The workshop “Function Spaces and Operator Theory” was organized by Prof. Le Hai Khoi (NTU Singapore) and Dr. Pham Trong Tien (VNU Hanoi) at the Vietnam Institute for Advanced Study in Mathematics from the 24 to 28 of June, 2019.

The aim of the workshop was to bring together experts in operator theory working on spaces of holomorphic functions. Particular topics of interest included boundary values of holomorphic functions, new developments in Hardy, Bergman, Dirichlet and Fock spaces, invariant and reducing subspaces of these spaces under linear operators, reproducing kernel estimates on different domains, etc.

On the first day of the workshop in Hanoi, 2 mini-courses for doctoral candidates and senior undergraduate students were given by the French professors. These courses not only provided students with basic introductory knowledge on some classical function spaces of holomorphic functions and operators on those spaces, but also initiated in students interests in further research on these fields.

On the following days in Tuan Chau, 11 talks were delivered by prominent professors from the USA, France, Korea, Singapore, by other experts from VNU-Hanoi, VNU-HCM, and PhD candidates from the USA as well as Vietnam. They presented the results which demonstrated the beautiful interaction between complex analysis and operator theory, such as Toeplitz, Hankel and (weighted) composition operators, among others. Many open questions were also proposed for further study, which are useful for possible future collaborative research between experts in the field. The atmosphere of the presentations and discussions on these days workshop were friendly and professional. 

On the last day of the workshop, participants discussed about possibilities to organize next workshops, which they hoped to be held in the near future.