Alan H. Durfee: Curriculum Vitae
- Mailing address: Department of Mathematics, Mount Holyoke
College, South Hadley, MA 01075
- Telephone: 413-538-2299 (work), 413-532-5413 (home)
- Fax: 413-538-3035
- Email: adurfee@mtholyoke.edu
- Web site: http://www.mtholyoke.edu/~adurfee
Education
- A.B. in Mathematics, Harvard University, 1966
- Ph.D. in Mathematics, Cornell University, 1971 (Thesis advisor:
Peter Kahn)
Employment
- University of California at Berkeley: Lecturer, 1971-73
- University of Washington, Seattle: Assistant Professor, 1973-1980
- Columbia University: Visiting Assistant Professor, 1977-79
- Smith College: Assistant Professor, 1980-84
- Mt. Holyoke College: Visiting Associate Professor, 1984-1987,
Associate Professor, 1987-1989, Professor, 1989-
Research Positions
- Mathematical Institute of the University of Bonn, Research Assistant,
Summer Semester, 1971
- The Institute for Advanced Study, Princeton, Member, 1974-76
- Max Planck Institute for Mathematics, Bonn, Member, 1983, and 9/87-2/88
- University of Pisa, Italy, Research Assistant, March-May 1988
- IREX scholar, Martin-Luther University, Halle (Saale), Germany,
January-April, 1991.
- Visiting Scholar, Massachusetts Institute of Technology, 1994-95.
- Visiting Professor, University of Bordeaux, May 15-June 15, 1996.
- Visiting Scholar, Harvard University, 1997-98.
- Visiting Scholar, University of Edinburgh April-May 2005.
Research Interests
The connections between topology and algebraic geometry: Singularities of
varieties and maps, Hilbert's
sixteenth problem, knot theory, Vassiliev invariants.
Grants
- National Science Foundation grant for summer research (Principal
Investigator): 1972-78, 80-81, 85-92
- National Science Foundation grant for Valley Geometry Seminar,
(co-Principal Investigator), 1983-2000
- Department of Education FIPSE grant, 1992-93
- National Science Foundation grant (departmental) for REU summer
program, 1988-2008.
Curriculum development
- Polygonal differential geometry (1992, partially funded by a grant
from the U.S. Department of Education). Lecture notes available.
- Fractals and chaos (Math 125), a course for non-mathematics
majors. This course is different from currently-published textbooks in
that it covers both the mathematical aspects of fractals and chaos as
well as real-world applications. The most recent version of the course
may be found at
www.mtholyoke.edu/courses/adurfee/courses.htm
(developed 1994-97).
- Introducing mathematics into an elementary music theory course
(joint with T. Johnson, Ithaca College, partially funded by a FIPSE
grant, 1997). Documentation can be found at
www.mtholyoke.edu/courses/adurfee/mac/mac.htm.
- Laboratories in mathematical experimentation, Springer,
1997. Projects for a sophomore course in mathematical investigation;
written by the members of the Department of Mathematics and Statistics,
Mount Holyoke College
- Mathematical finance (Math 339). This course covers
mathematical topics around the Black-Scholes formula for option
pricing (text: Hull, Options, futures and other
derivatives. Developed assignments involving downloading financial
information from the web and using statistical analysis to test these
theories. (On my home web page click on "Courses" for the course as
offered in the spring of 2007.)
Research Experiences for Undergraduates (REU) Projects
Complete documentation can be found at the web site
www.mtholyoke.edu/acad/math/reu/.
- Counting critical points of real polynomials in two variables (1989)
- Counting critical points of real polynomials in two variables II
(1992)
- Limiting tangents and normals to singularities of algebraic
surfaces (1994, joint with D. O'Shea)
- Curvature of singularities of algebraic curves and surfaces (1995)
- Polynomial knots I (1998)
- Polynomial knots II (2000, joint with D. O'Shea)
- Polynomial knots III (2002, joint with D. O'Shea)
- Polynomial knots IV (2004, joint with D. O'Shea)
- Polynomial knots V (2006, joint with D. O'Shea)
Recent lectures
- The self-linking of algebraic knots (10 minute talk at the Joint
Math Meetings, San Diego 1/08)
- Perturbations, deformations, and variations (after B. Mazur); MHC
department seminar, 11/07)
- Polynomial knots (Valley Geometry Seminar, 9/06)
- Klein's Erlangen program (20 minute talk at the Joint Math Meetings,
San Antonio 1/06)
- Klein's Erlangen program (Valley Geometry Seminar, 10/04)
Miscellaneous
- Associate editor, Journal of Knot Theory, 1992-2004.
- SAT II Mathematics Committee (College Board), 1994-1997.
- Committee on revisions of the quantitative measure section of the
GRE general test, 2004-2005 (Educational Testing Service).
- Review committee of the Department of Mathematics, University of
Pennsylvania, 2005.
Last updated 1/27/08