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Eric Klassen's Faculty Page

Eric P. Klassen
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Ph.D., Cornell University, USA, 1987

Detailed description of research

Shape Analysis.
We define two geometric objects (such as curves or surfaces) to have the "same shape" if one can be made to coincide with the other by a rigid motion or a rescaling. My recent research seeks to do geometric and statistical analyses of sets of shapes. For example, how can you quantify how different two shapes are? Is it possible to take the average of a collection of shapes? How can one determine the principal modes of variation of a collection of shapes? The main mathematical tools I use in this research are differential geometry (often applied to infinite dimensional spaces!), Lie group actions, and some functional analysis. Now and then, some topology finds its way in, too!