Structure of the Institute

Research

Studies

Links

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 email

Deputy Director
dr Ireneusz Krech

room:	205
tel.:	12 662-62-78
e-mail:	ireneusz.krech@uken.krakow.pl
Duty:	Thursdays 11.00-12.00 other consultation after appointment by an email

Deputy Director (Students and Education)
dr Bożena Rożek

room:	210
tel.:	12 662-62-72
e-mail:	bozena.rozek@uken.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. Piotr Błaszczyk, kierownik KEiPM
dr hab. Jacek Chmieliński, kierownik KAMiZ
dr hab. Justyna Szpond, kierownik KGiA
dr Grzegorz Malara, KG

Professors

dr hab. Leszek Gasiński
dr hab. Janusz Gwoździewicz
dr hab. Katarzyna Korwin-Słomczyńska
dr Gregoris Makrides
dr hab. Piotr Pokora
dr Nataliia Ponomarova
dr Mirosława Sajka
dr hab. Paweł Wójcik

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

Sandra Branicka
Maciej Zięba

Persons invited (advisors)

lic. Norbert Trzeciakiewicz, council secretary
retired professors of IM UP
member of the Scientific Students Organization

Office

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

Chair of Mathematical Analysis and Applications

Research Description

Research conducted at the Chair of Mathematical Analysis and Applications concern selected topics of real analysis and topology, functional analysis and operator theory, dynamical systems, differential equations, probability 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.
Nonlinear boundary value problem, variational methods, critical points theory.
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.

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. Jacek Chmieliński orcid.org/0000-0002-7460-9025
Professors:
dr hab. Leszek Gasiński orcid.org/0000-0001-8692-6442
dr Zbigniew Leśniak orcid.org/0000-0002-6717-6903
dr hab. Paweł Wójcik orcid.org/0000-0001-8527-012X
Assistant Professors:
dr Olena Andrusenko orcid.org/0000-0001-9986-5888
dr Beata Deręgowska orcid.org/0000-0001-6876-4857
dr Karol Gryszka orcid.org/0000-0002-3258-3330
dr Joanna Markowicz orcid.org/0000-0002-6688-5038
dr Paweł Pasteczka orcid.org/0000-0002-8593-0025
Assistants:
mgr Maria Skupień orcid.org/0000-0003-1480-0810
Cooperating Retired Professors:
prof. dr hab. Marek Cezary Zdun orcid.org/0000-0002-8120-3154
Professors:
dr Ireneusz Krech orcid.org/0000-0002-7820-0622
Assistant Professors:
dr Aleksandra Huczek orcid.org/0000-0003-4222-083X

Chair of Geometry and Algebra

Research Description

Main research carried at the Chair of Geometry and Algebra

Research conducted at the Department of Geometry and Algebra focuses on selected topics in complex algebraic and analytic geometry, commutative algebra, combinatorics, and Education 4.0.

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

The containment problem for symbolic and ordinary powers of homogeneous ideals.
Asymptotic invariants related to algebraic varieties and the ideals defining them, including Seshadri and Waldschmidt constants.
The problem of maximal rank for the restriction mapping of global sections for configurations of linear subspaces in projective spaces.
The problem of fat point schemes.
Arithmetic and geometry of parameter spaces of certain configurations of lines.
Finite projective planes.
Unexpected curves and the SHGH conjecture.
Positivity of line bundles on algebraic varieties.
Configurations of algebraic curves.
Algebraic invariants of curve configurations.
Hirzebruch-type inequalities.
Geography of log algebraic surfaces.
The freeness problem for hyperplane arrangements.
Improper intersections of subvarieties in projective spaces.
Combinatorial and algebraic properties of point configurations in projective spaces (geproci and geprofi sets).

The project-based method in mathematics education at all levels. Elements of STEAME and the professional preparation of teachers, mathematical modeling using VR.

Grants

,,Unexpected hypersurfaces of type $(d+k,d)$ in projective space $P^N$''- SONATA 2023/51/D/ST1/00118 (2024-2026)
,,$m$-syzygy plane curves'' - SONATA BIS 2023/50/E/ST1/00025 (2024-2028)
,,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 hab. Justyna Szpond orcid.org/0000-0002-2997-4023
Professors:
dr hab. Janusz Gwoździewicz orcid.org/0000-0002-2035-1073
dr hab. Piotr Pokora orcid.org/0000-0001-8526-9831
Assistant Professors:
dr Łucja Farnik orcid.org/0000-0003-4300-0206
dr Beata Gryszka orcid.org/0000-0001-8497-8943
dr Marek Janasz orcid.org/0000-0003-0534-7946
dr Magdalena Lampa-Baczyńska orcid.org/0000-0002-0174-7726
Assistants:
mgr Artur Bromboszcz orcid.org/0009-0003-8900-0153
mgr Izabela Leśniak orcid.org/0009-0002-0353-6997
mgr Łukasz Merta orcid.org/0000-0002-8899-8973
dr Marcin Zieliński orcid.org/0000-0002-4593-841X
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
Professors:
dr Grzegorz Malara orcid.org/0000-0001-5077-4942
prof. dr hab. Tomasz Szemberg orcid.org/0000-0002-4234-5838

Chair Education 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. Piotr Błaszczyk orcid.org/0000-0002-3501-3480
Professors:
dr hab. Irena Katarzyna Korwin-Słomczyńska orcid.org/0000-0002-7957-2583
Assistant Professors:
dr Barbara Barańska orcid.org/0000-0002-4000-8408
dr Anna Petiurenko orcid.org/0000-0002-0196-6275
dr Sławomir Przybyło orcid.org/0000-0001-8413-6754
dr Daniel Wójcik orcid.org/0000-0002-2264-0178
Senior Lecturers:
dr Lidia Zaręba orcid.org/0000-0002-8593-1327
Professors:
dr Bożena Rożek orcid.org/0000-0002-7219-9691
dr Gregoris Makrides orcid.org/0000-0002-7676-773X
dr Mirosława Sajka orcid.org/0000-0002-0209-7817