Mathematics and Statistics Departmental Colloquium Room 1634, Lederle Graduate Research Tower University of Massachusetts, Amherst
Refreshments at 3:45pm.     Talks begin at 4:00pm. Driving Directions   and   Campus Map

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Winter 2003 Schedule:

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		13 March	Georgia Benkart, University of Wisconsin
		4:00-5:00	Temperley-Lieb Combinatorics
		20 March	No colloquium
		27 March	No Colloquium: Scheduling problems
		3 April	Maury Bramson, University of Minnesota
		2:30-3:30	Application of fluid models to recurrence and central limits for queueing networks
		3 April	Alexandre Bobenko, TU Berlin
		4:00-5:00	Minimal surfaces from circle patterns: Geometry from combinatorics
		10 April	Coifman, Yale University
		4:30-5:30	Challenges to Analysis; High Dimensional Geometry and Approximation
		24 April	Mark Goresky, IAS
		4:00-5:00	Shift registers, elliptic curves and 2-adic numbers

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Abstracts

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Abstract
Temperley-Lieb algebras first arose in the study of transfer matrices in statistical mechanics. They have connections with knot and link invariants. They also have a beautiful combinatorics and representation theory. This talk will survey some of these topics.
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Over the past decade, fluid models have become one of the main tools for analyzing queueing networks. They can be used to study the recurrence and diffusive behavior of queueing networks, two of the main topics that are typically studied for probabilistic systems. The talk will provide a summary of this work.
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Abstract
The so called curse of dimensionality is well known in statistics and other fields involving dependence on a large number of parameters. In this talk we make the point that these are issues involving Harmonic Analysis In particular we will discuss various issues involved in approximating empirical functions of a large number of parameters including geometric analysis of data sets embedded in high dimensions . Such analysis can be achieved through Harmonic Analysis and operator theory on the data . We will also discuss effective low dimensional functional approximation (around 10-20 dimensions). These mathematical issues will be illustrated on a variety of examples from biology, chemistry, and mutimedia.
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Abstract
Pseudo-random sequences generated from various kinds of shift registers are used in a wide variety of modern digital communications such as stream cipher cryptographic systems, spread spectrum systems (like GPS and digital cellular telephones), and error correcting codes. Although the mechanics of a shift register are very simple, many questions involving their behavior require sophisticated mathematical tools. This lecture will cover the basics of shift register architecture, and will consider a few simple questions whose answers require Galois theory, elliptic curves, and 2-adic numbers.
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