Slides of some talks

• "Algebraic group actions on noncommutative spectra" (AMS special session, NCSU Raleigh, April 4, 2009) This is a shorter version of the next talk, "Prime ideals and group actions"; it covers the principal results of my papers Group actions and rational ideals and Algebraic group actions on noncommutative spectra. I did not actually cover the last part, on the stratification of the prime spectrum, in the talk and only showed some of these slides briefly while answering questions.
• "Prime ideals and group actions" (Hopf Algebras and Related Topics, a conference in honor of Susan Montgomery, USC Los Angeles, February 15, 2009) This talk describes some results concerning actions of affine algebraic groups on the prime spectrum of an arbitrary associative algebra. The articles on which the talk is based are Group actions and rational ideals and Algebraic group actions on noncommutative spectra.
• "Group actions and rational ideals" (AMS special session, UBC Vancouver, October 4, 2008) This talk describes some results on group actions on the spectrum of rational ideals for arbitrary associative algebras. The emphasis is on rational actions of affine algebraic groups. For the article on which most of the talk is based, click here. A more recent related preprint is here.
• "Koszul algebras and the master theorem" (Algebra Seminar, University of Pennsylvania, December 3, 2007) This is a report on joint work with Benoit Kriegk and Phung Ho Hai. The talk explains how algebraic tools from the theory of N-Koszul superalgebras can be used to derive generalizations of MacMahon's celebrated "master theorem". A version of the master theorem involving Berezinians is stated as well as some binomial identities that follow from it. The paper on which this talk is based is here.
• "How large can a finite group of matrices be?" (Blundon Lecture, Fredericton, October 13, 2007) This talk was given to an audience of undergraduate students. The goal was to give an introduction to group theory and some of its history, old and new. The problem of bounding the size of finite matrix groups over the rationals (Minkowski's Theorem) was discussed in some detail. The article on which this part of the talk was based can be found here.
• "Computing with multiplicative invariants" (Euler Symposium, Temple University, April 16, 2007) The talk gives an introduction to multiplicative invariants intended for a general audience. Perspectives for future computational work in the area are outlined and some open problems are stated.
• "Multiplicative invariant theory" (Lie Groups Seminar, Rutgers University, February 9, 2007) The talk gives an introduction to multiplicative invariant theory highlighting regularity and the Cohen-Macaulay property.
• "Koszul algebras and MacMahon's master theorem" (workshop "Noncommutative Algebraic Geometry" at Fudan University, Shanghai, Sept. 20, 2006) The talk explains some background and the main result of my paper Koszul algebras and the quantum MacMahon Master Theorem with Phung Ho Hai.
• "Orders of finite groups of matrices" (Seminaire AGATA at the University of Montpellier 2, June 8, 2006) The talk is based on my paper Orders of finite groups of matrices with Bob Guralnick.
• "Multiplicative Invariant Theory" (Seminaire AGATA at the University of Montpellier 2, June 8, 2006): a survey talk on multiplicative invariants with particular emphasis on the Cohen-Macaulay property, following the treatment in Chapter 8 of my book with the same title.