Université de Strasbourg

Alexandru Oancea

Biography - Alexandru Oancea

Sorbonne University, Paris & USIAS Fellow at the Institute for Advanced Mathematical Research (IRMA), University of Strasbourg and CNRS, France

Alexandru Oancea, USIAS Fellow 2021Alexandru Oancea obtained his PhD in mathematics in 2003 at the University of Paris-Sud Orsay, under the supervision of Professor Claude Viterbo. After a post-doctoral fellowship at ETH Zurich (Switzerland) between 2003 and 2005, where he worked with Professor Dietmar Salamon, he became an associate professor (maître de conférences) at the University of Strasbourg in 2005 and, subsequently, a research scientist (CR1) of the French National Centre for Scientific Research (CNRS) in 2010.

He has been professor of mathematics at Sorbonne University (France) since 2012 and is part-time professor at the École Normale Supérieure (2020-2021). From 2011-2012, and in 2017, he was a member of the School of Mathematics at the Institute for Advanced Study in Princeton (USA). He received the Science prize of the Académie des Marches de l'Est (now Académie rhénane) in 2010, and was the recipient of an ERC Starting Grant 2010-2016.

Professor Oancea’s research field is symplectic topology. He is particularly interested in the algebraic structures stemming from pseudo-holomorphic curve theory, with applications in dynamics, topology, and geometry.

During his Fellowship, Alexandru Oancea will be hosted by Professor Nalini Anantharaman at the Institute for Advanced Mathematical Research (IRMA).

Project - Applications of Poincaré duality in symplectic topology

01/09/2021 - 31/08/2023

Alexandru Oancea has recently proved, in collaboration with Kai Cieliebak (Augsburg, Germany) and Nancy Hingston (The College of New Jersey, USA), a Poincaré duality theorem in infinite dimensions involving Rabinowitz-Floer homology groups of the contact boundary of a Liouville domain. This theorem made it possible to give answers to questions arising from the closed geodesic problem in Riemannian geometry.

The goal of the USIAS project is to explore further ramifications of this duality theorem in symplectic topology. These concern (i) the construction of Floer theoretic quasimorphisms to understand the symmetry groups of contact boundaries of Liouville domains, (ii) a categorical lift of Poincaré duality in relation with topological quantum field theories (TQFT), and (iii) new vanishing theorems for symplectic homology with applications to Hamiltonian dynamics. Each of these three research directions address a core problem in symplectic or contact topology.

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Investissements d'Avenir