluca Crippa’s research group studies differential equations that derive from models from fluid dynamics and describe irregular behaviors, such as flow patterns of liquids that appear chaotic and turbulent. Geometric measure theory is an important mathematical tool for this research.

Professor Enno Lenzmann’s research group works on questions about partial differential equations that come from physics (such as astrophysics, quantum mechanics, and the theory of relativity). So-called nonlocal phenomena play a central role in these investigations.

The research seminar of the Analysis Research Group takes place every week during the semester on Wednesdays at 14:15.

The BZ Seminar in Analysis, which is organized in collaboration with the University of Zurich and the ETH Zurich, takes place once per semester, alternating its location between Basel and Zurich.