Publications

Note: In my research community, we tend to list authors of joint publications in alphabetical order, unless dictated by submission circumstances. All authors are expected to have equally substantial intellectual contribution to the paper. In particular, we kindly request not to apply the algorithm of This Cartoon to our lists ;-)

Book: T. Kaczynski, K. Mischaikow, et M. Mrozek, Computational Homology , Appl. Math. Sci. Vol. 157, Springer Verlag , NY 2004.

Recent research papers (Titles in blue are linked to PDF files of either author's preprint versions or open access publications)
46.
 M. Allili, G. Brouillette, and T. Kaczynski, Multidimensional discrete Morse theory, arXiv:2212.02424 [math.GT] Dec 2022.
45.
 R. Budney and T. Kaczynski, Bi-filtrations and persistence paths for 2-Morse functions,  arXiv:2110.08227 [math.AT] Oct 2021, to appear in Algebraic & Geometric Topology.
44.
 B. Batko, T. Kaczynski, M. Mrozek, and T. Wanner, Linking combinatorial and classical dynamics: Conley index and Morse decompositions, Foundations of Computational Mathematics (20) (2020), 967-1012, DOI 10.1007/s10208-020-09444-1 (open access)
43.
 M. Allili, T. Kaczynski,  C. Landi, and F. Masoni, Acyclic partial matchings for multidimensional persistence: algorithm and combinatorial Interpretation, published version in J Math Imaging Vis (61) (2019) 174-192, DOI 10.1007/s10851-018-0843-8.
42.
 M. Allili, T. Kaczynski,  C. Landi, and F. Masoni, Algorithmic construction of acyclic partial matchings for multidimensional persistence, in Discrete Geometry for Computer Imagery, eds. W.G. Kropatsch, N.M. Artner, I. Janusch, Proc. 20th IAPR Intl. Conf., DGCI 2017 Vienna, Springer 2017, 375-387.
41
 T. Kaczynski, M. Mrozek, and T. Wanner, Towards a formal tie between combinatorial and classical vector field dynamics, published version in J. Comput. Dynamics,  3 (1), (2016), 17-50.
40.
 C.J. Batkam, F. Colin, and T. Kaczynski, On differential systems with strongly indefinite variational structure, J. Fixed Point Theory & Appl. , 313-336, DOI 10.1007/s11784-015-0213-8.
39.
 M. Allili, T. Kaczynski, and C. Landi, Reducing complexes in multidimensional persistent homology theory, ArXiv:1310.8089v2 [cs.CG] 12 March 2015, published version in J. Symbolic Computation 78 (2017), 61–75.
38.
 M. Ethier and T. Kaczynski, Suspension models for testing shape similarity methods, published version in Special Session on Computational Topology in Image Context, eds. M. Ferri and P. Frosini, Computer Vision & Image Understanding 121 (2014), 13-20.

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Papers popularizing mathematics

4.
 S. Derivière, A. Trahan, and T. Kaczynski, Comment compter les trous dans une meule de fromage suisse : ou, l'homologie pour les gourmands, in Actes du Congrès AMQ Sherbrooke 2006 (2008), 127-131.
3.
 T. Kaczynski, Vivre en dimension 4 and Voyager en dimension 4, Accromath (open access), 1 (2006), 30-35.
2.
 T. Kaczynski, Life and travel in 4D, Pi in the Sky (open access), Dec. 2001.
1.
 T. Kaczynski, The red violin of science, Pi in the Sky, Dec. 2000.