Seminars:
Computational mathematics Thu 16:15-17:45
room 1016
Image and Data Processing Tue 11:30-13:00
room 1146
Differential equations and related issues Fri 12:15-13:45
room 1016
Partial differential equations Tue 12:15-13:45
room 1016
Daniel Wilczak, PhD
room:2060
address:Łojasiewicza 6, PL-30-348 Kraków, Poland
e-mail:Daniel.Wilczak@uj.edu.pl
www:http://www.ii.uj.edu.pl/~wilczak

Research interests:
  • qualitative theory of differential equations
  • computer assisted proofs in dynamical systems
  • GPU computing

CV light:
1999M.S. in mathematicsJagiellonian University
2003PhD in computer scienceJagiellonian University
2008 Apr.- 2009 Aug.postdocUniversity of Bergen, Norway
2009 Sept. - 2010 Aug.visiting researcherUniversity of Uppsala, Sweden
2011habilitation in computer scienceJagiellonian University
2011-2017ProfessorNowy Sącz WSB-NLU
2012 Sept. - 2013 Sept.v-ce directorInstitute of Computer Science, Jagiellonian University
2019 - presentProfessorInstitute of Computer Science and Computational Mathematics, Jagiellonian University

Awards and scholarships:
2003annual scholarschip for PhD studentsPolish Academy of Sciences
2006annual national scholarship for young scientistsFoundation for Polish Science
2007annual national scholarship for young scientists - continuationFoundation for Polish Science
2011triennial scholarship for outstanding young scientistsPolish Ministry of Science and Education

Research grants:
2011-2012Parallel and distributed algorithms in Computational Mathematics (head)Polish Ministry of Science and Education

PhD students:
  • (2019) Irmina Walawska Algorytmy ścisłego całkowania równań wariacyjnych i ich zastosowania do badania bifurkacji rozwiązań okresowych w Kołowym Ograniczonym Problemie Trzech Ciał

Publications:
  1. Irmina Walawska, Daniel Wilczak,
    Validated numerics for period-tupling and touch-and-go bifurcations of symmetric periodic orbits in reversible systems
    Communications in Nonlinear Science and Numerical Simulation, vol. 74C, 30-54 (2019)
  2. Roberto Barrio, Daniel Wilczak,
    Systematic Computer-Assisted Proof of Branches of Stable Elliptic Periodic Orbits and Surrounding Invariant Tori
    SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, vol. 16, 1618-1649 (2017)
  3. Daniel Wilczak, Piotr Zgliczyński,
    Connecting Orbits for a Singular Nonautonomous Real Ginzburg--Landau Type Equation
    SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, vol. 15, 495-525 (2016)
  4. Roberto Barrio, Sergio Serrano, Daniel Wilczak,
    Coexistence and Dynamical Connections between Hyperchaos and Chaos in the 4D Rössler System: A Computer-Assisted Proof
    SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, vol. 15, 356-390 (2016)
  5. Irmina Walawska, Daniel Wilczak,
    An implicit algorithm for validated enclosures of the solutions to variational equations for ODEs
    APPLIED MATHEMATICS AND COMPUTATION, vol. 291, 303-322 (2016)
  6. Roberto Barrio, María Angeles Martinez, Sergio Serrano, Daniel Wilczak,
    When chaos meets hyperchaos: 4D Rössler model
    PHYSICS LETTERS A, vol. 379, 2300-2305 (2015)
  7. Daniel Wilczak, Piotr Zgliczyński,
    C^r-Lohner algorithm
    Schedae Informaticae, vol. 20, 9-46 (2011)
  8. Daniel Wilczak,
    Uniformly hyperbolic attractor of the Smale-Williams type for a Poincaré map in the Kuznetsov system
    SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, vol. 9, 1263-1283 (2010)
  9. Warwick Tucker, Daniel Wilczak,
    A rigorous lower bound for the stability regions of the quadratic map
    PHYSICA D-NONLINEAR PHENOMENA, vol. 238, 1923-1936 (2009)
  10. Daniel Wilczak, Piotr Zgliczyński,
    Computer assisted proof of the existence of homoclinic tangency for the Henon map and for the forced-damped pendulum
    SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, vol. 8, 1632-1663 (2009)
  11. Daniel Wilczak, Piotr Zgliczyński,
    Period doubling in the Rössler system - a computer assisted proof
    FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, vol. 9, 611-649 (2009)
  12. Daniel Wilczak,
    Abundance of heteroclinic and homoclinic orbits for the hyperchaotic Rössler system
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, vol. 11, 1039-1055 (2009)
  13. Daniel Wilczak,
    Rigorous numerics for homoclinic dynamics
    The Joint Conference of ASCM 2009 and MACIS 2009, COE Lect. Note, 22, Kyushu Univ. Fac. Math., Fukuoka, 301-305 (2009)
  14. Daniel Wilczak, Piotr Zgliczyński,
    Topological method for symmetric periodic orbits for maps with a reversing symmetry
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, vol. 17, 629-652 (2007)
  15. Hiroshi Kokubu, Daniel Wilczak, Piotr Zgliczyński,
    Rigorous verification of cocoon bifurcations in the Michelson system
    NONLINEARITY, vol. 20, 2147-2174 (2007)
  16. Daniel Wilczak,
    Symmetric homoclinic solutions to the periodic orbits in the Michelson system
    Topological Methods in Nonlinear Analysis, vol. 28, 155-170 (2006)
  17. Daniel Wilczak,
    The existence of Shilnikov homoclinic orbits in the Michelson system: a computer assisted proof
    FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, vol. 6, 495-535 (2006)
  18. Daniel Wilczak, Piotr Zgliczyński,
    Heteroclinic Connections between Periodic Orbits in Planar Circular Restricted Three Body Problem - part II
    COMMUNICATIONS IN MATHEMATICAL PHYSICS, vol. 259, 561-576 (2005)
  19. Daniel Wilczak,
    Symmetric heteroclinic connections in the Michelson system - a computer assisted proof
    SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, vol. 4, 489-514 (2005)
  20. Daniel Wilczak,
    Chaos in the Kuramoto-Sivashinsky equations - a computer assisted proof
    JOURNAL OF DIFFERENTIAL EQUATIONS, vol. 194, 433-459 (2003)
  21. Daniel Wilczak, Piotr Zgliczyński,
    Heteroclinic Connections between Periodic Orbits in Planar Circular Restricted Three Body Problem - A Computer Assisted Proof
    COMMUNICATIONS IN MATHEMATICAL PHYSICS, vol. 234, 37-75 (2003)
  22. Daniel Wilczak,
    Computer assisted proof of chaotic dynamics in the Rössler map
    Topological Methods in Nonlinear Analysis, vol. 18, 183-190 (2001)
Division of Computational Mathematics, Institute of Computer Science, Łojasiewicza 6, 30-348 Kraków, Poland