Heather Dye, Ph.D.

Professor of Mathematics

Office: Voigt Science Hall 102B

Phone: (618) 537-6556

Education

Ph.D., Mathematics, University of IL at Chicago (2003)

M.A., Mathematics, University of Texas at Austin (1999)

B.S./B.A., Mathematics & Statistics, State University of New York - Buffalo (1996)

Teaching Interests

Calculus, linear algebra, geometry, graph theory

Research Interests

Knot theory, diagrammatic reasoning, and quantum computation

Publications

Dye, H. A. Diagrammatic Reasoning: Route Planning on Maps with ACT-R, Proceedings of the 8^th International Congress on Cognitive Modeling.

Dye, H. A. Non-trivial realizations of virtual link diagrams. J. Knot Theory Ramifications. 15 (2006), no. 8, 963--981.

Dye, H. A.; Kauffman, Louis H. Virtual knot diagrams and the Witten-Reshetikhin-Turaev invariant. J. Knot Theory Ramifications. 14 (2005), no. 8, 1045--1075.

Dye, H. A. Virtual knots undetected by 1- and 2-strand bracket polynomials. Topology Appl. 153 (2005), no. 1, 141—160.

Dye, H. A.; Kauffman, Louis H. Minimal surface representations of virtual knots and links. Algebr. Geom. Topol. 5 (2005), 509--535 (electronic).

Dye, H. A. Unitary solutions to the Yang-Baxter equation in dimension four. Quantum Inf. Process. 2 (2002), no. 1-2, 117--151 (2003).

Presentations

Poster: Diagrammatic Reasoning: Route Planning on Maps with ACT-R, The $8^{th} $ International Conference on Cognitive Modeling. Ann Arbor , MI. July 2007

Virtual Homotopy, AMS Special Session on Knots, 3-Manifolds, and Their Invariants. The Joint Mathematics Meeting. January, 2007. New Orleans, LA. January, 2007

Diagrammatic Reasoning, MAA Session on Research on the Teaching and Learning of Undergraduate Mathematics, The Joint Mathematics Meeting. New Orleans, LA. January, 2007

Diagrammatic Reasoning: Route Planning. Army Research Laboratory / United States Military Academy Technical Symposium, Aberdeen, MD and West Point, NY , October 2006

Are Diagrams Worth 1000 Words? MathFest, Knoxville, TN , August 2006

Modeling Diagrammatic Reasoning: Route Planning on a Grid Based Map. Army Research Laboratory / United States Military Academy Technical Symposium, Aberdeen, MD and West Point, NY , November 2005

The Witten-Reshetikhin-Turaev Invariant and Virtual Link Diagrams. Quantum Topology -- Contemporary Issues and Perspectives, Snowbird, UT, June 2005

Realizations of Virtual Link Diagrams. Knots in Washington 20, Washington , D. C., February 2005

Virtual Links and the Witten Reshetikhin-Turaev Invariant. Geometric Topology Seminar at Columbia University , September 2004

Poster: Using Surfaces to Detect Non-Trivial Virtual Knots. Reunion of the Mentoring Program for Women in Mathematics, Institute for Advanced Study, May 2003

Unitary Solutions to the Yang-Baxter Equation. Special Session on Quantum Computation and Information. The Joint Mathematics Meeting. Baltimore, MD , January 2003

Memberships

Pi Mu Epsilon

American Mathematical Society

MAA

Awards

Commanders Award for Public Service, May 2007

Davies Fellowship, Military Academy , January, 2005 – July 2007

VIGRE Fellowship, The University of Illinois at Chicago , Summer 2002

Departmental Fellowship, The University of Texas at Austin , Summer 1997

Outstanding Senior Finalist (Mathematics), State University of New York at Buffalo, 1996