Algebra Seminar: Karel Casteels (UCSB), 'An Introduction to Grobner Bases'

Event Date: 

Monday, April 29, 2013 - 2:00pm to 3:00pm

Event Location: 

  • 4607B South Hall

Event Contact: 

Ken Goodearl

Abstract: Last week I mentioned that the quantum minors contained in a given H-invariant prime ideal of quantum matrices form a Grobner basis for the ideal. I will give an outline of this proof on May 6th. In preparation for this, I will give a brief introduction to Grobner bases this week. These objects, while only developed in the 1960's as a generalization of both the Euclidean algorithm and Gaussian row reduction, have since formed a fundamental tool in commutative algebra and algebraic geometry. I will introduce their basic theory and applications. I will then discuss extensions of the theory to certain noncommutative algebras such as, of course, quantum matrices.