Computational mathematics Thu 16:15-17:45
room 1016
Image recognition Thu 14:15-15:45
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
address:Łojasiewicza 6, PL-30-348 Kraków, Poland

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
2011ProfessorNowy Sącz WSB-NLU
1.IX.2012-30.IX.2013v-ce director for student affairsInstitute of Computer Science, 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

2015-06DYNAMICS, TOPOLOGY AND COMPUTATIONS 2015 (DyToComp), Stefan Banach International Mathematical Center, Faculty of Mathematics and Computer Science UJ When chaos meets hyperchaos Będlewo - Polska
2015-068th Small Workshop on Interval Methods, Charles University in Prague Rigorous computation of Poincaré maps Praga - Republika Czeska
2014-12 Foundations of Computational Mathematics, Society for Foundations of Computational Mathematics Coexistence of chaos and hyperchaos Montevideo - Urugwaj
2014-07The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications , AIMS Continuation of stable elliptic periodic orbits Madryt - Hiszpania
2014-067th Small Workshop on Interval Methods, Uppsala Universitet The CAPD library - a C++ toolbox for validated numerics for dynamical systems Uppsala - Szwecja

  • I. Walawska, D. Wilczak,
    An implicit algorithm for validated enclosures of the solutions to variational equations for ODEs
    Applied Mathematics and Computation, Vol. 291C, 303-322 (2016)
  • D. Wilczak, P. Zgliczyński,
    Connecting orbits for a singular nonautonomous real Ginzburg-Landau type equation
    SIAM Journal on Applied Dynamical Systems, Vol. 15 (1), 495-525 (2016)
  • Roberto Barrio, Sergio Serrano, Daniel Wilczak,
    Coexistence and Dynamical Connections between Hyperchaos and Chaos in the 4D Rössler System: A Computer-Assisted Proof
    SIAM J APPL DYN SYST, 356-390 (2016)
  • Roberto Barrio, María Angeles Martinez, Sergio Serrano, Daniel Wilczak,
    When chaos meets hyperchaos: 4D Rössler model
    PHYS LETT A , 2300-2305 (2015)
  • Daniel Wilczak, Piotr Zgliczyński,
    C^r-Lohner algorithm
    SCHEDAE INFORMATICAE , 9-46 (2011)
  • D. 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, No. 4, 1263-1283 (2010)
  • D. Wilczak,
    Abundance of heteroclinic and homoclinic orbits for the hyperchaotic Rössler system
    Discrete and Continuous Dynamical Systems - Series B, Vol. 11, No. 4, 1039-1055 (2009)
  • D. Wilczak, P. Zgliczyński,
    Period doubling in the Rössler system - a computer assisted proof
    Foundations of Computational Mathematics, Vol. 9, No. 5, 611-649 (2009)
  • W. Tucker, D. Wilczak,
    A rigorous lower bound for the stability regions of the quadratic map
    Physica D, Vol. 238, No. 18, 1923-1936 (2009)
  • D. 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)
  • D. Wilczak, P. 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, No. 4, 1632-1663 (2009)
  • H. Kokubu, D. Wilczak, P. Zgliczyński,
    Rigorous verification of cocoon bifurcations in the Michelson system
    Nonlinearity 20, No.9, 2147-2174 (2007)
  • D. Wilczak, P. Zgliczyński,
    Topological method for symmetric periodic orbits for maps with a reversing symmetry
    Discrete and Continuous Dynamical Systems - Series A, Vol.17, No.3, 629-652 (2007)
  • D. Wilczak,
    Symmetric homoclinic solutions to the periodic orbits in the Michelson system
    Topological Methods in Nonlinear Analysis, Vol. 28, No. 1, 155-170 (2006)
  • D. Wilczak,
    The existence of Shilnikov homoclinic orbits in the Michelson system: a computer assisted proof
    Foundations of Computational Mathematics, Vol.6, No.4, 495-535 (2006)
  • D. Wilczak,
    Symmetric heteroclinic connections in the Michelson system - a computer assisted proof
    SIAM Journal on Applied Dynamical Systems, Vol.4, No.3, 489-514 (2005)
  • D. Wilczak, P. Zgliczyński,
    Heteroclinic Connections between Periodic Orbits in Planar Circular Restricted Three Body Problem - part II
    Communications in Mathematical Physics, Vol. 259, No.3, 561-576 (2005)
  • Daniel Wilczak, Piotr Zgliczyński,
    Heteroclinic Connections between Periodic Orbits in Planar Circular Restricted Three Body Problem - A Computer Assisted Proof
    COMMUN MATH PHYS, 37-75 (2003)
  • Daniel Wilczak,
    Chaos in the Kuramoto-Sivashinsky equations - a computer assisted proof
    J DIFFER EQUATIONS, 433-459 (2003)
  • Daniel Wilczak,
    Computer assisted proof of chaotic dynamics in the Rössler map
    TOPOL METHOD NONL AN, 183-190 (2001)
Division of Computational Mathematics, Institute of Computer Science, Łojasiewicza 6, 30-348 Kraków, Poland