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Tomasz Kaczynski

Professeur, Faculté des sciences
FAC. SCIENCES Mathématiques

Présentation

Sujet de recherche

Analyse globale et non linéaire, Logiciels (outils), Modélisation et simulation, Reconnaissance des formes et infographie, Topologie (Math)

Disciplines de recherche

Informatique, Mathématiques appliquées, Mathématiques fondamentales

Mots-clés

application multivoque, champ vectoriel combinatoire, homologie persistante, indice de Conley, indice de Morse, modélisation, reconnaissance de formes, sytème dynamique, topologie computationnelle, vision artificielle

Intérêts de recherche

Je m'intéresse à la topologie algébrique computationnelle et ses applications en Science et en Génie. Mes objectifs de recherche actuelles sont axés sur l'étude de relation entre les méthodes mathématiques discrètes et continues et à leurs applications aux systèmes dynamiques, à l'analyse de données multidimensionnelles et à des problèmes de vision par ordinateur.

Langues parlées et écrites

Anglais, Français, Polonais, Russe

Diplômes

(1987). (Post-doctorat, Stage postdoc.). University of Waterloo.

(1986). (Doctorat, Doctorat). McGill University.

(1981). (Maîtrise avec mémoire, Maîtrise - Maîtrise). Université de Varsovie.

(1979). (Baccalauréat, Baccalauréat). Université de Varsovie.

Publications

Articles de revue

  • T. Kaczynski, M. Mrozek, and T. Wanner. (2015). Towards a formal tie between combinatorial and classical vector field dynamics. Journal of Computational Dynamics (Article soumis).
  • M. Allili, T. Kaczynski, and C. Landi. (2015). Reducing complexes in multidimensional persistent homology theory. Journal of Symbolic Computation (Article soumis).
  • C.J. Batkam, F. Colin, and T. Kaczynski. (2014). On differential systems with strongly indefinite variational structure. J. Fixed Point Theory & Appl. 16 (1-2), 313-336. (Article publié).
  • M. Ethier and T. Kaczynski. (2014). Suspension models for testing shape similarity methods. Computer Vision & Image Understanding 121 13-20. (Article publié).
  • T. Kaczynski and M. Mrozek. (2013). The cubical cohomology ring: an algorithmic approach. Foundations of Comput. Math, 13 (5), 789–818. (Article publié).
  • N. Cavazza, M. Ethier, P. Frosini, T. Kaczynski, and C. Landi. (2013). Comparison of persistent homologies for vector functions: from continuous to discrete and back. Computers & Math. with Appl. 66 (4), 560-573. (Article publié).
  • P. Dłotko, T. Kaczynski, M. Mrozek, and T. Wanner. (2011). Coreduction homology algorithm for regular CW-complexes. Discrete & Comput. Geom. 46 (2), 361-388. (Article publié).
  • M. Allili, D. Corriveau, S. Derivière, M. Ethier, T. Kaczynski. (2011). Detecting critical regions in multidimensional data sets. Computers & Math with Appl. 61 (2), 499 -512. (Article publié).
  • S. Derivière, T. Kaczynski, and P.O. Vallerand. (2009). On the decomposition and local degree of multiple saddles. Annales Sci. Math. Qué. 33 (1), 45-62. (Article publié).
  • Kaczynski, T. (2008). Multivalued maps as a tool in modeling and rigorous numerics. Journal of Fixed Point Theory and Applications 4 (2), 151 -176. (Article publié).
  • T. Kaczynski, M. Mrozek, and A. Trahan. (2007). Ideas from Zariski topology in the study of cubical sets, cubical maps, and their homology. Canad. J. Math. 59 (5), 1008-1028. (Article publié).
  • M. Allili, D. Corriveau, S. Derivière, T. Kaczynski, and A. Trahan. (2007). Discrete dynamical system framework for construction of connections between critical regions in lattice height data. J. Mathematical Imaging and Vision 28 (2), 99-111. (Article publié).
  • T. Kaczynski, K. Mischaikow, and M. Mrozek. (2003). Computing homology. Homology, Homotopy & Appl. 5 (2), 233-256. (Article publié).
  • T. Kaczynski. (2001). Recursive coboundary formula for cycles in acyclic chain complexes. Top. Meth. Nonlin. Anal. 18 (2), 351-371. (Article publié).
  • M. Allili and T. Kaczynski. (2001). Geometric construction of a coboundary of a cycle. Discrete & Comput. Geom. 25 (1), 125-140. (Article publié).
  • M. Allili and T. Kaczynski. (2000). An algorithmic approach to the construction of homomorphismes induced by maps in homology. Trans. Amer. Math. Soc. 352 (2000), 2261-2281, (open access). 352 (5), 2261-2281. (Article publié).
  • T. Kaczynski, M. Mrozek, and M. Slusarek. (1998). Homology computation by reduction of chain complexes. Computers & Math. Appl. 35 (4), 59-70. (Article publié).
  • M. Allili and T. Kaczynski. (1997). Stability of index pairs for flows. Nonlinear Anal. TMA 30 (7), 4133-4122. (Article publié).
  • T. Kaczynski and M. Mrozek. (1997). Stable index pairs for discrete dynamical systems. Canad. Math. Bull. 40 (4), 448-455. (Article publié).
  • T. Kaczynski and M. Mrozek. (1997). Connected simple systems and the Conley functor. Topol. Meth. Nonlin. Anal. 10 (1) (1997) . 10 (1), 183-193. (Article publié).
  • G. Fournier, L. Gòrniewicz and T. Kaczynski. (1995). Essential critical points in product manifolds. Rocky Mountain J. Math. 20 (1), 899-907. (Article publié).
  • T. Kaczynski and M. Mrozek. (1995). Conley index for discrete multivalued dynamical systems. Topology and Its Appl. 65 (1995) 83-96. 65 (1), 83-96. (Article publié).
  • T. Kaczynski and R. Srzednicki. (1994). Periodic solutions of certain planar rational ordinary differential equations with periodic coefficients. Diff. and Integral Equ.7 (1) 1994, 37-47. 7 (1), 37-47. (Article publié).
  • M. Frigon and T. Kaczynski. (1993). Boundary value problems for systems of implicit differential equations. Math. Anal. and Appl. 179 (2), 317-326. (Article publié).
  • T. Kaczynski and H. Xia. (1993). Hopf bifurcation for implicit neutral functional differential equations. Canad. Math. Bull. 36 (3), 286-295. (Article publié).
  • T. Kaczynski and W. Krawcewicz. (1993). A local Hopf bifurcation theorem for a certain class of implicit differential equations. Canad. Math. Bull. 36 (2), 183-189. (Article publié).
  • T. Kaczynski and J. Wu. (1992). A topological transversality theorem for multi-valued maps in locally convex spaces with applications to neutral equations. Canad. J. Math. 44 (5), 1003-1013. (Article publié).
  • T. Kaczynski. (1992). Unbounded multivalued Nemytskii operators in Sobolev spaces and their applications to discontinuous nonlinearity. Rocky Mountain J. Math. 22 (2), 635-643. (Article publié).
  • L.H. Erbe, W. Krawcewicz, and T. Kaczynski. (1990). Solvability of two-point boundary value problems for systems of nonlinear differential equations of the form y''=g(t,y,y',y''). Rocky Mtn. J. Math. 20 (4), 899-907. (Article publié).
  • T. Kaczynski and V. Zeidan. (1989). An application of Ky-Fan fixed point theorem to an optimization problem. J. Nonlin. Anal. -TMA 13 (3), 259-262. (Article publié).
  • T. Kaczynski and W. Krawcewicz. (1988). Solvability of boundary value problems for the inclusion utt - uxx in g(t,x,u) via the A-proper mapping theory. Zeitschrift für Analysis und Ihre Anwendungen 7 (4), 337-346. (Article publié).
  • T. Kaczynski. (1987). An extension of the Borsuk fixed point theorem. Bull. Acad. Pol. Sci. 35 (5-6), 315-319. (Article publié).
  • K. Geba, A. Granas, T. Kaczynski, and W. Krawcewicz. (1985). Homotopie et équations non linéaires dans les espaces de Banach. C.R. Acad. Sci. Paris, Series I 300 303-306. (Article publié).
  • T. Kaczynski. (1983). Quelques théorèmes de points fixes dans des espaces ayant suffisamment de fonctionnelles linéaires. C.R. Acad. Sci. Paris, 296, série I, 1983, 873-874. 296 873-874. (Article publié).

Livres

  • T. Kaczynski, K. Mischaikow, et M. Mrozek. (2004). Computational Homology. (Applied Mathematical Series, 157). Springer. (Article publié).

Rapports

  • Allili M, Kaczynski T, Landi C. (2015). Reducing complexes in multidimensional persistent homology theory, ArXiv:1310.8089v2 [cs.CG]. Cornell University. 19 p.
  • T. Kaczynski, M. Mrozek, and T. Wanner. (2014). Towards a formal tie between combinatorial and classical vector field dynamics, IMA Preprint Series #2443. University of Minnesota. 40 p.

Articles de conférence

  • T. Kaczynski (presenter), P. Dlotko, and M. Mrozek. (2010). Computing the cubical cohomology ring. Proceedings of the Workshop on Computational Topology in Image Context 2010, 137-142. (Article publié).
  • M. Allili, M. Ethier (presenter), and T. Kaczynski. (2010). Critical region analysis of scalar fields in arbitrary dimensions. Proceedings SPIE-IS&T Volume 7530, 7530–7537. (Article publié).
  • T. Kaczynski. (1999). Conley index for set-valued maps: From theory to computation. Banach Center Publ. Vol 47, Polish Acad. Sci., 57-65. (Article publié).
  • M. Allili and T. Kaczynski. (1998). Stability of index pairs for flows. Univ. Jagel. Acta Math. 36, (Article publié).
  • M. Frigon, L. Gòrniewicz and T. Kaczynski. (1996). Differential inclusions and implicit equations on closed subsets of Rn. Proc. of the First World Congress of Nonlinear Analysts '92,W. de Gruyter, Berlin - New York, 1797-1806. (Article publié).
  • T. Kaczynski. (1991). Implicit differential equations which are not solvable for the highest derivative. Lecture Notes in Math. 1475, 218-224. (Article publié).
  • T. Kaczynski. (1989). On differential inclusions of second order. Lecture Notes in Pure & Appl. Math. 118 Marcel Dekker, 343-352. (Article publié).

Autres contributions

Gestion d'évènements

  • Member of the Scientific Committee. ACAT School (Applied and Computational AlgebraicTopology School), Bologna, Italy. (Atelier).
  • Organizer (jointly with J. Dubois, M. Frigon, R. Gagnon, and A, Granas). Gilles Fournier Memorial Conference, Sherbrooke, Qc, Canada. (Conférence).
  • Organizer (jointly with M. Allili). Gilles Fournier Memorial Conference on Classical and Computational Topological Methods, Bishop’s U., Sherbrooke, Qc, Canada. (Conférence).
  • Organizer (jointly with M. Allili). Minisymposium on Topological Image Analysis, SIAM (Soc. Industrial & Appl. Math.) Imaging Science Conf., San Diego, CA, USA. (Conférence).
  • Organizer (jointly with J.P. Lessard). Scientific Session on Computational and Topological Methods in Dynamical Systems at the 2015 Canad. Math. Soc. Winter Meeting, Montreal, Qc, Canada. (Conférence).
  • Organizer (jointly with M. Frigon and A. Granas). Second Gilles Fournier Memorial Conference, Sherbrooke, Qc, Canada. (Conférence).
  • Organizer (jointly with K. Mischaikow, O. Cornea, M. Dellnitz, M. Mrozek, and H. Oka). Second Workshop on Conley Index and Related Topics, Sherbrooke, Qc, Canada. (Atelier).
  • Co-organizer (jointly with K. Kuperberg and J. Keesling). Special Session on Current trends in topology, 28th Summer Conf. on Topology and Its Appl., Nippising, Ont, Canada. (Conférence).

Activités de collaboration internationale

  • Co-investigator,_. Collaboration à long-terme avec Patrizio Frosini (U Bologna) and Claudia Landi (U Modena Reggio-Emilia) sur pa persistance multidimensionnelle. Partiellement financée par la SD de CRSNG de TK et des sources italiennes.
  • Co-investigator. Collaboration à long terme avec Konstantin Mischaikow (avant Georgia Inst. of Tech., présentement Rutgers U.) sur les dystèmes dynamiques, homologie computationnelle et sujets connexs. Partiellement financée par la SD de CRSNG de TK et par CDSNS Georgia Tech.
  • Co-investigator. Collaboration à long terme avec Marian Mrozek, (U Jagellonne, Krakow, Polonge) sur les systèmes dynamiques, homologie computationnelle et sujets adjacents. Parteillement financée pat la SD de CRSNG de TK, de sources polonaises, et par IMA USA.
  • Co-investigator. Collaboration à long terme avec Thomas Wanner (George Mason) sur les algorithmes en homologie, combinatorial vector fields, and related topics. Partiellement financée par la SD de CRSNG de TK et par IMA USA.

Présentations

  • (2015). Combinatorial and classical vector field dynamics. 2015 CMS Winter Meeting, Scientific Session on Computational and Topological Methods in Dynamical Systems. Montreal
  • (2015). Towards a formal tie between combinatorial and classical vector field dynamics. International Congerence on Dynamics, Topology, and Computations. Bedlewo
  • (2015). Towards a formal tie between combinatorial and classical vector field dynamics. 2015 CMS Summer Meeting, Symposium Rigorous Computation for Differential-Equation Problems. Charlottetown
  • (2015). Towards a formal tie between combinatorial and classical vector field dynamics. McGill University Analysis Seminar. Montréal
  • (2014). Discrete and classical vector field dynamics. Foundations of Computational Mathematics conference, Workshop on Computational Dynamics. Montevideo
  • (2014). Vers un lien formel entre les champs vectoriels combinatoires et classiques. Séminaires du Centre SAG (Structures Algébriques et Géométriques). Sherbrooke
  • (2014). Shape similarity measures: continuous versus discrete. CSUCI (California State University at Channel Islands) Student Seminar. Camarillo
  • (2014). Multiparameter persistent homology for shape descriptors: continuous versus discrete. IMA (Institute for Mathematics and Its Applications) Annual Program Seminar. Minneapolis
  • (2014). A bridge between continuous and discrete multiparameter persistent homologies. U Texas Dallas Analysis Seminar. Dallas
  • (2013). A bridge between continuous and discrete multiparameter persistent homologies. Special Session on Applied Topology, Mathematical Congress of the Americas. Guanajuato
  • (2013). A bridge between continuous and discrete multiparameter persistent homologies. Special Session on New Trends in Topology, 28th Summer Conference on Topology & Applications. Nippising
  • (2013). Multiparameter persistent homology for shape comparison: from continuous to discrete. Minisymposium on Applied and Computational Topology, Annual Meeting CAIMS. Québec
  • (2012). Suspension of a measuring function. BIRS Workshop on Topological Data Analysis and Machine Learning Theory, Banff Center. Banff
  • (2012). Suspension of a measuring function. Applied and computational topology: ATMCS 5 Conference, ICMS (Intl. Center for Math. Sci.). Edinburgh
  • (2012). Detection of chaotic dynamics via combinatorial index pairs. Kathmandu University Science Seminar. Dhulikhel
  • (2012). Cohomology Ring: Algorithmic Approach. Joint Math Meetings Amer Math Soc, Special Session on Generalized Cohomology Theories in Engineering Practice. Boston
  • (2011). Calcul de l'anneau de cohomologie. Séminaires du Centre SAG (Structures Algébriques et Géométriques). Sherbrooke
  • (2011). Computing Cohomology Ring. Workshop on Computational Topology, Fields Institute. Toronto
  • (2011). Topological Issues Arising in Imaging Science and Engineering. Lectures given at U. Modena - Reggio Emilia. Reggio Emilia
  • (2010). Computing the cubical cohomology ring. Computational Topology in Image Context. Chipiona
  • (2010). Singular Zones in Discrete Data Sets. Workshop on Computational Topology and Dynamics, U. Canterbury. Christchurch
  • (2010). Singular Zones in Discrete Data Sets. Geometric and Computational Topology Conference FG60. Bertinoro
  • (2010). Detection of interesting dynamics via combinatorial index pairs. Lecture at Universität Leipzig. Leipzig
  • (2009). Detection and Classification of Critical Points in Mulitidimensional Data Sets. Lectures at Jagiellonian University. Krakow
  • (2009). Critical points for image analysis. Lecture at Jan Kochanowski U. Kielce