Daniel S. Silver
Education
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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.)
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(with Susan Williams) Lehmer's Question, Graph Complexity Growth and Links, New York J. Math. (2021), in press.
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A Colorful Approach to Knot Theory (or: “How Happy I Could Be With Ether”), 2020 Lewis-Parker Lecture, Alabama J. Math., in press.
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(with Susan Williams) Group presentations for links in thickened surfaces, J. Knot Theory Ramifications 30 (2021), no. 3, 2150022, 19 pp.
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(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.
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(with Susan Williams) Links in surfaces and Laplacian modules, J. Knot Theory Ramifications 29 (2020).
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(with Lorenzo Traldi and Susan Williams) Goeritz and Seifert matrices from Dehn presentations, Osaka J. Math. 57 (2020), no. 3, 663–677.
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(with Susan Williams) Tangles and links: A view with trees, Journal of Knot Theory and its Ramifications 27 (2018), no. 12, 1850061, 7 pp.
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(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.
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(with Susan Williams) On the component number of links from plane graphs, J. Knot Theory Ramifications 24 (2015), no. 1, 1520002, 5 pp.
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(with Stefan Friedl and Susan Williams) Splittings of knot groups, Math. Ann. 362 (2015), no. 1-2, 401 - 424.
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(with J. Scott Carter and Susan Williams) Invariants of links in thickened surfaces , Algebraic and Geometric Topology, 14 (2013), 1377 -- 1394.
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(with J. Scott Carter and Susan Williams) Three dimensions of knot coloring , American Mathematical Monthly, 121 (2014), 506--514.
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(with Susan Williams) Virtual genus of satellite links , Journal of Knot Theory and its Ramifications, 22 (2013), 1350008 (4 pages).
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(with Susan Williams) Twisted Alexander invariants of twisted links , Journal of Knot Theory and its Ramifications, 21 (2012), 1250118 (17 pages).
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(with Susan Williams) On modules over Laurent polynomial rings , Journal of Knot Theory and its Ramifications, 21 (2012), 1250007--1250010.
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(with Susan Williams) Alexander-Lin twisted polynomials, Journal of Knot Theory and its Ramifications, 20 (2011), 427--434.
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(with Susan Williams) On a theorem of Burde and de Rham, Journal of Knot Theory and its Ramifications, 20 (2011), 713--720.
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(with Wilbur Whitten) Knot group epimorphisms, II, preprint, 2009.
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(with Jonathan Hillman and Susan Williams) On reciprocality of twisted Alexander polynomials, Algebraic and Geometric Topology, 10 (2010), 1017 -- 1026.
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(with Susan Williams and Wilbur Whitten) Knot groups with many killers, Bulletin of the Australian Mathematical Society, 81 (2010), 507 -- 513.
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(with Susan Williams) Dynamics of twisted Alexander invariants Topology and its Applications, 156 (2009), 2795--2811.
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(with Susan Williams) Twisted Alexander polynomials and representation shifts, Bull. London Math. Soc., 41 (2009), 535--540.
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(with Susan Williams) Nonfibered knots and representation shifts, Proceedings of Postnikov Memorial Conference, Banach Center Publications, 85 (2009), 101--107.
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(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.
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(with Mikami Hirasawa and Kunio Murasugi) When does a satellite knot fiber?, Hiroshima Journal of Mathematics, 38 (2008), 411--423.
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(with Susan Williams) Lehmer's question, knots and surface dynamics, Mathematical Proceedings of the Cambridge Philosophical Society, 143 (2007), 649-661.
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(with Susan Williams) Twisted Alexander polynomials detect the unknot, Algebraic and Geometric Topology, 6 (2006), 1893-1907.
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(with Susan Williams) Crowell's derived group and twisted polynomials, Journal of Knot Theory and its Ramifications, 15 (2006), 1079-1094.
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(with Alexander Stoimenow and Susan Williams) Euclidean Mahler measure and twisted links, Algebraic and Geometric Topology, 6 (2006), 581-602.
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(with Susan Williams) Lifting representations of Z-groups, Israel Journal of Mathematics, 152 (2006), 313-331.
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(with Wilbur Whitten) Knot group epimorphisms,Journal of Knot Theory and its Ramifications, 15 (2006), 153-166.
Resources on History of Knot Theory
- A 5-Minute History of Knot Theory
- Smokey pas de deux gif produced by artist at American Scientist
- When Smokes Gets in Your Eyes
- James Clerk Maxwell’s hand-drawn zoetrope illustration of three smoke rings (Copyright is owned by Cavendish Museum and reproduced here with their permission)
- Why Knot? An elementary exposition on Knots and Fox colorings for undergraduates