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Intrinsic ergodicity and uniqueness of equilibrium states of dynamical systems led (dr hab. Dominik Kwietniak, JU prof.)

Pursuant to §7 (1) and (3) of Resolution No. 61/X/2022 of the Senate of the Jagiellonian University of 26 October 2022 on the terms and conditions for admission to the Doctoral School of Exact and Natural Sciences at the Jagiellonian University in the academic year 2023/2024, the Director of the Doctoral School of Exact and Natural Sciences announces

a competition for 1 doctoral student at Mathematics education programme.The research and PhD scholarship will be financed by the NCN research project Preludium Bis 4, Intrinsic ergodicity and uniqueness of equilibrium states of dynamical systems led by Dominik Kwietniak (PI).


Description of the research project:

The main scientific goal of this PhD project is to study equilibrium states in topological dynamics and ergodic theory. Of course, measures of maximal entropy are treated as equilibrium states of constant potentials. We want to prove that, roughly speaking, in large families of dynamical systems, every sufficiently regular potential (observable) has a unique equilibrium state (action-invariant Borel probability measure realizing the topological pressure of the potential). Furthermore, we would like to show that this unique equilibrium state has good statistical properties. We will also explore possible applications of this theory. There are numerous concrete open questions motivated, implicitly or explicitly, by recent literature and fitting to our project.

Candidate profile:

The candidate should demonstrate a strong interest in research in ergodic theory and topological dynamics. He/She should be highly motivated to pursue PhD on the topic of the grant and conduct research on the questions proposed in the project. His/her student records should indicate that he/she is capable of doing mathematical research at a top-level. Prior knowledge of problems and techniques related to the present project is not necessary but is very welcome. Ditto a proven publication record. Potential candidates should contact the PI, Dominik Kwietniak, as soon as possible. Expected knowledge of English at least at B2 level

The competition will be conducted by the Admission Committee and the results will be the basis for the admission of the selected candidate(s).

Competition schedule:

  1. Announcement of the competition on the Doctoral School website: no later than 30.08.2023
  2. Opening of the competition (start accepting applications in the IRK): 13.09.2023
  3. Deadline for submitting applications (closing date for IRK applications): 15.09.2023
  4. Entrance examinations: 19-20.09.2023
  5. Announcement of results: 22.09.2023
  6. Enrollment: 25-26.09.2023
  7. Enrollment (reserve list): 27.09.2023
  8. Expected start date of education: 01.10.2023

Admissions procedure

  • Detailed terms and procedures of admission - tailored to the Mathematics study programme according to the current Recruitment rules for the 2023/2024 academic year can be downloaded HERE
  • Application and entry documents for Matehmatics study programme can be downloaded HERE

Additionally required documents due to the specifics of the research:

Please upload your application documents to the electronic IRK system(

Higher education certificates obtained abroad should:

  1. bear an Apostille when the country issuing the document is covered by the Convention Abolishing the Requirement of Legalisation for Foreign Public Documents, done at The Hague on 5 October 1961 (Journal of Laws of 2005, No. 112, item 938), or
  2. by subject to legalisation, in other cases.

In particularly justified cases, at the request of the Grant Manager, the Director of the NŚiP Doctoral School may waive the requirement to provide apostille or to submit diplomas of higher education or other documents for legalisation.

Any document issued in a language other than Polish or English must be accompanied by a certified translation into Polish or English.


It is possible to apply for a place in the Doctoral House. Receipt of a place is determined by the availability of vacant places and the fulfilment of the conditions described on the Doctoral Student Society website.


A person admitted to a doctoral school commences education and acquires the rights of a doctoral student upon taking the oath. The taking of the oath is done by personally signing the oath in the office of the Mathematics Programme. 

Health Insurance – important changes

As of 1.10, the rules for the registration of doctoral students for health insurance by the University are being changed. After this date:

1. Citizens of Poland, European Union [EU], European Free Trade Association [EFTA] and holders of the Pole's Card, up to the age of 26 should be insured as members of their families, if these have insurance in the EU/EFTA. The insurance is confirmed by a valid EHIC (European Health Insurance Card) card issued in the country of insurance application. Once they have reached the age of 26, they will apply for health insurance coverage at the Jagiellonian University.

2. Other doctoral students (from outside the EU, EFTA) have to pay for their own voluntary health insurance at the Social Security Health institution [ZUS] (on the basis of a contract concluded with the Polish National Health Fund [NFZ] facility) or take out a commercial insurance with a guarantee amount of no less than EUR 30000. They may have both of these insurances. It is insufficient to have only medical packages (subscriptions) in private facilities, as these do not cover the costs of possible hospitalisation. We recommend that each candidate, in particular a foreign candidate, takes out insurance for the duration of the journey and a minimum of the first month of stay in Poland (until the formalities have been completed upon arrival). 

Theory of holomorphic functions of several complex variables in the topic Applications of the Lempert theory (Prof. dr hab. Włodzimierz Zwonek)

Theory of holomorphic functions of several complex variables in the topic Applications of the Lempert theory (Prof. dr hab. Włodzimierz Zwonek)

<font color=red> Mathematics </font>(19.08.2021)<br /> Extension property and function theory methods

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