## dr hab. Jarosław Mederski, prof. IM PANAssociate Professor at Institute of MathematicsPolish Academy of Sciences ul. Śniadeckich 8, 00-656 Warsaw, Poland jmederski at impan dot pl MathSciNet Google Scholar |

Seminar Variational Methods and PDEs

Research interests:

- 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:

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 - J. Mederski:
*The Brezis-Nirenberg problem for the curl-curl operator*,

J. Funct. Anal. 274 (5), (2018), 1345-1380 DOI 10.1016/j.jfa.2017.12.012 arXiv:1609.03989 - 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 10.1063/1.4982038 arXiv: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.2017.02.019 arXiv: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.2015.11.006 arXiv: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 10.1080/03605302.2016.1209520 arXiv: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/s00205-015-0870-1 arXiv: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/s00526-014-0770-5 arXiv: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/s00205-014-0778-1 arXiv: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:

- Nonlinear Maxwell equations — a variational approach, Karlsruher Institut für Technologie (KIT), 2018
- C/C++, UMK 2009-2016
- Bazy danych sem. zimowy, UMK 2009-2016
- Bazy danych sem. letni, UMK 2009-2016
- Wstęp do matematyki finansów i ubezpieczeń, UMK 2009-2016

Other:

- 12.2010 - 07.2011 - I passed all actuarial examinations at the Polish Financial Supervision Authority (Polish: Komisja Nadzoru Finansowego (KNF)): Financial Mathematics, Life insurance mathematics, Mathematics of other property and casualty insurance, Probability and Statistics
- Master C++ Brainbench certificate nr 10229562