All the researchers on the list can be reached via university email. The email addresses are created according to the template: first_name.last_name@uj.edu.pl (with all the diacritical marks removed).

##### Leokadia Białas-Cież

I study several approximation and interpolation problems, polynomial inequalities in various norms (also on algebraic sets, and their applications, e.g. in numerical analysis or pluripotential theory.

**approximation, interpolation, polynomial inequalities and applications, (pluripotential theory, numerical analysis**

##### Marcin Bilski

I study properties of real algebraic and analytic varieties. Recently I work on algebraic approximation of continuous maps between real algebraic sets. I am interested both in theoretical problems (such as characterizing classes of algebraic maps suitable for approximation and in developing numerical methods of approximation (which are important for applications.

**real algebraic geometry, analytic geometry, numerical algebraic geometry**

##### Antoni Leon Dawidowicz

I study the asymptotical properties of differential and integro-differential equations. Moreover I am also interested in mathematical statistics. My mathematical interests are focused mainly on the application of mathematics in biology and medicine

**partial differential equations, mathematical statistics**

##### Maciej Denkowski

In complex geometry I am particulary interested in analytic intersection theory and Lojasiewicz inequalities. In real geometry, recently, I have been studying the medial axis, its structure and its relation to the singularities of the set it is computed for. I have a preference for geometric methods and a particular interest in multifunctions (with the Kuratowski semi-continuity and thus in parametrised families and phenomena with parameter (e.g. Lojasiewicz inequalities with a uniform exponent in singularity theory.

**singularity theory, complex analytic geometry, o-minimal structures and subanalytic geometry**

##### Sławomir Dinew

I study geometrically motivated nonlinear elliptic equations and the associated nonlinear potential theories. My studies are centered around equations of Hessian type such as the complex Monge-Ampere equation and its generalizations

**nonlinear analysis, geometric analysis, complex geometry**

##### Andrzej Grzesik

My research is mainly focused on extremal graph theory, in particular innovative methods based on graph limits. This is a new concept of representing large graphs, that led to new ways of dealing with hard problems in graph theory

**graph theory, extremal combinatorics, discrete mathematics, graph limits**

##### Zbigniew Hajto

I study various applications of differential Galois theory to several problems in algebraic and differential geometry, especially computational aspects of integrability in dynamical systems and analytic mechanics. Recently I work on generalization of the Picard-Vessiot theory in formally real and p-adic algebraic geometry.

**differential algebra, Galois theory, algebraic methods in differential equations**

##### Paweł Idziak

I study properties of algebraic and combinatorial structures used in mathematical modelling in computer science

**theoretical computer science, computational complexity, algorithmics, logic in computer science**

##### Tomasz Kania

I study both algebraic and geometrical aspects of infinite-dimensional spaces, often using tools from logic & set theory. I am also interested in modelling of financial markets.

**Banach spaces and their operators; geometry of Banach spaces, ideals and representations of Banach algebras, set-theoretic methods in analysis**

##### Łukasz Kosiński

several complex variables with particular emphasis put on the theory of holomoprhically invariant function and on geometric function theory (Stein manifolds, density property, labyrinths, proper maps. The second branch of my interest is the theory of function spaces (in particular, Dirichlet type spaces in several variables

**Several Complex Variables, Function Spaces**

##### Marcin Kozik

I study and develop algebraic structural properties of various computational problems. These algebraic properties are used to construct efficient algorithms to solve/optimize/approximate said problems.

**computational complexity, approximation and universal algebra**

##### Dominik Kwietniak

I study various aspects of dynamical systems, often connected to other fields of mathematics, like combinatorics, number theory or descriptive set theory. Recently, I am interested in classification problems for Cantor dynamical systems and related invariants, like entropy or simplices of invariant measures.

**topological dynamics, symbolic dynamics, and ergodic theory**

##### Piotr Micek

Research description: My work lies often in the intersection of combinatorics and theoretical computer science. I like research on structural- and extremal-side of graph theory, including applications in theoretical computer science.

**combinatorics, structural graph theory, order theory, graph colorings**

##### Stanisław Migórski

Hemivariational inequalities, optimal control problems for systems governed by variational inequalities, mathematical theory of contact mechanics for solids and fluids, inverse and identification problems, mathematical models for nonsmooth and multivalued problems in mechanics

**Applied Mathematics**

##### Marian Mrozek

I study computational and algorithmic methods in dynamics and topology with particular emphasis on topological invariants of dynamical systems such as fixed point index, Conley index, connection matrices, Conley-Morse graphs. Recently, I am particularly interested in combinatorial dynamical systems important in discretization methods for dynamical systems as well as the Big Data problem in the context of sampled dynamical systems

**topological dynamics, computational topology, computational dynamics, dynamics in finite topological spaces**

##### Wiesław Pawłucki

Research description: geometry of real algebraic, semialgebraic and subanalytic sets with applications to analysis, approximation theory and number theory

**singularity theory, real geometry, differential analysis, real function theory**

##### Szymon Peszat

I am interested; in long time behavior of solutions to stochastic partial differential equations, uniqueness and existence of invariant measures, stability, ergodicity, strong Feller property and gradient estimates of transition semigroups, equations of fluid mechanics; Navier--Stokes, Burgers, equations with white noise boundary conditions, applications of stochastic control in mathematical finance; investor problems, agent/principal problems, systems of equations on lattices.

**stochastic analysis, stochastic partial differential equations, equations of fluid dynamics, Levy processes, mathematical finance, stochastic control theory**

##### Rafał Pierzchała

I am ineterested in applications of semianalytic/subanalytic/o-minimal geometry to analysis and approximation theory

**analysis, approximation theory, semianalytic and subanalytic geometry, o-minimal geometry**

##### Adam Roman

I work on the problems related to software quality & software testing: mutation testing, effective test design techniques, static code metrics (data-flow related metrics, test optimization problems using AI & machine learning techniques (like test suite reduction, defect localization techniques etc., software quality models (like defect prediction, reliability prediction etc.

**Software testing and quality; AI & machine learning**

##### Maciej Ulas

I am interested in arithmetic properties of various integer sequences of combinatorial and number-theoretic origin. Moreover, I study Diophantine equations both from theoretical and computational point of view.

**elementary number theory, arithmetic properties of integer sequences of combinatorial origin, Diophantine equations**

##### Bartosz Walczak

I study structural and computational aspects of various combinatorial optimization problems in graph classes, with particular focus on coloring problems and on classes of graphs with geometric representations. Currently, I am leading a research project "Colorings, cliques, and independent sets in graph classes" https://bartoszwalczak.staff.tcs.uj.edu.pl/abstract.pdf

**graph theory, discrete geometry, algorithms**

##### Michał Wojtylak

I am interested in modern methods of matrix theory: perturbation theory, stability, matrix polynomials, also by complex analysis methods and machine learning methods. All this is in connection with robustness analysis of mathematical modelling of real life systems. I am looking for candidates interested either in theoretical approach or in practical applications (or in both

**linear algebra and its applications in control and system theory, machine learning and numerical analysis**

##### Włodzimierz Zwonek

I work in the fields of invariant functions and metrics like the Kobayashi, Caratheodory and Bergman distances, pluricomplex Green function. The relation of the extremal problem related to the functions with the interpolation theory (Nevanlinna-Pick problem is also in the scope of my interest. Various problems related to the Lempert theorem turned out to be better understood by the study of special domains like the symmetrized bidisc, the tetrablock and the spectral ball originating from the control theory. The domains provide a good source of (counterexamples in some problems related to the invariant functions and different notions of convexity

**several complex variables, pluripotential theory**