The Analysis and Geometry Group of the Department is involved in a variety of fields, going from Harmonic Analysis, Complex Analysis and Partial Differential Equations to Differential Geometry, Dynamical Systems and Mathematical Physics.
The research in Partial Differential Equations includes both pure and applied topics, such as for instance the analysis of Schrödinger and semi-linear wave equations, inverse problems with application in optics, and the least gradient problem. The investigations in Harmonic Analysis include the theory of Fourier restrictions and its geometric applications. The interest in Complex Analysis revolves around one-variable questions (for example the study of entire functions and the distribution of zeros, with connections to number-theoretical problems) as well as a wide spectrum of subjects in Several Complex Variables. In Geometry, the issues considered range from the study of (discrete and continuous) group actions to Conformal Geometry, with questions at times stemming from General Relativity and Quantum Field Theory.
Activities, running projects, research networks
- European Several Complex Variables Consortium,
- At the confluence of Geometry, Analysis and Mathematical Physics, sponsored by the Humboldt foundation,
- Complex Geometry of Real Manifolds (PI Florian Bertrand, Co-PI Giuseppe Della Sala), sponsored by the University Research Board of AUB
- Affine-Algebraic Methods in Complex-Analytic Geometry (PI Rafael Andrist), sponsored by the University Research Board of AUB. Projects for Master students.