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prof. dr hab. Marian Mrozek
Zakład Matematyki Komputerowej profesor zwyczajny Kierownik Zakładu Matematyki Komputerowej
Kontakt:
  • tel. +48 18 44 99 250
  • e-mail: Marian.Mrozek@wsb-nlu.edu.pl
  • pokój: C230
Dyżury:
  • (wtorki), g. 09:00 - 10:00, w te wtorki, w które mam rozpisane w harmonogramie zajęcia

Biografia:

Matematyk i informatyk. Uzyskał stopień doktora matematyki na Uniwersytecie Jagiellońskim w 1982 roku, a tytuł profesora nauk matematycznych w 1999 roku. Pracownik naukowy UJ od 1977 roku, a WSB-NLU od 1997 roku. W latach 1991-1993 i 1996-1997 pracował jako profesor wizytujący na Georgia Tech w Atlancie w USA. Wypromował szóstkę doktorów. Wielokrotnie zapraszany do prezentowania swoich wyników na prestiżowych, międzynarodowych konferencjach i seminariach w wielu ośrodkach naukowych, w szczególności w Institute for Advanced Study w Princeton, USA. Autor ponad siedemdziesięciu publikacji naukowych oraz jednej monografii. Do największych jego osiągnięć należy zaliczyć przeprowadzenie komputerowo wspieranego dowodu istnienia chaosu w równaniach Lorenza. Wynik ten uznany został przez Encyclopedia Britannica za jedno z czterech największych osiągnięć w matematyce w 1995 roku. W 2008 roku został laureatem nagrody Ministra Nauki i Szkolnictwa Wyższego za wybitne osiągnięcia w dziedzinie badań na rzecz rozwoju nauki.

Obszar zainteresowań:

Dynamika i topologia obliczeniowa, rozpoznawanie obrazów, topologia sieci sensorowych oraz algorytmika układów ciągłych.

Publikacje:

Papers 73. P. Dłotko, T. Kaczynski, M. Mrozek Computing The Cubical Cohomology Ring, published version in: Proceedings of the 3rd International Workshop on Computational Topology in Image Context, Chipiona, Spain, November 2010 (Rocio Gonzalez Diaz Pedro Real Jurado (Eds.)), Image A Vol. 3(2010), 137–142. 72. S. Harker, K. Mischaikow, M. Mrozek, V. Nanda, H. Wagner, M. Juda, P. Dłotko The Efficiency of a Homology Algorithm based on Discrete Morse Theory and Coreductions, published version in: Proceedings of the 3rd International Workshop on Computational Topology in Image Context, Chipiona, Spain, November 2010 (Rocio Gonzalez Diaz Pedro Real Jurado (Eds.)), Image A Vol. 1(2010), 41-47. 71. P. Dłotko, T. Kaczynski, M. Mrozek, Th. Wanner, Coreduction Homology Algorithm for Regular CW-Complexes, Discrete and Computational Geometry, accepted. 70. M. Mrozek, M. Żelawski, A. Gryglewski, S. Han, A. Krajniak, Extraction and analysis of linear features in multidimensional images by homological methods, Pattern Recognition, accepted. 69. M. Mrozek, Th. Wanner Coreduction homology algorithm for inclusions and persistent homology, Computers and Mathematics with Applications, accepted. 68. M. Juda, M. Mrozek, $Z_2$-Homology of 2-manifolds may be computed in $O(n\log^{*}(n))$ time, preprint. 67. M. Mrozek, Cech Type Approach to Computing Homology of Maps, published version in: Discrete and Computational Geometry, 44.3(2010), 546-576, DOI: 10.1007/s00454-010-9255-2. 66. M. Mrozek, B. Batko Homology of representable sets, published version in: Annales Polonici Mathematici 97.3(2010), 243-252. 65. M. Mrozek, M. Żelawski, A. Krajniak, A. Gryglewski, S. Han, Homological methods in feature extraction of multidimensional images, published version in: Proceedings of the 2009 2nd International Congress on Image and Signal Processing, Tianjin, Chiny, IEEE 2009, 1061-1066. 64. M. Mrozek, R. Srzednicki, Topological approach to rigorous numerics of chaotic dynamical systems with strong expansion, published version in: Foundations of Computational Mathematics, DOI: 10.1007/s10208-009-9053-5. 63. M. Mrozek, B. Batko, Coreduction Homology Algorithm published version in: Discrete and Computational Geometry, 41(2009), 96-118. 62. M. Mrozek, P. Pilarczyk, N. Żelazna, Homology Algorithm Based on Acyclic Subspace published version in: Computers and Mathematics with Applications, 55(2008), 2395–2412. 61. M. Mrozek, The Method of Topological Sections in the Rigorous Numerics of Dynamical Systems published version in: Canadian Applied Mathematics Quarterly, 14(2006), 209-222. 60. M. Mrozek, R. Srzednicki, Conley index of Poincare maps in isolating segments published version in: Nonlinear Analysis, Theory, Methods and Applications, 70(2009) 2123–2131. 59. M. Mrozek, Index Pairs Algorithms published version in: Foundations of Computational Mathematics, 6(2006), 457-493. 58. Bogdan Batko, M. Mrozek, The Euler-Poincare characteristic of index maps published version in: Topology and its Applications, 154(2007), 859-866. 57. Tomasz Kaczynski, M. Mrozek, Anik Trahan, Ideas from Zariski topology in the study of cubical sets, cubical maps, and their homology published version in: Canadian J. Math. 59(2007), 1008-1028. 56. K. Mischaikow, M. Mrozek, P. Pilarczyk, Graph Approach to the Computation of the Homology of Continuous Maps, published version in: Foundations of Computational Mathematics, 5(2005), 199-229 55. M. Mrozek, K. Wójcik, A discrete version of a geometric method for detecting chaotic dynamics, published version in: Topology and its Applications, 152(2005), 70-82. 54. T. Kaczynski, K. Mischaikow, M. Mrozek, Computing Homology, published version in: Homotopy, Homology and Applications, 5(2003), 233-256. 53. M. Mrozek, P. Pilarczyk, The Conley Index and Rigorous Numerics of Attracting Periodic Orbits, published version in: Variational and Topological Methods in the Study of Nonlinear Phenomena, V. Benci et al. Editors, Progress in Nonlinear Differential Equations and Their Applications, Vol. 49, Birkhauser, Boston, Basel, Berlin 2002. 52. K. Mischaikow, M. Mrozek, The Conley Index Theory, published version in: Handbook of Dynamical Systems III: Towards Applications, Editors: B. Fiedler, G. Iooss, N. Kopell, Elsevier Science B. V., Singapore 2002, Editor: B. Fiedler, 393-460. 51. M. Mrozek, P. Zgliczyński, Set arithmetic and the enclosing problem in dynamics, published version in: Annales Polonici Mathematici, 74(2000), 237-259. 50. M. Mrozek, J. Reineck and R. Srzednicki, On a Generalization of the Conley index, published version in: Conley index theory, Banach Center Publications, 47(1999), 157-171. 49. M. Mrozek, Construction and properties of the Conley index, published version in: Conley index theory, Banach Center Publications, 47(1999), 29-40. 48. K. Mischaikow, M. Mrozek, J. Reiss and A. Szymczak, Construction of Symbolic Dynamics from Experimental Time Series, published version in: Physical Review Letters, 82(1999), p. 1144. 47. K. Mischaikow, M. Mrozek, J. Reineck, Singular Index Pairs, published version in: Proceedings of the Conference "Topological Methods in Differential Equations", Univ. Iag. Acta Math., 36(1998), 223-226. 46. M. Mrozek, Algorithms and the Conley index theory, published version in: Proceedings of the Conference "Topological Methods in Differential Equations", Univ. Iag. Acta Math., 36(1998), 227-230. 45. M. Mrozek and J. Urbaniec, Evolution of Mathematical Proof, published version in: Foundations of Science, 2(1997), 77-85. 44. T. Kaczynski M. Mrozek and M. Slusarek, Homology Computation by Reduction of Chain Complexes, published version in: Computers and Mathematics with Applications, 35(1998), no. 4, 59--70. 43. M. Mrozek and M. Zelawski, Heteroclinic connections in the Kuramoto-Sivashinsky equation, published version in: Reliable Computing, 3(1997), 277-285. 42. Mrozek, M. The Conley Index and Rigorous Numerics, published version in: Nonlinear Analysis and Boundary Value Problems for Ordinary Differential Equations, CISM Courses ans Lectures Vol. 371, Springer Verlag, Wien, 1996, p.175-196. 41. Mrozek, M. Inheritable properties and computer assisted proofs in dynamics, published version in: Scientific Computing and validated numerics, G. Alefeld, A. Frommer and B. Lang editors, Akademie Verlag, Berlin, pp. 245-253. 40. Mrozek, M. An algorithmic approach to the Conley index theory ( Version revised after publication is here ), published version in: J. Dyn. Diff. Equ. 11(1999), 711-734. 39. Mischaikow, K. and Mrozek, M. and Szymczak, A. Chaos in the Lorenz equations: a computer assisted proof. Part III: the classical parameter values, published version in: J. Diff. Equ. 169(2001), 17-56. 38. Mrozek, M. Rigorous numerics of chaotic dynamical systems, published version in: Chaos - the Interplay between Stochastic and Deterministic Behaviour, P. Garbaczewski ... (eds), Lect. Notes in Physics, 457(), 283-296. 37. Mrozek, M. and Reineck, J. and Srzednicki, R. The Conley index over a circle, published version in: J. Dynamics and Differential Equations, 12(2000), 385--409. 36. Mrozek, M. and Reineck, J. and Srzednicki, R. The Conley index over a base, published version in: Trans. AMS 352(2000), 4171-4194. 35. Kaczynski, T. and Mrozek, M. Connected simple systems and the Conley functor, published version in: Topol. Methods Nonlin. Anal., 10(1997), 183-193. 34. Mrozek, M. Rigorous error analysis of numerical algorithms via symbolic computations, published version in: J. Symb. Comp. 22(1996),435-458. 33. Mischaikow, K. and Mrozek, M. Chaos in the Lorenz equations: a computer assisted proof. Part II: details, (with figures, zipped) published version in: Mathematics of Computation, 67(1998), 1023-1046. 32. Mischaikow, K. and Mrozek, M. and Reineck, J. Singular index pairs, published version in: J. Dyn. Diff. Equ. 11(1999), 399-426. 31. Mrozek, M. Topological invariants, multivalued maps and computer assisted proofs, (with figures, zipped) published version in: Computers & Mathematics, 32(1996),83-104. (Click here for a no-figures version) 30. Kaczynski, T. and Mrozek, M. Stable index pairs for discrete dynamical systems, published version in: Bulletin Canadian Math. Soc., 40(1997), 448-455. 29. Mrozek, M. From the Theorem of Ważewski to computer assisted proofs in dynamics, published version in: Panoramas of Mathematics, Banach Center Publications, 34, 105-120. 28. Mischaikow, K. and Mrozek, M. Chaos in Lorenz equations: a computer assisted proof, published version in: Bull. Amer. Math. Soc. (N.S.), 33(1995), 66-72. 27. McCord, Ch. and Mischaikow, K. and Mrozek, M. Zeta Functions, Periodic Trajectories and the Conley Index, published version in: J. Diff. Equ, 121(1995), 258-292. 26. Kaczynski, T. and Mrozek, M. Conley index for discrete multivalued dynamical systems, published version in: Topology & its Appl., 65(1995), 83-96. 25. Mischaikow, K. and Mrozek, M. Isolating neighborhoods and chaos, published version in: Jap. J. Ind. & Appl. Math., 12(1995), 205-236. 24. Mrozek, M. Shape index and other indices of Conley type for continuous maps in locally compact metric spaces, published version in: Fundamenta Mathematicae, 145(1994), 15-37. 23. Mrozek, M. and Srzednicki, R. On time-duality of the Conley index, Results in Mathematics, 24(1993), 161-167. 22. Degiovanni, M. and Mrozek, M. The Conley index for maps in absence of compactness, Proc. Royal Soc. Edinburgh, 123A(1993), 75-94. 21. Mrozek, M. and Rybakowski, K.P. Discretized ordinary differential equations and the Conley index, J. of Dynamics and Differential Equations, 4(1992), 57-63. 20. Mrozek, M. and Rybakowski, K.P. Nontrivial full bounded solutions of time-periodic semilinear PDEs, Proc. Roy. Soc. Edinburgh, 117A(1991), 305-315. 19. Mrozek, M. The Conley index on compact ANR's is of finite type, Results in Mathematics, 18(1990), 306-313. 18. Mrozek, M. and Rybakowski, K.P. A cohomological Conley index for maps on metric spaces, Journal of Diff. Equations, 90(1991), 143-171. 17. Mrozek, M. Normal Functors and Retractors in Categories of Endomorphisms, Univ. Iag. Acta Math., 29(1992), 181-198. 16. Mrozek, M. The Morse Equation in Conley's Index Theory for Homeomorphisms, Topology and its Applications, 38(1991), 45-60. 15. Mrozek, M. Open index pairs, the fixed point index and rationality of zeta functions, Erg. Th. and Dyn. Syst., 10(1990), 555-564. 14. Mrozek, M. A cohomological index of Conley type for multivalued admissible flows, J. Diff. Equations, 84(1990), 15-51. 13. Mrozek, M. Leray Functor and the Cohomological Conley Index for Discrete Time Dynamical Systems, Transactions of the Amer. Math. Soc., 318(1990), 149-178. 12. Mrozek, M. Index pairs and the Fixed Point Index for Semidynamical Systems with Discrete Time, Fund. Mathematicae, 133(1989), 177-192. 11. Mrozek, M. and Srzednicki, R. The Continuity Axiom in Multi-Valued Dynamical Systems, Rivista di Matematica Pura ed Applicata, 3(1988), 87-97. 10. Mrozek, M. Some Remarks on the Garay's Conjecture, Acta Math. Hungarica, 57(1991), 53-59. 9. Mrozek, M. Strongly Isolating Invariant Sets and Strongly Isolating Blocks, Bull. Acad. Pol. Sc. Ser. Sci. Math., 35(1987), 1-2. 8. Mrozek, M. Transitively Reduced and Transitively Closed Event Networks, Networks, 19(1989), 47-72. 7. Mrozek, M. A Note on Minimum-Dummy-Activities PERT Networks, RAIRO Rech. Oper., 18(1984), 415-421. 6. Mrozek, M. and Zaionc, M. A Computer Model of Evolution and Ecological Processes, Modell. Sim. and Control, 1(1984), 59-63. 5. Mrozek, M. Periodic and Stationary Trajectories of Flows and Ordinary Differential Equations, Univ. Iag. Acta Math., 27(1988), 29-37. 4. Mrozek, M. The Fixed Point Index of a Translation Operator of a Semiflow, Univ. Iag. Acta Math., 27(1988), 13-22. 3. Mrozek, M. and Zaionc, M. Simulation model of evolution in a simplified ecological system, Wiad. Ekol., 27(1981), 49-59. 2. Mrozek, M. Generalized Inverse of a Finite Graph, Fund. Inform. , 4(1981), 499-509. 1. Mrozek, M. Inverse Limits of Torus-Groups and Minimal Sets of some Almost Periodic Continuous Flows -, Zesz. Nauk. UJ, Pr. Mat., 21(1979), 29-50.