The project concerns various issues related to the model theory and proof theory of first- and second-order arithmetic. The three main research topics are:

• Models of collection principles, in particular expansions of models that satisfy collection but not induction for a given class of formulas.
• The first-order consequences of second-order statements (in particular combinatorial statements) over various base theories in second-order arithmetic.
• The development of a theory of proof sizes and proof speedup for subtheories of arithmetic.

The candidate should have research experience (documented by publications or preprints) in at least one of the following areas of mathematical logic: nonstandard models of arithmetic, proof theory of arithmetic, reverse mathematics.

The project aims to bring together the paradigms of databases on one hand and knowledge representation and reasoning on the other hand, mainly in the area of query processing and reasoning.

Eligible candidates should hold a PhD degree in computer science and have an excellent background in one or more of the following fields:

• database theory
• knowledge representation and reasoning
• logic in computer science.

Application deadline: November 16, 2024

The remote online public defence of the doctoral dissertation will take place on 18 November 2024 at 16:00.

Title of the dissertation: Equivariant Khovanov Homotopy Types
Supervisor: Assoc. Prof. Maciej Borodzik (Institute of Mathematics Polish Academy of Sciences, University of Warsaw)

The link to the defence meeting will be made available after prior registration by e-mail rnd.matinf@uw.edu.pl.

The registration of participants will be open until 15th November 2024.

Two Master's degree student scholarships in the project "Integrative analysis of single-cell genomics data" funded by the National Science Centre, Poland (2020/39/D/NZ2/03461). Successful candidates will work on the development of computational methods for analysis of experimental data from single-cell sequencing.