06.11.2024, 14:00 - 16:00
– Campus Golm, Building 9, Room 2.22 and via Zoom
Institutskolloquium
Graphon Models for Inhomogeneous Random Graphs
Olga Klopp (Paris), Nicolas Verzelen (Montpellier)
Florian Bertrand (American University of Beirut), Francine Meylan (Uni Freiburg)
14:00 Florian Bertrand (American University of Beirut) : Analytic discs in Complex Analysis
15:30 Francine Meylan (University of Friburg, Switzerland):On some Rigidity properties of holomorphic maps
Florian Bertrand (American University of Beirut) : Analytic discs in Complex Analysis
In this talk, I will present a survey on the method analytic discs in complex analysis. Initiated by Riemann and Hilbert, the method of analytic discs appeared later on as a powerful technique in Several Complex Variables with the works of Bishop, Lempert or Bedford-Gaveau. Such discs are indeed natural invariants and are particularly adapted to the study of geometric properties of domains and their holomorphic maps.
The following uniqueness theorem of Cartan serves as a starting point for this talk: Biholomorphic maps of a bounded domain in the complex space are uniquely determined by its value and first derivatives at a given point of the domain.
We will then address the following question: When is a bihomorphic map on a submanifold of the complex space uniquely determined by a its value and (possibly higher) derivatives at a given point of the manifold?