All the researchers on the list can be reached via university email. The email addresses are created according to the template: firstname.lastname@example.org (with all the diacritical marks removed).
List of scientific advisors (computer science and mathematics)
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.
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.
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.
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
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
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.
I study properties of algebraic and combinatorial structures used in mathematical modelling in computer science
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.
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
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.
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.
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.
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
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
Research description: geometry of real algebraic, semialgebraic and subanalytic sets with applications to analysis, approximation theory and number theory
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.
I am ineterested in applications of semianalytic/subanalytic/o-minimal geometry to analysis and approximation theory
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.
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.
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
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
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