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Daniel S. Silver

Daniel S. Silver

Professor Emeritus
Department of Math and Statistics

Education

  • B.S. 1976
    Trinity College, Hartford, Connecticut
    Mathematics Major

  • Ph.D. in Mathematics, 1980
    Yale University, New Haven, Connecticut

Research Interests

My research is in topology. I am especially interested in knots and links. Since 1995 I have been working with Susan G. Williams on applications of symbolic and algebraic dynamical systems to knot theory. I have also written articles and book reviews on the history of mathematics and science.


Publications

Mathematics Publications: (reprints and preprints are available on request.)

  • (with Lorenzo Traldi) Peripheral elements in reduced Alexander modules: an addendum, Journal of Knot Theory and its Ramifications 33 (2024), no. 9, 2471001, 4 pp. 

  • (with Lorenzo Traldi and Susan Williams) Core groups, Journal of Knot Theory and its Ramifications 33 (2024), no. 5, 2450013, 25 pp. 

  • (with Susan Williams) Lehmer's Question, Graph Complexity Growth and Links, New York J. Math.,  27 (2021),  981–1008

  • A Colorful Approach to Knot Theory (or: “How Happy I Could Be With Ether”), 2020 Lewis-Parker Lecture, Alabama J. Math., Volume 44 (1) (2022), 8–16

  • (with Susan Williams) Group presentations for links in thickened surfaces, J. Knot Theory Ramifications 30 (2021), no. 3, 2150022, 19 pp.

  • (with Susan Williams) Persistent invariants of tangles, Chapter 14 of Encyclopedia of Knot Theory, (eds. C. Adams, E. Flapan, A. Henrich, L. Kaufman, L. Ludwig, S. Nelson), Routledge, 2020.

  • (with Susan Williams) Links in surfaces and Laplacian modules, J. Knot Theory Ramifications 29 (2020).

  • (with Lorenzo Traldi and Susan Williams) Goeritz and Seifert matrices from Dehn presentations, Osaka J. Math. 57 (2020), no. 3, 663–677.

  • (with Susan Williams) Tangles and links: A view with trees, Journal of Knot Theory and its Ramifications 27 (2018), no. 12, 1850061, 7 pp.

  • (with Susan Williams) What is a virtual knot? Notices of the American Mathematical Society, 64 (2017), no. 5, 461–464.

  • (with Stefan Friedl and Susan Williams) The Turaev and Thurston norms, Pacific Journal of Mathematics 284 (2016), 365-382.

  • (with Kalyn Lamey and Susan Williams) Vertex-colored graphs, bicycle spaces and Mahler measure, Journal of Knot Theory and its Ramifications 25 (2016), no. 6, 1650033, 22 pp.

  • (with Susan Williams) On the component number of links from plane graphs, J. Knot Theory Ramifications 24 (2015), no. 1, 1520002, 5 pp.

  • (with Stefan Friedl and Susan Williams) Splittings of knot groups, Math. Ann. 362 (2015), no. 1-2, 401 - 424.

  • (with J. Scott Carter and Susan Williams) Invariants of links in thickened surfaces , Algebraic and Geometric Topology, 14 (2013), 1377 -- 1394.

  • (with J. Scott Carter and Susan Williams) Three dimensions of knot coloring , American Mathematical Monthly, 121 (2014), 506--514.

  • (with Susan Williams) Virtual genus of satellite links , Journal of Knot Theory and its Ramifications, 22 (2013), 1350008 (4 pages).

  • (with Susan Williams) Twisted Alexander invariants of twisted links , Journal of Knot Theory and its Ramifications, 21 (2012), 1250118 (17 pages).

  • (with Susan Williams) On modules over Laurent polynomial rings , Journal of Knot Theory and its Ramifications, 21 (2012), 1250007--1250010.

  • (with Susan Williams) Alexander-Lin twisted polynomials, Journal of Knot Theory and its Ramifications, 20 (2011), 427--434.

  • (with Susan Williams) On a theorem of Burde and de Rham, Journal of Knot Theory and its Ramifications, 20 (2011), 713--720.

  • (with Wilbur Whitten) Knot group epimorphisms, II, preprint, 2009.

  • (with Jonathan Hillman and Susan Williams) On reciprocality of twisted Alexander polynomials, Algebraic and Geometric Topology, 10 (2010), 1017 -- 1026.

  • (with Susan Williams and Wilbur Whitten) Knot groups with many killers, Bulletin of the Australian Mathematical Society, 81 (2010), 507 -- 513.

  • (with Susan Williams) Dynamics of twisted Alexander invariants Topology and its Applications, 156 (2009), 2795--2811.

  • (with Susan Williams) Twisted Alexander polynomials and representation shifts, Bull. London Math. Soc., 41 (2009), 535--540.

  • (with Susan Williams) Nonfibered knots and representation shifts, Proceedings of Postnikov Memorial Conference, Banach Center Publications, 85 (2009), 101--107.

  • (with J. Scott Carter, Mohamed Elhamdadi, Masahico Saito and Susan Williams) Virtual knot invariants from group biquandles and their cocycles, Journal of Knot Theory and its Ramifications, 18 (2009), 957--972.

  • (with Mikami Hirasawa and Kunio Murasugi) When does a satellite knot fiber?, Hiroshima Journal of Mathematics, 38 (2008), 411--423.

  • (with Susan Williams) Lehmer's question, knots and surface dynamics, Mathematical Proceedings of the Cambridge Philosophical Society, 143 (2007), 649-661.

  • (with Susan Williams) Twisted Alexander polynomials detect the unknot, Algebraic and Geometric Topology, 6 (2006), 1893-1907.

  • (with Susan Williams) Crowell's derived group and twisted polynomials, Journal of Knot Theory and its Ramifications, 15 (2006), 1079-1094.

  • (with Alexander Stoimenow and Susan Williams) Euclidean Mahler measure and twisted links, Algebraic and Geometric Topology, 6 (2006), 581-602.

  • (with Susan Williams) Lifting representations of Z-groups, Israel Journal of Mathematics, 152 (2006), 313-331.

  • (with Wilbur Whitten) Knot group epimorphisms,Journal of Knot Theory and its Ramifications, 15 (2006), 153-166.

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