The research activities of the Analysis group are divided into four focus areas:
Complex Analysis is a powerful tool in engineering, for example in hydrodynamics, signal analysis and control theory, and theoretical physics. These applications again lead to exciting new problems in complex analysis.
Harmonic Analysis develops a signal into a collection of pure waves (harmonics), and then use this development to analyze the signal, including its compression and transmission.
Noncommutative Geometry extends the natural correspondence between geometric spaces and commutative algebras to the noncommutative case. This allows us to extend the classical tools—such as measure theory, topology, differential calculus and Riemannian geometry—to the noncommutative situation.
Arithmetical Physics has become a vast area, which, among many other things, explores the possibility of describing phenomena below the Planck length by using fields and rings other than the usual real and complex numbers.