October 3, 2007
Arek Goetz
San Francisco State University
| TITLE: The dynamics and geometry of the macroscopic and microscopic world of cells in piecewise rotations.
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ABSTRACT:
Take a big pizza, divide into several cones. Permute the cones and
shift the whole plate. This defines a map $T$ in the plane, called a
piecewise rotation. The division into groups of points that follow
under iteration of $T$ the same pattern of visits to the cones results
in spectacularly beautiful and mysterious structures. In
the talk we illustrate the dynamical, geometric, algebraic, and
computer tools used in the attempts to understand the structures. Most
of the talk will be accessible to undergraduate and graduate students.
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4:10 PM in TH 211 |
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refreshments
served in TH 935 at 3:30 PM |
October 17, 2007
Jon McCammond
University of California at Santa Barbara
| TITLE: From Coxeter to Artin and his braids.
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ABSTRACT:
The goal of this talk is to describe a class of groups called
Artin groups that are closely related to the better known Coxeter groups.
No prior familiarity with either class of groups will be presumed. The
basic relationship is that Artin groups generalize braid groups in the
same way that Coxeter groups generalize key properties of the symmetric
groups. Lots of colored markers will be used.
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4:10 PM in TH 211 |
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refreshments
served in TH 935 at 3:30 PM |
October 31, 2007
| TITLE: Preview of advanced courses for Spring 2008.
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ABSTRACT:
The professors for the advanced classes that will be offered in the Spring of 2008 will present a short preview of their courses.
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4:10 PM in TH 211 |
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refreshments
served in TH 935 at 3:30 PM |
November 14, 2007
Serge Preston
Portland State University
| TITLE: Dissipation.
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ABSTRACT: Dissipation is the general name of a class of processes by which physical, mechanical, chemical and biological systems lose useful energy and undergo structural (or, as a rule, destructural) changes. It is through the dissipative processes the entropy is increasing, defects are multiplying and growing (breaking bridges, pipes and planes), and the return to the equilibrium is typically achieved. Yet dissipation can also produce instabilities like the one that was responsible for the abnormal short life of the first US satellite Explorer I. As such it may also be used as a way to produce controllable favorable changes in a system. That is why the mathematical modeling of dissipative processes is so interesting and useful.
In this talk we present an overview of the tools of mathematical modeling of dissipative events and give some examples of such starting from the simple harmonic oscillator with friction and the positional forces in Mechanics to the dissipative potentials in Thermodynamics and the "double bracket systems" of the universal Dynamics.
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4:10 PM in TH 211 |
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refreshments
served in TH 935 at 3:30 PM |
November 28, 2007
Anthony Quas
University of Victoria
| TITLE: Distances in Positive Density Sets.
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ABSTRACT: Given a set of distances D, one can consider the graph G_{d,D} on R^d where two points are adjacent if they are separated by a distance belonging to D. One then asks for its chromatic number (the smallest number of colours so the points of R^d can be coloured in such a way that no two points separated by a distance in D are given the same colour). The case where D={1} is the Hadwiger-Nelson problem and it is known that 4<=\chi(G_{2,{1}})<=7. If the colour classes are required to be measurable, we obtain the measurable chromatic number \chi_m(G_{d,D}). It is known that 5<=\chi_m(G_{2,{1}})<=7.
In the case where D is unbounded, it turns out that \chi_m(G_{d,D})=\infty. We give a conceptual new proof of this and discuss possible extensions to the general (non-measurable) case.
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