Research

Submitted papers

  • M. Khovanov, R. Sazdanovic. Bilinear pairings on two-dimensional cobordisms and generalizations of the Deligne category arXiv:2007.11640
  • J.A. Baldwin, N. Dowlin, A.S. Levine, T. Lidman, R. Sazdanovic. Khovanov homology detects the figure-eight knot. arxiv:2007.01269
  • Caprau, N. Gonzalez, C. Ruey Shan Lee, A. Lowrance, R. Sazdanovic, M. Zhang, On Khovanov Homology and Related Invariants, arxiv:2002.05247
  • R. Sazdanovic, V. Summers, Torsion in the Magnitude homology of graphs. arxiv:1912.13483
  • Chandler, R. Sazdanovic, S. Stella, M. Yip, On the Strength of Chromatic Symmetric Homology for graphs. arxiv:1911.13297
  • Chandler, R. Sazdanovic, A Broken Circuit Model for Chromatic Homology Theories. arxiv:1911.13226
  • Gasparovic, M. Gommel, E. Purvine, R. Sazdanovic, B. Wang, Y. Wang, L. Ziegelmeier, Local Versus Global Distances for Zigzag Persistence Modules, Computational Geometry Theory and Applications arXiv:1903.08298
  • Chandler, A. M. Lowrance, R. Sazdanovic, V. Summers, Torsion in thin regions of Khovanov homology, 19 pp. arxiv:1903.05760

Published papers

  • Khovanov, R. Sazdanovic, A categorification of the Chebyshev polynomials, to appear in Jorunal of Pure and Applied Algebra, 23 pp. arXiv:2003.11664
  • M. Hajij, J.S. Levitt, R. Sazdanovic Big Data approaches to knot theory: Understanding the structure of the Jones polynomial http://arXiv:1912.10086 accepted for publication.
  • Sazdanovic, D. Scofield, Extremal Khovanov homology and the girth of a knot, to appear in J. of Knot Theory and its Ramifications arxiv:2003.05074
  • Adamaszek, H. Adams, E. Gasparovic, M. Gommel, E. Purvine, R. Sazdanovic, B. Wang, Y. Wang and L. Ziegelmeier. On homotopy types of Vietoris-Rips complexes of metric gluings. Journal of Applied and Computational Topology, 2020, 32 pp. http://arXiv:1712.06224
  • Gonzalez, A. Ushakova, R. Sazdanovic, J. Arsuaga, Prediction in cancer genomics using topological signatures and machine learning (accepted, peer reviewed, Topological Data Analysis. Abel Symposia, Vol. 15, (2020) ISBN 978-3-030-43407-6}, 23 pp.
  • Gasparovic, M. Gommel, E. Purvine, R. Sazdanovic, B. Wang, Y. Wang, L. Ziegelmeier. The Relationship Between the Intrinsic Cech and Persistence Distortion Distances for Metric Graphs, Journal of Computational Geometry, Vol. 10, No. 1 (2019), 477-499. http://arXiv:1812.05282
  • Cooper, V. de Silva, R. Sazdanovic, On Configuration Spaces and Simplicial Complexes. New York Journal of Mathematics Vol. 25 (2019), 723--744. NYJM
  • Nelson, N. Oyamaguchi, R. Sazdanovic, Psyquandles, Singular Knots and Pseudoknots, Tokyo J of Math. 2019, 25 pp. http://arXiv:1710.08481
  • Sazdanovic, Khovanov homology and torsion, in Reiter, Philipp (Ed.), Simon Blatt (Ed.) and Armin Schikorra (Ed.). New Directions in Geometric and Applied Knot Theory. Proceedings of: Geometric Energies with Links to Applications, Topology, and Open Problems, University of Basel, September 2015. 13 pp. De Gruyter 2018.
  • Sazdanovic, D. Scofield, Patterns in Khovanov link and chromatic graph homology, J of Knot Theory and its Ramifications, 27 No. 02, 1840007 (2018), 43 pp. http://arXiv:1801.01225
  • Adamaszek, H. Adams, E.  Gasparovic, M. Gommel, E.  Purvine, R. Sazdanovic, B. Wang, Y.  Wang, L. Ziegelmeier, Vietoris--Rips and Cech Complexes of Metric Gluings, 34th Symposium Computational Geometry (SoCG), 3:1-3:15, 2018.
  • Gasparovic, M. Gommel, E.  Purvine, R. Sazdanovic, B. Wang, Y.  Wang, L. Ziegelmeier A complete characterization of the one-dimensional intrinsic Cech persistence diagrams for metric graphs. E. Chambers, B. Fasy, L. Ziegelmeier (eds), Research in Computational Topology. Association for Women in Mathematics Series, vol 13, 33–56, 2018. Proceedings for Workshop for Women in Computational Topology Institute for Mathematics and its Applications, Minneapolis, MN 2016 http://arXiv:1702.07379
  • Sazdanovic, M. Yip, A categorification of the Stanley symmetric chromatic function, Journal of Combinatorial Theory, Series A, 154 (2018), 218-246. arXiv:1506.03133
  • Lowrance, R. Sazdanovic, Khovanov homology, chromatic homology, and torsion, Topology and its Applications. 222 (2017) 77--99 http://arXiv:1609.03585
  • Kauffman, S. Jablan, R. Sazdanovic, M. Stosic, A. Zekovic, Unknotting and Maximum Unknotting Numbers, J. of Knot Theory and its Ramifications, 25 (9) (2016), 42 pp.
  • Guan, W. Tang, H. Krim, J. Keiser, A.J. Rindos, R. Sazdanovic, A Topological Collapse for Document Summarization, 2016 IEEE 17th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC) (2016), 1-5.
  • Gerdes, S. Jablan, Lj, Radovic, R. Sazdanovic, Plaited polyhedra: A knot theory point of view, J. of Knot Theory and its Ramifications, 26 (2016), 13 pp.
  • Jablan, R. Sazdanovic, From Conway notation to LinKnot, Proceedings of ICTS Program: Knot 2013, Contemporary Mathematics series of the American Mathematical Society, Volume: 670 (2016) ISBN: 978-1-4704-2257-8, 63-92. AMSCont
  • Khovanov, R. Sazdanovic, Categorifications of the polynomial ring, Fundamenta Mathematicae, 230 (3) (2015), 251-280. arXiv:1101.0293
  • Sazdanovic, M. Yip, A categorification of the Stanley symmetric chromatic polynomial, Discrete Mathematics and Theoretical Computer Science, FPSAC 2015 Proceedings (2015), 631-642 DMTCS
  • Khovanov, R. Sazdanovic, A Categorification of One-Variable Polynomials, Discrete Mathematics and Theoretical Computer Science, FPSAC 2015 Proceedings (2015), 937-948 DMTCS
  • Przytycki, R. Sazdanovic, Torsion in Khovanov homology of semi-adequate links, Fundamenta Mathematicae 225 (2014), 277-303. arXiv:1210.5254
  • H. Kauffman, S. Jablan, Lj. Radovic, R. Sazdanovic, Reduced Relative Tutte, Kauffman Bracket and Jones Polynomials of Virtual Link Families, J. of Knot Theory and Its Ramifications, 22 (4) (2013), 21 pp. arXiv:1106.2785
  • Baranovsky, R. Sazdanovic, Graph homology and graph configuration spaces, Journal of Homotopy and Related Structures, Vol 7 (2012), 1-13. arXiv:1208.5781
  • Jablan, Lj. Radovic, R. Sazdanovic, A. Zekovic, Mirror-curves and knot mosaics, Computers and Mathematics with Applications, Vol 64, Issue 4, (2012) 527-543. arXiv:1106.3784
  • Sazdanovic, Diagrammatics in Art and Mathematics, Symmetry 4, (2012) 285-301.  MDPI/2073-8994/4/2/285
  • Jablan, Lj. Radovic, R. Sazdanovic, Knots and Links in Architecture, Pollack Periodica, Vol. 7 (2012), 65-76.
  • Jablan, Lj. Radovic, R. Sazdanovic, A. Zekovic, Knots in Art, Symmetry 4, (2012) 302-328. MDPI
  • Jablan, Lj. Radovic, R. Sazdanovic, Nonplanar graphs derived from Gauss codes of virtual knots and links, J Math. Chem., Vol. 49, No. 10 (2011) 2250-2267.
  • Jablan, R. Sazdanovic, Diagram dependent knot invariants and properties, "Introductory Lectures on Knot Theory" "Selected Lectures on Knot Theory and its Applications to Physics and Biology, World Scientific edition 'Knots and Everything' 46 (2011) ISBN 978-9814307994
  • Jablan, Lj. Radovic, R. Sazdanovic, Knots and Links Derived from Prismatic Graphs, MATCH Commun. Math. Comput. Chem. Vol 66 No. 1 (2011) 65-92.
  • Jablan, Lj. Radovic, R. Sazdanovic, Pyramidal knots and links and their invariants, MATCH Commun. Math. Comput. Chem. Vol 65 No. 3 (2011) 541-580.
  • Pabiniak, J. Przytycki, R. Sazdanovic, On the first group of the chromatic cohomology of graphs, Geometriae Dedicata, Vol 140, No. 1 (2009) 19-48.
  • Jablan, R. Sazdanovic, Braid Family Representatives, J. of Knot Theory and Its Ramifications, 17 (7) (2008) 817-833. arXiv:math/0504479
  • Jablan, R. Sazdanovic, Unlinking number and unlinking gap, J. of Knot Theory and Its Ramifications, 16 (10) (2007) 1331-1355. arXiv:math/0503270
  • Jablan, R. Sazdanovic, Knots, Links, and Self-avoiding Curves, Forma, 22 (1) (2007), 5-13.
  • Jablan, Lj. Radovic, R. Sazdanovic, Basic polyhedra in knot theory. Kragujevac J. Math. 28 (2005) 155-164
  • Kappraff, S. Jablan, G.W. Adamson, R. Sazdanovic, Golden Fields, Generalized Fibonacci Sequences, and Chaotic Matrices, Forma, 19 (4), (2004) 367-387

Books

  • Jablan, R.Sazdanovic, “LinKnot: Knot Theory by Computer”, World Scientific edition “On Knots and Everything” 21 (2007) pp. 500 ISBN 978-981-277-223-7 Official web  Book and software

Book Chapters

  • Nanda, R. Sazdanovic, Simplicial Models and Topological Inference in Biological Systems, Discrete and Topological Models in Molecular Biology, ed. N. Jonoshka, M. Saito, Springer Natural Computing Series, 2014, 109-141 (peer reviewed) Springer PDF
  • Sazdanovic, Khovanov link homology, to appear in the collection A Concise Encyclopedia of Knot Theory, ~8 pp. (peer reviewed, mostly expository)

 

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