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Abdelmalek Abdesselam (University of Virginia)-Introduction to the Renormalization Group
Mathematics - Colloquium
Friday, November 6, 2009
11:00 AM-12:00 PM
Stratton Hall
203
ABSTRACT: Ever since its introduction by Kenneth G. Wilson in the seventies, the renormalization group has been the main conceptual tool used by physicists in order to make meaningful calculations with functional integrals. The latter are, largely conjectural, infinite-dimensional probability measures over spaces of functions which one can try to construct rigorously using a scaling limit of similar measures where the continuum is discretized by finer and finer grids.
The renormalization group is a dynamical system corresponding to averaging over the short distance fluctuations of the random function and zooming out by a fixed scale ratio. Fixed points of this dynamical system correspond to the possible scaling limits one can achieve. The renormalization group provides a far reaching generalization of the familiar central limit theorem, in a situation where the random variables are dependent, in a way which is subordinated to the geometry of the space labeling these variables. In this nontechnical presentation, we will provide an introduction to the basic ideas of the renormalization group on the example of the usual central limit theorem, and the next simplest example: the so-called hierarchical model.
Suggested Audiences:
Adult, College
E-mail:
ma-chair@wpi.edu
Last Modified: October 23, 2009 at 4:04 PM
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Abdelmalek Abdesselam (University of Virginia)-Introduction to the Renormalization Group
Mathematics - Colloquium
Friday, November 6, 2009
11:00 AM-12:00 PM
Stratton Hall
203
ABSTRACT: Ever since its introduction by Kenneth G. Wilson in the seventies, the renormalization group has been the main conceptual tool used by physicists in order to make meaningful calculations with functional integrals. The latter are, largely conjectural, infinite-dimensional probability measures over spaces of functions which one can try to construct rigorously using a scaling limit of similar measures where the continuum is discretized by finer and finer grids.
The renormalization group is a dynamical system corresponding to averaging over the short distance fluctuations of the random function and zooming out by a fixed scale ratio. Fixed points of this dynamical system correspond to the possible scaling limits one can achieve. The renormalization group provides a far reaching generalization of the familiar central limit theorem, in a situation where the random variables are dependent, in a way which is subordinated to the geometry of the space labeling these variables. In this nontechnical presentation, we will provide an introduction to the basic ideas of the renormalization group on the example of the usual central limit theorem, and the next simplest example: the so-called hierarchical model.
Suggested Audiences: Adult, College
E-mail: ma-chair@wpi.edu
Last Modified: October 23, 2009 at 4:04 PM
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