Research of Susan Williams

My research area is symbolic dynamics. My earlier work is on problems of classification of shifts of finite type and sofic systems, and the existence of factor maps (or sliding block codes) between such systems. Since 1995 I have been working with Dan Silver on some applications of symbolic dynamics and algebraic dynamics to knot theory.

Irina Teneva wrote a master's thesis with me on Random Lattice Tangles.

To request a reprint or preprint, send me an e-mail or use the snail-mail address on my home page.

The links below are to pdf files of preprints. If the paper has been published, the preprint is generally in the final form accepted by the journal. Papers dating from the current century are also available on ArXiv.

Book:

Editor, Symbolic Dynamics and its Applications, Proc. Symp. Applied Mathematics, AMS, Providence 2004. I also contributed the first chapter, Introduction to symbolic dynamics.

Web article:

Brian Marcus and Susan Williams (2008) Symbolic dynamics. Scholarpedia, 3(11):2923

Recent Publications:

• (with Daniel Silver) Lifting representations of Z-groups, Israel Journal of Mathematics 152 (2006), 313--331.
• (with Daniel Silver) Alexander groups of long virtual knots, J. Knot Theory and its Ramifications 15 (2006), 43--52.
• (with Daniel Silver) An invariant for open virtual strings, J. Knot Theory and its Ramifications 15 (2006), 143--152.
• (with Daniel Silver and Alexander Stoimenow) Euclidean Mahler measure and twisted links, Algebraic and Geometric Topology 6 (2006), 581--602.
• (with Daniel Silver) Crowell's derived group and twisted polynomials, J. Knot Theory and its Ramifications 15 (2006), 1079--1094.
• (with Daniel Silver) Twisted Alexander polynomials detect the unknot, Algebraic and Geometric Topology 6 (2006), 1893--1901.
• (with Daniel Silver) Lehmer's question, knots and surface dynamics, Mathematical Proceedings of the Cambridge Philosophical Society 143 (2007), 649--661.
• (with Daniel Silver) Nonfibered knots and representation shifts, Algebraic Topology --Old and New, Banach Center Publications 85 (2009), 101--107.
• (with Daniel Silver) Twisted Alexander polynomials and representation shifts, Bull. London Math. Soc. 41 (2009), 535--540
• (with J. Scott Carter, Mohamed Elhamdadi, Masahico Saito and Daniel Silver) Virtual knot invariants from group biquandles and their cocycles, J. Knot Theory and its Ramifications 18 (2009), 957--972.
• (with Daniel Silver) Dynamics of twisted Alexander invariants, Topology and its Applications 156 (2009), 2795--2811.
• (with Daniel Silverand Wilbur Whitten) Knot groups with many killers, Bull. Australian Math. Soc. (to appear).

Preprints:

• (with Jonathan Hilllman and Daniel Silver) On reciprocality of twisted Alexander invariants, May 2009.
• (with Daniel Silver) Alexander-Lin twisted polynomials, August 2009.
• (with Daniel Silver) On a theorem of Burde and de Rham, August 2009.

• Toeplitz minimal flows which are not uniquely ergodic, Zeitschrift für Wahrscheinlichkeitstheorie verw. Geb. 67 (1984), 95--107.
• (with B. Marcus and K. Petersen) Transmission rates and factors of Markov chains, Conference in Modern Analysis and Prob. (New Haven, 1982), Contemp. Math. 26 (1984), 279--293.
• A sofic system with infinitely many minimal covers, Proc. Amer. Math. Soc. 98 (1986), 503--506.
• A sofic system which is not spectrally of finite type, Ergodic Theory and Dynamical Systems 8 (1988), 483--490.
• Covers of non-almost finite type sofic systems, Proc. Amer. Math. Soc. 104 (1988), 245--252.
• Notes on renewal systems, Proc. Amer. Math. Soc. 110 (1990), 851-853.
• Lattice invariants for sofic shifts, Ergodic Theory and Dynamical Systems, 11 (1991), 787-802.
• (with Paul Trow) Core dimension group constraints for factors of sofic shifts, Ergodic Theory and Dynamical Systems 13 (1993), 213-224.
• (with Daniel Silver) Augmented group systems and shifts of finite type, Israel Journal of Mathematics 95 (1996), 231-251.
• (with Daniel Silver) Knots, links and representation shifts, Proceedings of the 13th Annual Western Workshop on Geometric Topology (1996), 36-45.
• (with J. C. Parker, C. B. Cave, J. L. Ardell and C. R. Hamm) "Vascular tree structure affects lung blood flow heterogeneity simulated in three dimensions," Modeling in Physiology (1997), 1370-1382.
• (with Daniel Silver) Generalized n-colorings of links, Proceedings of the 1995 Conference in Knot Theory, Banach Center Publications 42 (1998), 373-386.
• (with Daniel Silver) Knot invariants from symbolic dynamical systems, Trans. Amer. Math. Soc. 351 (1999), 3243-3265.
• (with Daniel Silver) Groups with uncountably many subgroups of finite index, Journal of Pure and Applied Algebra 140 (1999), 75-86.
• (with Daniel Silver) Periodic links and augmented groups, Math. Proc. Cambridge Phil. Soc. 127 (1999), 217-236.
• (with Daniel Silver) Virtual tangles and a theorem of Krebes, J. Knot Theory and its Ramifications 8 (1999), 941-945.
• (with Istvan Kovacs and Daniel Silver) Determinants of commuting-block matrices, Amer. Math. Monthly 106 (1999), 950-952.
• (with Daniel Silver) Coloring link diagrams with a continuous palette, Topology 39 (2000), 1225-1237.
• (with Daniel Silver) Virtual knot groups, Knots in Hellas '98 (World Scientific 2000), 440-451.
• (with David Krebes and Daniel Silver) Persistent invariants of tangles, J. Knot Theory and its Ramifications 9 (2000), 471-478.
• (with Daniel Silver) A generalized Burau representation for string links, Pacific J. Math. 197 (2001), 241-255.
• (with Daniel Silver) Alexander groups and virtual links, J. Knot Theory and its Ramifications 10 (2001), 151-160.
• (with Jenelle McAtee and Daniel Silver) Coloring spatial graphs, J. Knot Theory and its Ramifications 10 (2001), 109-120.
• (with K.H. Kim and F.W. Roush) Duality and its Consequences for Ordered Cohomology of Finite Type Subshifts, Combinatorial and Computational Mathematics: Present and Future (S. Hong et alia, eds.), World Scientific, Singapore, 2001, p. 243-265.
• (with Daniel Silver) Mahler measure, links and homology growth, Topology 41 (2002), 979-991.
• (with Daniel Silver) Torsion numbers of augmented groups: with applications to knots and links, L'Enseignement Mathematiques 48 (2002), 317-343.
• (with Daniel Silver) Polynomial invariants of virtual links, J. Knot Theory and its Ramifications 12 (2003), 987-1000.
• (with Daniel Silver) Mahler measure of Alexander polynomials, J. London Math. Soc. (2) 69 (2004), 767-782.
• (with Daniel Silver) On a class of virtual knots with unit Jones polynomial, J. Knot Theory and its Ramifications 13 (2004), 367-371.
• (with Jozef Przytycki and Daniel Silver) 3-Manifolds, tangles and persistent invariants, Mathematical Proceedings of the Cambridge Philosophical Society 139 (2005), 291-306.
• (with Daniel Silver) An invariant of finite group actions on shifts of finite type , Ergodic Theory and Dynamical Systems 25 (2005), 1985-1996.

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