## 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 Assistant Professor (on leave) at Nicolaus Copernicus University MathSciNet Google Scholar |

Research interests:

- Currently (since 2012): variational methods, nonlinear PDEs: Schrödinger and Maxwell equations, Klein-Gordon equations; Born Infeld theory
- (before 2012): topological methods for set-valued maps, degree theory and fixed point index, differential incusions and control theory
- Large simulations on parallel computers, molecular dynamics

Short CV:

- 2019/2020: Humboldt Research Fellowship for Experienced Researchers Department of Mathematics, Karlsruher Institut für Technologie (KIT), Germany
- 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 (with Distinction) documents
- 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: PI of a grant Sonata - National Science Centre, Poland (Grant No. 2014/15/D/ST1/03638) (3 years until 07.2018)
- 10.2010 - present: Assistant Professor (on leave) 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, supervisor: Prof. Wojciech Kryszewski

in 2010 awarded dissertation*Approximations and homotopy invariants for set-valued maps under constraints* - 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
- 2005: M.S. in Mathematics at Nicolaus Copernicus University
- 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, Nicolaus Copernicus University, PhD defended (with Distinction) in 12.2019 under my supervision
- Michał Gaczkowski, Assistant Professor, Warsaw University of Technology
- 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

A new PhD position is available.

The successfull candidate will obtain the state PhD Scholarship as well as the scholarship of the NCN grant. If you have any questions, please don't hesitate to contact me jmederski at impan dot pl . Deadline is in June 2020, but feel free to contact me earlier.Publications:

- 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*,

to appear in Archive for Rational Mechanics and Analysis 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*,

submitted 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, financial and actuarial mathematics, SQL and databases - Oracle, C++ programming. Teaching materials (in Polish):

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