The Kolchin Seminar in Differential Algebra

Hunter College - Room HW706

Saturday-Sunday May 10-11 2003


Saturday Session

Ziming Li
University of Waterloo, Ontario, Canada
Exponential Solutions of D-finite Systems
2:00 - 3:00PM

Abstract: A D-finite system is a finite set of linear homogeneous PDE's whose solution space is of finite dimension over the field of constants. We present an algorithm for computing exponential solutions of a D-finite system whose coefficients are rational functions. This algorithm will be used as a basis for factoring D-finite systems.

Jerry Ianni
LaGuardia Community College, CUNY
Symmetry in 12-Tone Rows
3:30 - 4:30

Abstract:We will discuss four fundamental transformations of 12-Tone Rows, transposition, retrograde, inversion, and cyclic shift, that generate transformation spaces. A 12-Tone Row is called symmetric if it is invariant under some transformation. Symmetries will be analyzed both algebraically and geometrically using groups of permutations, coset spaces, clock diagrams, and combinatorial analysis. Some computations obtained using GAP that show the relative scarcity of symmetries will be presented. The primary reference for this expository talk is the paper "How Rare is Symmetry in Musical 12-Tone Rows?" by David J. Hunter and Paul T. von Hippel from the February 2003 issue of The American Mathematical Monthly.

Ziming Li
University of Waterloo, Ontario, Canada
Factoring D-finite Systems
5:00 - 6:00 PM

Abstract: Given a D-finite system L with rational function coefficients, we outline an algorithm for computing all the linear differential ideals containing the linear differential ideals generated by L. The algorithm is a generalization of the Beke-Schlesinger algorithm for factoring linear ODE's, which reduces the problem of computing factors to finding exponential solutions of associated equations.


Sunday Session

Ziming Li
Texas Tech University
Informal discussion
10:30 - 12:00AM


Coffee and tea will be served beginning at 1:30 PM on Saturday, and at 10:00 AM on Sunday
Room HW706

Click here for directions to Hunter College and location of room