Back to Commutative Algebra Seminar: Spring 2016
Commutative Algebra Seminar
Date: Friday, Jan 29, 2016
Time: 3:10PM - 4:00PM
Location: LCB 222
Graeme Milton
University of Utah
Title |
Superfunctions and the algebra of subspace collections |
Abstract |
A natural connection between rational functions of several real or complex variables, and subspace collections is explored. A new class of function, superfunctions, are introduced which are the counterpart to functions at the level of subspace collections. Operations on subspace collections are found to correspond to various operations on rational functions, such as addition, multiplication and substitution. It is established that every rational matrix valued function which is homogeneous of degree 1 can be generated from an appropriate, but not necessarily unique, subspace collection: the mapping from subspace collections to rational functions is onto, but not one to one. For some applications superfunctions may be more important than functions, as they incorporate more information about the physical problem, yet can be manipulated in much the same way as functions. Orthogonal subspace collections occur in many physical problems, but we’ll show an example of the use of non-orthogonal ones, which when substituted in orthogonal ones greatly accelerate the convergence of Fast Fourier transform methods. |
Commutative Algebra