Associate Professor at Institute of Mathematics
Polish Academy of Sciences
ul. Śniadeckich 8, 00-656 Warsaw, Poland jmederski at impan dot pl
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Since 2012: variational methods, nonlinear PDEs: Schrödinger and Maxwell equations, Klein-Gordon equations, Born Infeld theory, mathematical physics
Before 2012: topological methods for set-valued maps, degree theory and fixed point index, differential incusions and control theory
Other: Financial mathematics, Large simulations on parallel computers, Molecular dynamics
Short CV:
2020: laureate of the Wacław Sierpiński Scientific Award of the III Department of the Polish Academy of Sciences
01.2021 - 01.2024: PI of the grant Opus - National Science Centre, Poland (Grant No. 2020/37/B/ST1/02742)
2021 - 2024: member of the Jury "Kazimierz Kuratowski Award"
2019 - 2022: member of the Scientific Council of the Institute of Mathematics of the Polish Academy of Sciences
2019 - 2022: member of the Scientific Council of Juliusz P. Schauder Center for Nonlinear Studies
11.2019 - 04.2021: Humboldt Research Fellowship for Experienced Researchers Department of Mathematics, Karlsruher Institut für Technologie (KIT), Germany
08.2018 - 07.2023: PI of the grant Sonata Bis - National Science Centre, Poland (Grant No. 2017/26/E/ST1/00817)
05.2018 - 11.2018: Visiting Professor at the Department of Mathematics, Karlsruher Institut für Technologie (KIT), Germany
03.2018 - present: Associate Professor at the Institute of Mathematics of the Polish Academy of Sciences
01.2018: Habilitation in Mathematics, dissertation: Theory of critical points of strongly indefinite functionals and time-harmonic solutions of Maxwell equations with a nonlinear polarization of subcritical growth, distinction of the dissertation by the Scientific Council of Institute of Mathematics of the Polish Academy of Sciences
10.2016: Scholarship of the Minister of Science and Higher Education for young outstanding scientists (3 years: 2016-2019)
10.2016: 1st Individual Award of the Rector of the Nicolaus Copernicus University for scientific achievements
09.2016 - 02.2018: Assistant Professor at the Institute of Mathematics of the Polish Academy of Sciences
07.2015 - 07.2018: PI of the grant Sonata - National Science Centre, Poland (Grant No. 2014/15/D/ST1/03638)
10.2010 - 07.2020: Assistant Professor at Nicolaus Copernicus University
10.2011 - 09.2012: Postdoctoral Fellow at Justus Liebig Universität Gießen, advisor: Prof. Thomas Bartsch
12.2009: PhD in Mathematics (with Distinction) at Nicolaus Copernicus University, PhD thesis: Approximations and homotopy invariants for set-valued maps under constraints, supervisor: prof. Wojciech Kryszewski, in 2010 dissertation was awarded by the NCU Rector
2009: Scholarship for Ph.D. Students - Step in the Future, ZPORR, 2009
2007: Team Award of the NCU Rector for research
2006: M.S. in Computer Science at Nicolaus Copernicus University, thesis: Asynchronous algorithm of molecular dynamics and its object-oriented implementation, supervisor: prof. dr hab. Piotr Bała
2005: M.S. in Mathematics at Nicolaus Copernicus University, thesis: Fixed point index for Krasnosel'skii-type set-valued maps, supervisor: prof. dr hab. Wojciech Kryszewski
2002-2005: Scholarship of Ministry of National Education for achievements in studies
1999: 4th place in International Baltic Way Mathematical Team Contest, Iceland
1999: 3rd prize in Mathematical Olympiad, Poland
Grant NCN SONATA BIS: Nonlinear equations involving the curl-curl operator, 08.2018-07.2023, PI: Jarosław Mederski
The local co-investigators involved in the project:
Bartosz Bieganowski, Assistant Professor, Polish Academy of Sciences and Assistant, Nicolaus Copernicus University, PhD defended (with Distinction) in 12.2019 under my supervision
Michał Gaczkowski, Assistant Professor, Warsaw University of Technology
Kamil Dunst, PhD student, Polish Academy of Sciences
Jacopo Schino, PhD student, Polish Academy of Sciences
Panayotis Smyrnelis, Assistant Professor, Polish Academy of Sciences, from 01.12.2019 Marie Skłodowska-Curie Individual Fellowship at Basque Center for Applied Mathematics
Publications:
J. Mederski, J. Schino: Least energy solutions to a cooperative system of Schrödinger equations with prescribed L^2-bounds: at least L^2-critical growth,
submitted arXiv:2101.02611
P. d'Avenia, J. Mederski, A. Pomponio:
Nonlinear scalar field equation with competing nonlocal terms,
submitted arXiv:2010.13184
M. Gaczkowski, J. Mederski, J.Schino:
Multiple solutions to cylindrically symmetric curl-curl problems and related Schrödinger equations with singular potentials,
submitted arXiv:2006.03565
B. Bieganowski, J. Mederski: Normalized ground states of the nonlinear Schrödinger equation with at least mass critical growth,
submitted arXiv:2002.08344
J. Mederski, A. Szulkin: Sharp constant in the curl inequality and ground states for curl-curl problem with critical exponent,
submitted arXiv:2002.00613
B. Bieganowski, J. Mederski:
Bound states for the Schrödinger equation with mixed-type nonlinearites,
submitted arXiv:1905.04542
J. Mederski, J. Schino, A. Szulkin:
Multiple solutions to a nonlinear curl-curl problem in R^3,
Arch. Rational Mech. Anal. 236 (2020) 253-288
DOI 10.1007/s00205-019-01469-3
arXiv:1901.05776
J. Mederski: General class of optimal Sobolev inequalities and nonlinear scalar field equations,
submitted arXiv:1812.11451
B. Bieganowski, J. Mederski: Note on semiclassical states for the Schrödinger equation with nonautonomous nonlinearities,
Appl. Math. Lett. 88 (2019), 149-155,
arXiv:1808.09148
J. Mederski: Nonradial solutions of nonlinear scalar field equations,
Nonlinearity 33 (2020), 6349-6380, doi:10.1088/1361-6544/aba889 arXiv:1711.05711
J. Mederski: Nonlinear time-harmonic Maxwell equations in a bounded domain: lack of compactness,
survey, Sci. China Math. 61 (2018), no. 11, 1963-1970
doi.org/10.1007/s11425-017-9312-8
T. Bartsch, J. Mederski: Nonlinear time-harmonic Maxwell equations in domains,
J. Fixed Point Theory Appl. 19 (2017), no. 1, 959-986
DOI 10.1007/s11784-017-0409-1
(the special issue in honour of Prof. Paul Rabinowitz) arXiv:1610.06338
P. d'Avenia, J. Mederski, A. Pomponio: Vortex ground states for Klein-Gordon-Maxwell-Proca type systems,
J. Math. Phys. 58 (2017), no. 4, 041503, 19 pp.,
DOI 10.1063/1.4982038arXiv:1603.04649
B. Bieganowski, J. Mederski: Nonlinear Schrödinger equations with sum of periodic and vanishig potentials and sign-changning nonlinearities,
Communications on Pure and Applied Analysis 17(1) (2018)143-161,
DOI 10.3934/cpaa.2018009, arXiv:1602.05078
T. Bartsch, J. Mederski: Nonlinear time-harmonic Maxwell equations in an anisotropic bounded medium,
J. Funct. Anal. 272 (2017), no. 10, 4304-4333
DOI 10.1016/j.jfa.2017.02.019arXiv:1509.01994
J. Mederski: Nonlinear time-harmonic Maxwell equations in R^3: recent results and open questions,
Lecture Notes of Seminario Interdisciplinare di Matematica Vol. 13 (2016), 47–57
link
Q. Guo, J. Mederski: Ground states of nonlinear Schrödinger equations with sum of periodic and inverse-square potentials,
J. Differential Equations 260 (2016), no. 5, 4180–4202
DOI 10.1016/j.jde.2015.11.006arXiv:1412.6022
J. Mederski: Ground states of a system of nonlinear Schrödinger equations with periodic potentials,
Comm. Partial Differential Equations 41 (2016), no. 9, 1426–1440
DOI 10.1080/03605302.2016.1209520arXiv:1411.5582
J. Mederski: Ground states of time-harmonic semilinear Maxwell equations in R^3 with vanishing permittivity,
Arch. Rational Mech. Anal., 218 (2), (2015), 825-861
DOI 10.1007/s00205-015-0870-1arXiv:1406.4535
P. d'Avenia, J. Mederski: Positive ground states for a system of Schrödinger equations with critically growing nonlinearities,
Calc. Var. Partial Differential Equations 53 (2015), no. 3-4, 879–900
DOI 10.1007/s00526-014-0770-5arXiv:1403.3211
T. Bartsch, J. Mederski: Ground and Bound State Solutions of Semilinear Time-Harmonic Maxwell Equations in a Bounded Domain,
Arch. Rational Mech. Anal. 215 (1), (2015), 283-306
DOI 10.1007/s00205-014-0778-1arXiv:1310.4731
J. Mederski: Solutions to a nonlinear Schrödinger equation with periodic potential and zero on the boundary of the spectrum,
Topol. Methods Nonlinear Anal. 46 (2015), no. 2, 755–771 arXiv:1308.4320
J. Mederski: Vietoris-Begle theorems for nonclosed maps, Topol. Methods Nonlinear Anal. 41 (2013), no. 1, 191-205.
J. Mederski: Graph approximations of set-valued maps under constraints, Topol. Methods Nonlinear Anal. 39 (2012), no. 2, 361-389.
J. Mederski: Equilibria of nonconvex valued maps under constraints, J. Math. Anal. Appl. 389 (2012), no. 2, 701-704.
J. Mederski: Fiberwise absolute neighborhood extensors for a class of metrizable spaces, Topology Appl. 156 (2009), no. 13, 2295-2305.
J. Mederski, Ł. Mikulski, P. Bała: Asynchronous Parallel Molecular Dynamics Simulations,
Parallel Processing and Applied Mathematics, Lecture Notes in Computer Science Volume 4967 (2008), pp 439-446.
W. Kryszewski, J. Mederski: Fixed point index for Krasnoselskii-type set-valued maps on complete ANRs,
Topol. Methods Nonlinear Anal. 28 (2006), no. 2, 335-384.
Teaching mathematical analysis, pdes, financial and actuarial mathematics, SQL and databases - Oracle, C++ programming: