PhD in Mathematics [Theory of holomorphic functions of several complex variables in the topic...

Within the National Science Center (Narodowe Centrum Nauki), Preludium BIS 3 project entitled Applications of the Lempert theory, a selection committee set up at the School will conduct recruitment for the PhD study programme Mathematics

The project manager, prof. dr hab. Włodzimierz Zwonek offers an opportunity to complete the PhD studies and prepare the PhD thesisin the following area: Theory of holomorphic functions of several complex variables in the topic Applications of the Lempert theory.

The duration of the project is 48 months. The offered scholarship amounts to approx. PLN 4 140 / month gross (approx. PLN 3 700 / month net) before the mid-term evaluation (up to 24 months) and PLN 4 900 / month gross (approx. PLN 4 400 / month net) after a mid-term evaluation. After the interviews and the evaluation of the candidates, the Chairman of the committee presents a report to the Director containing a list of candidates recommended for admission to the school as part of the research project.

It is planned that the scientific part of the project will be based on the advanced consequences of the Lempert Theorem that is an important result in the theory of holomorphic functions of several complex variables and may go in different directions. It is expected that during the carrying out of the project a numer of results will be obtained that could be derived as direct or less obvious consequences of the Lempert Theorem. In particular it may contain the extension of the Lempert Theorem to a wider class of domains. Other problems that the project would contain are related with theextension property (up to now solved only for the bidisc, strongly linearly convex domains and the symmetrized bidisc). Existing results on the description of the extension sets showed surprisingly close relations with the Lempert Theorem. In particular, it led to a construction of the two-dimensioanl domain that is not convex but the Lempert Theorem holds on it. On the other side, the domain has a finite universal Caratheodory set which makes the domain first (except for the polydisc) in a reasonable class of domains with such a property. The problem whether on could find a description of such domains in a general case seems to be very difficult. Nevertheless, a special case of two-dimensional domains admitting universal sets consisting of three elements seems to me more promising.

In the project relations to different parts of functional analysis, theory of harmonic mappings, Nevanlinna-Pick interpolation problem and von Neumann type inequalities are also possible.

The candidate should have a master's degree in mathematics. It would be optimal if the candidate's thesis was from a complex analysis or a functional analysis, but it is not necessary. More important are achievements during studies, willingness to conduct scientific research and willingness to work on open problems requiring new knowledge in the field of theoretical mathematics, reading mathematical publications and, above all, finding satisfaction from working on the challenges related to solving open mathematical problems.

More information regarding this admission is available under the link: https://bit.ly/PhD_in_Mathematics_1 

https://science.phd.uj.edu.pl/en_GB/start