Theodore B. Stanford
School Address
Department of Mathematical Sciences
New Mexico State University
Las Cruces, NM 88003-8801
Phone: (575) 646-7810
E-mail: stanford@nmsu.edu
1. Education
·Ph.D. Mathematics, Columbia University, May 1993
·M.A. Mathematics, Columbia University, May 1988
·B.S. Mathematics, Brigham Young University, August 1986
2. Employment
August 2000 Assistant Professor of Mathematics, New
Mexico State University.
1997-2000 Assistant Professor of Mathematics, United States Naval Academy.
1996-97 Visiting Lecturer, Department of Mathematics, University of
Nevada at Reno.
1994-96 Adjunct Assistant Professor, Department of Mathematics, UC Berkeley.
1993-94 Visitor, Department of Mathematics, University of Geneva, Switzerland.
1992-93 (Summers) Visitor, The Geometry Center, University of Minnesota.
1991-93 Instructor, Columbia University, New York, NY
1990-91 (Summers) Researcher, Center for Communications Research, Princeton,
N.J.
1988-91 Teaching Assistant, Columbia University New York, NY.
1989 (Summer) Cryptologic Mathematician, NSA, Fort Meade, MD.
1986-87 Teaching Assistant, Brigham Young University, Provo, UT.
3. Grants
2001 NMSU Department of Mathematical Sciences Summer
Research Award.
1998-99 Naval Academy Research Council Summer Grants
1993-96 National Science Foundation Postdoctoral Research Fellowship
1992-93 Sloan Doctoral Dissertation Fellowship
4. Publications
4.1. Knots and surfaces. A guide to discovery mathematics (with David W. Farmer). Mathematical World, 6. American Mathematical Society, Providence, RI, 1996. viii+101 pp. ISBN: 0-8218-0451-0.
4.2. The functioriality of Vassiliev-type invariants of links, braids, and knotted graphs. Random knotting and linking (Vancouver, BC, 1993). Journal of Knot Theory and its Ramifications 3 (1994), 247-262.
4.3. Braid commutators and Vassiliev invariants. Pacific Journal of Mathematics 174 (1996), 269-276.
4.4. Finite-type of invariants of knots, links, and graphs. Topology 35 (1996), 1027-1050.
4.5. Computing Vassiliev's invariants. Topology and its Applications 77 (1997), 261-276.
4.6. On Gusarov's Groups of Knots (with Ka Yi Ng). Mathematical Proceedings of the Cambridge Philosophical Society 126 (1999), 63-76.
4.7. Four observations on n-triviality and Brunnian links. Journal of Knot Theory and its Ramifications 9 (2000), 213-219.
4.8. Brunnian links are determined by their complements (with Brian Mangum). Algebraic and Geometric Topology 1 (2001), 143-152.
4.9. Validity of threshold crossing analysis of symbolic dynamicsfrom chaotic time series (with Erik Bollt, Ying-Cheng Lai, and Karol Zyczkowski). Physical Review Letters, 85 16 (2000), 3524-3527.
4.10. What Symbolic Dynamics Do We Get With A Misplaced Partition? On the Validity of Threshold Crossings Analysis of Chaotic Time-Series (with Erik Bollt, Ying-Cheng Lai, and Karol Zyczkowski). Physica D. 154 3-4 (2001), 259-286.
4.11. Vassiliev invariants and knots modulo pure braid subgroups. To appear in the Annals of Mathematics. (Accepted 1999) Preprint available at math.GT/9805092.
4.12. On the z-degree of Kauffman polynomial of a tangle decomposition (with ark Kidwell). "Knots, Braids and Mapping Class-Groups-Papers Dedicated to Joan S. Birman" (editors Gilman, Menasco, and Lin), 85-93, AMS/IP Studies in Advanced Mathematics. 2001.
4.13. On knot invariants which are not of finite type (with Rolland Trapp). "Knots, Braids and Mapping Class Groups-Papers Dedicated to Joan S. Birman" (editors Gilman, Menasco, and Lin), 171-175 AMS/IP Studies in Advanced Mathematics. 2001.
4.14. Braid commutators and delta finite-type invariants. "Knots in Hellas '98 (Delphi)", Series of Knots and Everything 24, World Scientific Publishing, River Edge, NJ, 2000.
4.15. Brunnian braids and some of their generalizations. To appear in the Bulletin of the London Mathematical Society. Preprint available at math.GT/9907072.
4.16. A move on diagrams that generates S-equivalence of knots (with Swatee Naik). To appear in the Journal of Knot Theory and its Ramifications. Preprint available at math.GT/9911005.
4.17. On invariants of Morse knots (with Jacob Mostovoy).Topology and its Applications 121 (2002), 105-118.
4.18. On a map from pure braids to knots (with Jacob Mostovoy). To appear in the Journal of Knot Theory and its Ramifications. Preprint available at math.GT/9907088. (Accepted 2002).
4.19. Finite-type invariants based on local moves (with Jacob Mostovoy and James Conant). In preparation.
4.20. Topological entropy with respect to non-generating partitions (with Erik Bolt and Mark Kidwell). In preparation.
4.21. Some computational results on mod 2 finite-type invariants of knots and string links. In preparation.
4.22. Free Newton with applications to the concordance group of two-strand string links. In preparation.
4.23. The linking numbers of a knotted graph, and a criterion for graph planarity. In preparation.
4.24. The space of tilings of a torus by squares. In preparation.
5. Selected Presentations (When available, titles of talks are given in italics)
5.1 Colloquium Talks. These are invited, one-hour talks given to a general mathematical audience. All talks are given in the mathematics department at the indicated university. Talks given as part of a job interview are not included.
5.1.1. Brigham Young University, September 1993.
5.1.2. University of Geneva, Switzerland, November 1993.
5.1.3. n-Triviality in knots, braids, and groups. University of Nevada, Reno, February 1996.
5.1.4. n-Triviality in knots, braids, and groups. Santa Clara University, April 1996.
5.1.5. Free groups, free group rings, braids, and tangles. University of Nevada, Reno, April 1997.
5.1.6. On the kernel and image problems for Vassiliev invariants. George Washington University, Octover 1997.
5.1.7. Knots, surfaces, and matrices. United States Naval Academy, January 1998.
5.1.8. Free Newton polynomials and the concordance group of two-strand string links. George Washington University, February 1999.
5.1.9. Brunnian links, braids, and free group elements. United States Naval Academy, February 1999.
5.1.10. Brunnian links are determined by their complements. New Mexico State University, October 2002.
5.2 Seminar Talks These are invited, one-hour talks, given to a more specialized mathematical audience, usually a group of topologists. All talks given in the mathematics department at the indicated university. Talks given at my local institution are not included.
5.2.1. University of Minnesota, July 1993 (two talks).
5.2.2. University of Paris VII, March 1994 (two talks).
5.2.3. University of Bern, Switzerland (the "Borel Seminar"), May 1994
(two talks).
5.2.4. University of Dijon, France, May 1994.
5.2.5. University of Nantes, France, June 1994.
5.2.6. Brigham Young University, January 1995.
5.2.7. University of California, Riverside, October 1995.
5.2.8. Columbia University, October 1997.
5.2.9. Columbia University, March 1998.
5.2.10. University of Rochester, November 1998.
5.2.11. Symbolic dynamics from a misplaced partition. UNAM, Cuernavaca, Mexico, February 2002. (Dynamical Systems Seminar).
5.2.12. Cinvestav, Mexico City, February 2002.
5.2.13. Finite-type invariants based on doubled-delta moves. University of California, San Diego, November 2002.
5.3. Special Sessions at Meetings of the American Mathematical Society Speakers in these sessions are invited by the organizers, and talks are usually 20 minutes each. The title of the session is in quotes.
5.3.1. The functoriality of finite-type invariants of knots, links, and knotted graphs. "Random Knotting", Vancouver, August 1993.
5.3.2. Milnor invariants of singular knots. "Knot Theory", Orlando, January 1996.
5.3.3. Extending the Gassner representation from pure braids to tangles, and some rational functions that generate Milnor invariants. "Knot Theory and Quantum Topology", Baltimore, January 1998.
5.3.4. Vassiliev's knot invariants and the lower central series of the pure braid groups. "Quantum Topology", Manhattan, Kansas, March 1998.
5.3.5. Symmetries of 2-strand string links up to concordance. "Symmetries of Knots and 3-Manifolds", Buffalo, NY, April 1999.
5.3.6. Brunnian braids and links, n-triviality, and group commutators. "Knots and 3-Manifolds," Buffalo, NY, April 1999.
5.3.7. Finite and nilpotent quotients of braid groups and link groups. "Combinatorial Group Theory," New York, NY, November 2000.
5.3.8. On the nonexistence of a mod 2 Kontesevich integral. "Topology of Links," Las Vegas, NV, April 2001.
5.3.9. Generalizations of Gusarov's groups of knots. "Low Dimensional Topology," San Diego, CA, January 2002.
5.3.10. Twist sequences and finite quotients of knot groups. "Quantum Topology", Portland, OR
5.3.11. The Burau and Gassner representations for tangles. "Algebraic Toplogy Based on Knots", Baltimore, MD, January 2003.
5.4. Other Conference Presentations.
5.4.1. Semi-Annual Math/Physics meeting, University of Strasburg, May 1994.
5.4.2. "Knots in Huia" conference, Auckland, NZ, December 1994.
5.4.3. Knot theory conference, Oberwolfach, Germany, September 1995.
5.4.4. Vassiliev invariants and the lower central series of the pure braid group. "Knots in Washington" miniconference, University of Maryland at College Park, November 1997.
5.4.5. A generalized Magnus expansion, with applications to string links. "Knots in Washington" miniconference, United States Naval Academy, February 1998.
5.4.6. Knots modulo braid commutators. "Knots in Hellas" conference, Delphi, Greece, August 1998.
5.4.7. A move on diagrams that generates S-equivalence of knots. "Knots in Washington" miniconference, George Washington University, May 1999.
5.4.8. Free Newton expansions and two-strand string links. Seminar at the Research Institute for Mathematical Sciences at Kyoto University (RIMS), Japan, September 2001.
5.4.9. Computational results on mod 2 finite-type invariants of knots and string links. Workshop on knots and three-manifolds,RIMS, Kyoto, September 2001.
5.4.10. Some groups of knots. A day of talks dedicated to the work of Mikhail Goussarov (1958-1999), RIMS, Kyoto, September 2001.
5.4.11. Finite-type invariants based on doubled-delta moves. "Knots in Washington", George Washington University, January 2003.
5.4.12. High school outreach activities at New Mexico State University. MAA Session on Strategies for increasing the Diversity of Students in Mathematics, AMS/MAA Joint Meetings, Baltimore, MD, January 2003.
6a. Courses Taught (prior to NMSU). (numbers in parantheses indicate multiple sections)
Fundamentals of College Mathematics, Fall 1996 (2).
College Algebra, Fall 1991, Spring 1992 (2), Fall 1996.
Knots and Surfaces, Spring 1993.
Calculus I, Fall 1996, Spring 1997 (2), Fall 1997 (2), Fall 1998, Fall
1999, Spring 2000.
Calculus II, Spring 1998 (2).
Probability, Spring 1999 (2), Fall 1999.
Abstract Algebra, Fall 1994, Spring 1996, Spring 2000.
Real Analysis, Spring 1995.
Topology, Spring 1997.
6b. Courses Taught (at NMSU)
Math 191, Calculus I, Spring 2003.
Math 192, Calculus II, Spring 2001.
Math 210G, Mathematics Appreciation, Fall 2000, Spring 2002.
Math 280, Linear Algebra, Spring 2002.
Math 330, Discrete Mathematics, Fall 2001.
Math 453, Introduction to Topology, Spring 2001.
Math 481, Modern Algebra I, Fall 2000.
Math 541-542, Topology I and II, Fall 2002-Spring 2003.
Math 643, Topology III, Fall 2001.
7. Ph.D. Students
·Khaled Bataineh, NMSU, May 2003.
·John Sanders, current Ph.D. student, NMSU.
·Candelario Castaneda, current Ph.D. student, NMSU.
·Mohammed Yasein, current Ph.D. student, NMSU.
8. Service at NMSU
2000-2001
Hiring Committee
Library and Reading Room Committee
2001-2002
Hiring Committee
Basic Notions Seminar
Computer Advisory Committee
2002-2003
Basic Notions Seminar
Computer Advisory Committee
Math Majors and Minors Committee
NMSU Faculty Senate
Math Majors and Minors Committee
Faculty Advisor, Pi Mu Epsilon Mathematical Honor Soci