Structure of the Institute

The structure of the Institute of Mathematics

Authorities and Office

Directors of the Institute

Director
prof. dr hab. Tomasz Szemberg

room:	220
tel.:	12 662-62-73
e-mail:	szemberg@up.krakow.pl
Duty:	Tuesdays 9:00-10:00 other consultation after appointment by an email

Deputy Director
dr Ireneusz Krech

room:	205
tel.:	12 662-62-78
e-mail:	Ireneusz.Krech@up.krakow.pl
Duty:	until further notice - only by e-mail

Deputy Director (Students and Education)
dr Bożena Rożek

room:	210
tel.:	12 662-62-72
e-mail:	bozena.rozek@up.krakow.pl
Duty:

The Council of the Institute

Members with the right to vote

Directors IM

prof. dr hab. Tomasz Szemberg, Director IM - Chairman
dr Ireneusz Krech, Deputy Director (general),
dr Bożena Rożek, Deputy Director (students and education)

Chairs

dr hab. prof. UP Piotr Błaszczyk, KPM
dr hab. prof. UP Jacek Chmieliński, KAM
dr hab. prof. UP Katarzyna Korwin-Słomczyńska, KA
dr hab. prof. UP Leszek Gasiński, KZM
dr Mirosława Sajka, KEM
dr Grzegorz Malara, KG

Professors

dr hab. Janusz Gwoździewicz
dr habil. Piotr Pokora
dr hab. Justyna Szpond
dr hab. prof. UP Andrzej Wiśnicki

Representatives of other employees of the Institute

mgr Beata Gryszka
dr Zbigniew Leśniak
mgr Anna Petiurenko
dr Lidia Zaręba

Representatives of students and Ph. D. students of the Institute

Aleksandra Gałecka (1 rok, II stopień)
Sandra Branicka
Daria Wątorek
mgr Marcin Zieliński
Maciej Zięba

Persons invited (advisors)

Ewa Kuźma, council secretary
retired professors of IM UP
member of the Scientific Students Organization

Office

Technician:
mgr Adriana Kura
Secretary:
Ewa Kuźma
Research technician:
dr Paweł Solarz orcid.org/0000-0002-5047-885X

Chair of Mathematical Analysis

Research Description

Research conducted at the Chair of Mathematical Analysis concern selected topics of real analysis and topology, functional analysis and operator theory, functional and operator equations as well as approximation and stability in various meanings.

The list of currently implemented topics includes in particular the following issues:

Geometry of Banach and Hilbert spaces; approximate methods and stability in functional analysis and operator theory; isometric operators, orthogonality and like relations; linear preservers (exact, approximate, local) for some relations and quantities; operator equations; minimal and generalized minimal projections and their extensions.
Topics on real analysis and topology connected, in particular, with families of negligible (e.g. in sense of measure or topology) sets in various algebraic structures (in particular in Polish Abelian groups), as well as their connections with regularity conditions for additive, convex and other mappings, satisfying a particular functional equation or inequality.
Functional equations and inequalities in one or several variables, extensions of conditional functional equations, stability, set-values functions, selected differential and difference equations, iterative roots, iterative groups (in particular in the ring of formal power series).
Means and their analytical properties; Hardy inequality for means and its generalizations.

Grants

P. Wójcik, "Równania Fredholma i Daugaveta w geometrii przestrzeni Banacha", Miniatura-2, 2018/02/X/ST1/00313 (18.01.2019 - 17.01.2020).

Members

Chair:
dr hab. prof. UP Jacek Chmieliński
Professors:
dr hab. prof. UP Andrzej Wiśnicki
Assistant Professors:
dr Beata Deręgowska orcid.org/0000-0001-6876-4857
dr Paweł Pasteczka orcid.org/0000-0002-8593-0025
dr Paweł Wójcik orcid.org/0000-0001-8527-012X
Assistants:
mgr Aleksandra Huczek orcid.org/0000-0003-4222-083X
dr Joanna Markowicz orcid.org/0000-0002-6688-5038

Chair of Geometry

Research Description

Main research carried at the Chair of Geometry

The containment problem for symbolic and ordinary powers of homogeneous ideals.
Asymptotic invariants of projective varieties and their ideals, in particular Seshadri constants and Waldschmidt constants.
The maximal rank problem for restriction mapping of global sections for arrangements of linear subspaces in projective spaces.
The effect of points fattening.
Arithmetic and geometry of parameter spaces of some configurations of lines.
Finite projective planes.
Unexpected curves and SHGH conjecture.
Positivity of line bundles on algebraic varieties.
Bäcklund's theorem in affine differential geometry. The corresponding Bäcklund transformation: geometric aspects and relation to differential equations.
Differential geometry of surfaces in Galilean or pseudo-Galilean space.
Arrangements of algebraic curves
Invariants of curve arrangements
Hirzerbuch-type inequalities for curve arrangements
Geography of log-surfaces

Grants

,,Arithmetic and geometric approach to asymptotic invariants in algebra and algebraic geometry'' - OPUS 2019/35/B/ST1/00723 (2020-2023)
,,Line arrangements and their algebraic and geometric properties'', PRELUDIUM 2018/31/N/ST1/02101, (2019-2021)
,,Arithmetic and geometry of parameter spaces of line arrangements'' PRELUDIUM 2016/23/N/ST1/01363, (2017-2019)
,,Positivity of line bundles on algebraic surfaces'', SONATINA 2018/28/C/ST1/00339 (2018-2021)
"Varieties and homogeneous ideals with symmetries", HARMONIA 2018/30/M/ST1/00148 (2018-20020) "Singular curves on algebraic surfaces" - SONATA 2018/31/D/ST1/00177 (2018-2020)

Members

Chair:
dr Grzegorz Malara orcid.org/0000-0001-5077-4942
Professors:
prof. dr hab. Tomasz Szemberg orcid.org/0000-0002-4234-5838
Dr. habil. Piotr Pokora orcid.org/0000-0001-8526-9831
Assistant Professors:
dr Łucja Farnik orcid.org/0000-0003-4300-0206
dr Magdalena Lampa-Baczyńska orcid.org/0000-0002-0174-7726
dr hab. Justyna Szpond orcid.org/0000-0002-2997-4023
Assistants:
mgr Marek Janasz orcid.org/0000-0003-0534-7946
mgr Mohammad Zaman Fashami
Senior Lecturers:
dr Jakub Kabat orcid.org/0000-0002-0758-0568
dr Maria Robaszewska orcid.org/0000-0003-0254-8515
Cooperating Retired Professors:
prof. dr hab. Kamil Rusek
prof. dr hab. Tadeusz Winiarski

Chair of Applications of Mathematics

Research Description

Main research carried at the Chair

Nonlinear boundary value problem, variational methods, critical points theory.
Problems of constructive theory of functions related to algebraic geometry, pluripotential theory and numerical methods.
Generalization to algebraic and semi-algebraic sets the basic theorems of the approximation theory concerning Markow-type inequalities, Bernstein property, Plesniak property and constructions of admissible meshes.
Continuous and discrete dynamical and semi-dynamical systems on an interval, the circle and the plane, topological conjugacy, fractional iterates.
Connections between approximate and exact solutions of functional, integral, difference and differential equations, Ulam's type stability (including Hyers-Ulam and Aoki-Rassias types, superstability and hyperstability) and its connections to the fixed point theorems.
Set-valued functions satisfying some inclusions and functional equations and their selections, iteration theory for multifunctions.
Probability theory and its applications, statistical data analysis, the statistics of the distribution of the first digits, econometric research.

Members

Chair:
dr hab. prof. UP Leszek Gasiński
Assistant Professors:
dr Agnieszka Kowalska orcid.org/0000-0002-3754-5376
dr Paweł Kozyra orcid.org/0000-0002-1224-6361
dr Ireneusz Krech orcid.org/0000-0002-7820-0622
dr Zbigniew Leśniak orcid.org/0000-0002-6717-6903
Assistants:
mgr Maria Skupień orcid.org/0000-0003-1480-0810
Cooperating Retired Professors:
prof. dr hab. Adam Płocki
prof. dr hab. Andrzej Smajdor
prof. dr hab. Marek Cezary Zdun orcid.org/0000-0002-8120-3154

Chair and Foundations of Mathematics

Research Description

We study:

fundamental theorems of mathematics like the Pythagorean theorem, IVT, FTA or Euler's formula from the historical perspective, as well as from the prespective of Reverse Mathematics and Philosophy of Mathematical Practice;
relations between visual and analytic aspects of mathematics, like diagram and formula.

We develop a model:

of history of calculus that includes nonstandard analysis as a tool for interpretation of the 17th and 18th century mathematics;
of paradigm shift from ancient Greek to the early modern mathematics.

Some other topics include:

the stability of the Cauchy functional equation over Orlicz spaces;
the impact of IT technologies on teaching and learning mathematics.

Grants

"Infinity and infinitely small" - OPUS 2018/31/B/HS1/03896 - (2019-2022)

Members

Chair:
dr hab. prof. UP Piotr Błaszczyk
Professors:
prof. dr Gregoris Makrides
Assistants:
mgr Marlena Fila orcid.org/0000-0001-6273-9220
mgr Marta Giza orcid.org/0000-0002-5790-433X
mgr Łukasz Merta
mgr Anna Petiurenko orcid.org/0000-0002-0196-6275
dr Daniel Wójcik orcid.org/0000-0002-2264-0178

Chair of Algebra

Research Description

Main research carried at the Chair of Algebra

Algebra, algebraic geometry, universal algebra, functional analysis, topology, dynamical systems, incl.:

Approximate roots of quasi-ordinary polynomials, their properties derived from properties of an output quasi-ordinary polynomial, especially irreducibility of such approximate roots, their Wall-Eggers tree and their logarithmic contact with an output quasi-ordinary polynomial.

Quasi-ordinary polynomials and quasi-ordinary-singularities. In particular, irreducibility criteria for such polynomials.

Algebraic structures related to logic. Fregean algebras and varieties. Polynomially rich algebras. Unification in algebras.

Asymmetric truncated Toeplitz operators. Conjugations in models spaces. Algebraic structures generated by unilateral weighted shifts on the l2 spaces on directed trees.

Nonlinear functional analysis. Metric fixed point theory. Theory of Markov operators. Geometric group theory. Type theory and its applications to computer-assisted mathematics.

Asymptotic properties of orbits and generalizations of the notion of periodicity in dynamical systems. Limit properties and the topology of limit sets.

Members

Chair:
dr hab. prof. UP Katarzyna Korwin-Słomczyńska
Professors:
dr hab. prof. UP Janusz Gwoździewicz
Assistant Professors:
dr Karol Gryszka orcid.org/0000-0002-3258-3330
dr Marek Niezgoda orcid.org/0000-0003-0730-2960
Assistants:
dr Beata Gryszka orcid.org/0000-0001-8497-8943
dr Sławomir Przybyło orcid.org/0000-0001-8413-6754

Chair of Mathematics Education

Research Description

Research conducted at the Chair of Mathematics Education concern different aspects of mathematics teaching and learning processes at all levels of education. The research interest is also focused on pre-service and in-service mathematics teachers' training.

In particular, our research topics are:

defining, verifying and developing teachers' mathematical knowledge for teaching;
mathematics teacher beliefs and identity;
understanding of mathematical concepts;
the process of generalization in mathematics;
developing students' mathematical activity;
teaching a student with learning difficulties in mathematics;
chosen aspects of student's geometrical thinking;
mistakes, false convictions and misconceptions and their role in the process of learning mathematics;
early algebra learning difficulties and conceptions of teaching;
eye-tracking empirical research on strategies of solving a problem and analysis its formulation;
eye-tracking as a research method in mathematics education;
teaching and learning mathematics with technology, new methods at mathematics education;
pre-school and the early grades of primary school mathematical education;
comparative studies in mathematics education;
analysis and design of mathematics textbooks, resources and teaching materials; verifying didactical proposals through empirical research;
"mathematical culture" of a student and a teacher;
affective factors in the teaching and learning of mathematics;
cognitive transgressions in the history of the development of mathematical concepts;
affective transgressions in the learning of mathematics;
axiological and teleological perspectives in mathematics education.

Research conducted at the Chair concern as well some aspects of theoretical mathematics - for example classification of symmetry reductions for some partial differential equations.

Grants

,,Diagnosis of substantive and didactic competences of teachers undertaking post-graduate studies qualifying for teaching mathematics as another subject'' PRELUDIUM 2018/31/N/HS6/03976 (2019 - 2022) ,,Trends in Mathematics Education Research (TiMER)'' - Initiatives for supporting Emerging Communities for Mathematics Education Research in Eastern Europe (2019-2020)

Members

Chair:
dr Mirosława Sajka orcid.org/0000-0002-0209-7817
Assistants:
dr Barbara Barańska orcid.org/0000-0002-4000-8408
mgr Piotr Gracjasz orcid.org/0000-0001-5340-4285
mgr Marcin Zieliński orcid.org/0000-0002-4593-841X
Senior Lecturers:
dr Bożena Rożek orcid.org/0000-0002-7219-9691
dr Lidia Zaręba orcid.org/0000-0002-8593-1327
Cooperating Retired Professors:
dr hab. Marianna Ciosek
dr hab. Henryk Kąkol
dr hab. Maciej Klakla
prof. dr hab. Helena Siwek