The Kolchin Seminar in Differential Algebra

Saturday-Sunday May 10-11 2003

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__Saturday Session __

** Ziming Li**
University of Waterloo, Ontario, Canada

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

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

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.
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**Texas Tech University

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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
**