## Complex Analysis Research Unit (CARU)

Complex Analysis is an active and classical area of Mathematics, its roots go back to the 18th century. As such, it is deeply interconnected with other areas of Analysis, with Topology, Algebraic Geometry, Differential Geometry and Partial Differential Equations. More recently, this area has also been noticed by a wider public through developments in Complex Dynamics and the captivating pictures of fractals that result from the study of Complex Dynamics. Complex Analysis also finds applications in Analytic Number Theory and in Physics, for example in classical Hydrodynamics and in Quantum Field Theory.

The *Complex Analysis Research Unit* from the American University of Beirut focuses on the geometric aspects of Complex Analysis while emphasizing its connections to Algebraic Geometry, Differential Geometry and Partial Differential Equations.

The unit is established under the Center for Advanced Mathematical Sciences (CAMS) at the American University of Beirut, with founding members who have benefited from CAMS support over the last decade, advancing the Center's mission through international collaborations and events involving the local mathematical community.

### Founding Members

- Rafael Andrist, Assistant Professor, Department of Mathematics, AUB
- Florian Bertrand, Associate Professor, Department of Mathematics, AUB
- Giuseppe Della Sala, Associate Professor, Department of Mathematics, AUB

### Selected Publications

- Cordaro, P., Della Sala, G. and Lamel, B.:
*The Borel map in locally integrable structures*, Math. Ann. 377 (2020), no. 3-4, 1155-1192 - Della Sala, G., Lamel, B. and Reiter, M.:
*Sufficient and necessary conditions for local rigidity of CR mappings and higher order infinitesimal deformations*, Ark. Mat. 58 (2020), n. 2, 213-242 - Bertrand, F., Della Sala, G. and Lamel, B.:
*Jet determination of smooth CR automorphisms and generalized stationary discs*, Math. Z. 294 (2020), 1611-1634. - Andrist, R. and Ugolini, R.:
*A new notion of Tameness*, J. Math. Anal. Appl. 472 (2019), 196-215 - Bertrand, F., Blanc-Centi, L. and Meylan, F.:
*Stationary discs and finite jet determination for non-degenerate generic real submanifolds*, Advances in Mathematics, Volume 343 (2019) 910-934. - Andrist, R. and Kutzschebauch, F.:
*The fibred density property and the automorphism group of the spectral ball*, Math. Ann. 370 (2018), 917-936 - Bertrand, F., Blanc-Centi, L.:
*Stationary holomorphic discs and finite jet determination problems*, Math. Ann., Volume 358 (2014), 477-509 - Andrist, R.:
*Stein spaces characterized by their endomorphisms*, Trans. Amer. Math. Soc. 363 (2011), 2341-2355

### Upcoming Events

TBA

### Previous Events

Bernhard Lamel (Texas A&M University at Qatar, Qatar) - [Poster]

- Title: Holomorphic Mappings: Regularity and finite determination
- Date and time: March 1, 2023 at 4:00pm (Beirut time)
- Venue: Bliss Hall, Room 205

- Francine Meylan (The University of Fribourg, Switzerland) - [Poster]
**CAMS-Mathematics Seminar: On Exotic Symmetries of Homogeneous Submanifolds**- Tuesday, November 29, 2022 at 11:00AM - Bliss Hall, Room 206
**CAMS Public Lecture:****A Journey Through Complex Analysis**- Wednesday, November 30, 2022 at 4:00PM - College Hall, Auditorium B1
**CAMS-Mathematics Special Talk:****Teaching High School Students While Doing Research**- Tuesday, November 29, 2022 at 6:30PM - College Hall Auditorium B1

- Undergraduate Students: Seok Ban, Amir Jaber Chehayeb, Adam Salha and Walid Tabbara