Here is some basic information about this web page (This web page is under construction.)
I created this web page in the September of 2007 in connection with a seminar at Iowa State University. This seminar began in August, 2007.
This seminar meets at 2:10 on Wednesdays in Carver 408.
During the 2006-2007 academic year, I ran a seminar at the Institute for Mathematics and its Applications (IMA) at the University of Minnesota. I wrote some notes in connection with that seminar. I am reusing some of those notes. Here is a link to those IMA notes.
Here is the list of talks for the seminar.
December: The seminar will not meet during December.
November 28:The seminar will not meet.
November 21: The seminar will not meet (university holiday).
November 16: Kenneth R. Driessel, Border Bases: Mourain's criterion and algorithm (continued)
November 14: Kenneth R. Driessel, Border Bases: Mourrain's criterion and algorithm .
November 07: Kenneth R. Driessel, Border Bases (continued).
October 31: Kenneth R. Driessel, Border Bases (continued).
October 24: Kenneth R. Driessel, Border Bases.
The Buchberger algorithm has input consisting of a monomial order and a finite list of polynomials. The output is a Groebner basis for the ideal generated by the given polynomials. We shall see that the Groebner basis is often not a continuous function of the given polynomials. Consequently, we shall start to discuss border bases which are a generalization of Groebner bases. (There are seminar notes concerning border bases on the web site mentioned above.)
October 17: Kenneth R. Driessel, Computing Groebner Bases and Computing in Quotients of Polynomial Rings.
October 10: Kenneth R. Driessel, Groebner Bases (continued).
October 3: Kenneth R. Driessel, Groebner Bases.
We will continue to discuss the Groebner basis chapter (chapter 2) in the book "Ideals, Varieties, and Algorithms" by Cox, Little and O'Shea.
September 26: Kenneth R. Driessel, Monomial Ideals.
We will discuss the Groebner basis chapter (chapter 2) in the book "Ideals, Varieties, and Algorithms" by Cox, Little and O'Shea.
September 19: Kenneth R. Driessel, Hermite's root counting theorem (continued).
September 12: Kenneth R. Driessel, Hermite's root counting theorem.
For more information see the IMA notes. In particular, see the notes "Hermite's Quadratic Form" and "Hermite's Quadratic Form Revisited".
September 5: Kenneth R. Driessel, Closure operators and the Zariski topology.
August 29: Kenneth R. Driessel, Closure operators and Galois connections, Decomposition of algebras using idempotents.
For more information see the IMA notes. In particular, see the notes "Closure Operators and Galois Connections" and "Decomposition of Algebras Using Idempotents".
August 22: Kenneth R. Driessel, Quadratic forms.
For more information see the IMA notes. In particular, see the notes "Quadratic Forms".
August 20: Seminar organization.
Last update: November 26, 2007
Kenneth R. Driessel, driessel@iastate.edu