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Connections between linear algebra and topology/An invitation to graduate study at the University at Albany

by

Mark Steinberger and Jackie Palermo
SUNY @ Albany

October 25, 2007
5:00 pm
Bailey Hall

Refreshments will be served at 4:45 in Bailey 204


Abstract:

This two-part presentation will discuss our grad program as well as address the following question: When are two periodic matrices related by a nonlinear change of variables? Here, a real, square matrix is periodic if it's kth power is the identity matrix for some k>0. Periodic matrices are important in studying groups of symmetries. When two matrices are related by a linear change of variables, (i.e., when they are "similar matrices"), they can be seen as representing the same transformation with respect to different ways of viewing Rn as a vector space. A nonlinear change of variables is more radical. In 1935, de Rham conjectured that two periodic matrices that are related by a nonlinear change of variables should be linearly similar. He was wrong! We discuss the differences between linear, differentiable and continuous change of variables, relating linear algebra to basic notions in multivariable calculus and topology.


For additional information, send e-mail to math@union.edu or call (518) 388-6246.
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