Analysis and Geometry

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Analysis and Geometry

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, http://e-scv.fmf.uni-lj.si
Rafael Andrist, Florian Bertrand and Giuseppe Della Sala have establised a CAMS Research Unit in Complex Analysis.
2024-2025: Nonimaging Models in Geometric Optics (Ahmad Sabra), sponsored by a URB grant.
2024-2025: Extremal Curves of Invariant Metrics (Florian Bertrand and Giuseppe Della Sala), sponsored by a URB grant.

Previous activities and projects

2020-2023: At the confluence of Geometry, Analysis and Mathematical Physics (Rafael Andrist, Richard Aoun, Florian Bertrand and Giuseppe Della Sala), sponsored by the Humboldt foundation, https://sites.aub.edu.lb/humboldt/
2023 CIMPA Summer school on Complex Analysis and Geometry, sponsored by CIMPA, IMU and CAMS.
2021-2023: Three Models in geometric optics (Ahmad Sabra), sponsored by a URB grant.
2020-2022: Affine-Algebraic Methods in Complex-Analytic Geometry (Rafael Andrist), sponsored by a URB grant.
2020-2022: Comportement en Temps Long des Equations Dispersives Semilinéaires (Tristan Roy), sponsored by CEDRE.
2021-2022: Classification of Invariants in Complex Analysis (Florian Bertrand and Giuseppe Della Sala), sponsored by The Mamdouha El-Sayed Bobst FAS Deanship Fund grant.
2019-2021: Complex Geometry of Real Manifolds (Florian Bertrand and Giuseppe Della Sala), sponsored by a URB grant.
2016-2018: Geometry of Invariant Metrics (Florian Bertrand), sponsored by CEDRE.
2016-2018: The Method of Analytic Discs (Florian Bertrand), sponsored by a URB grant.

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