Colby Math/Stats Colloquium |
Fall 2009 |
Talks (unless otherwise indicated) are in Mudd 405 from 4 - 5 PM on Mondays. |
Refreshments begin at 3:30. |
Abstract |
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Sept. 14 |
Fernando Gouvêa
Colby College |
One of the biggest mathematical arguments of the twentieth century was about an assumption known as "the axiom of choice". It seems very plausible at times, then seems totally ridiculous when we look at it the other way. We'll explain what it is and give an example of why it is controversial, by showing that it seems to imply that it is possible to predict the future. The only prerequisite for this talk is to know about sets, functions, and the real numbers. |
Sept. 21 |
Scott Taylor
Colby College |
Spheres of all dimensions are among the most basic of all geometric objects. The geometric structure of spheres in higher dimensions, however, can often be hard to grasp. The Hopf fibration is a beautiful description of a 3-dimensional sphere sitting inside 4-dimensional space. I'll describe what the Hopf fibration is and show how it can be used to create some surprising pictures of a 3-dimensional sphere. |
Sept. 25 Talk Cancelled |
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Sept. 28 |
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October 5 Olin 1 |
Keith Devlin
Stanford University |
and other mysteries of everyday life (that can be explained only with mathematics) In this talk, Devlin provides answers to some of life's more perplexing puzzles. In addition to golf balls, he looks at:
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Tuesday October 6 7:30 PM Olin 1 |
Keith Devlin
Stanford University |
At four distinct stages in the development of modern society, a mathematical development changed — in a fundamental, dramatic, and revolutionary way — how people understand the world and live their lives. (A fifth such change may be taking place during our lifetime, but only history will say if this is really the case.) Those advances occurred around 5,000 B.C.E. and in the 13th, 16th, and 17th centuries. Devlin will look at how human life and cognition changed on each of those three occasions, with the main focus being risk management and the view of the future that effective risk-management techniques enable. Based in part on Devlin's latest book The Unfinished Game: Pascal, Fermat and the Seventeenth Century Letter that Made the World Modern, Basic Books 2008. |
October 19 |
Leo Livshits
Colby College |
A What is ... ? colloquium Which sets of Real numbers are small? To think about the question we need to agree on what "small" means. For example, we might interpret "small" as having very few elements. To put that interpretation aside, let us just focus on infinite subsets of R. If we think about intervals, we can compare these by length, with "smaller" meaning "shorter". If we look at the set of all integers in R, this set seems "long", but "sparse" (i.e. not thick). The set of all rational numbers seems "thicker", as does the set of all irrational numbers. In my talk, among other things, I will try to convince you that the set of irrationals is "larger", "thicker" and "longer" than the set of rationals, and in developing the ideas underlying such a comparison, crack open a door to a fascinating mathematical subject. |
October 26 |
Elisenda Grigsby
Boston College |
Knots are remarkably tricky to study: it is difficult to tell, just by staring at pictures of two knots, whether they are the same or different. We confront this problem through the use of knot invariants, algebraic objects associated to knots that do not depend upon how the knots are drawn. I will discuss one of these: Heegaard Floer knot homology, first introduced by Ozsvath-Szabo and Rasmussen, and further developed by a number of people. ÊKnot Floer homology is now completely combinatorial (a computer can be programmed to calculate it), and it can tell you a number of wonderful things about the knot that are difficult to determine by other means. |
November 2 |
Jim Scott
Colby College |
The study of: a) Word origins b) Bugs c) Skin d) None of the above (<- correct!) Epidemiologists study the how, what, when, why, who, and where of diseases (loosely defined) - from AIDS to yersinia pestis (the plague). In this talk, I'll discuss the origins of modern day Epidemiology, present some of the tools that epidemiologists use (hint: statistics!), and highlight a number of examples of epidemiology in action. By the end of the talk, you'll know things like what the #1 cause of fatalities is worldwide AND why you should never attend an elephant necropsy without wearing a safety mask! |
November 9 |
Fernando Gouvêa
Colby College |
Here's an unusual way to make a million dollars: solve a math problem! Of course, these problems are rather hard. In 2000 the Clay Mathematics Institute announced that it would offer a prize of a million dollars to anyone who could settle any of seven problems. One of those has since been solved, so that there are six remaining mathematical ways to make your million. We will outline some of the Clay Millennium Problems and give an idea about why they are important. |
November 16
Olin 1 |
Jon Camire
Unum |
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November 23 | ||
November 30 |
Neil Hoffman
U. T. Austin |
Circles, annuli, mobius bands, and tori are all examples of low-dimensional manifolds. I will give a gentle, friendly introduction to the topology of manifolds by looking at various ways of creating them starting with symmetries of Rn. |
December 7 |
Tom Berger
Colby College |
When you push a phone key, two tones are sent. How does the exchange decipher these tones to know which number you pushed? When you turn on your FM radio, how does it know which station to choose? Filters. This talk will look at some filters and the mathematics used to design those filters: calculus (the Fourier Transform, the Laplace Transform), number theory (continued fractions), linear algebra (2x2 matrices), polynomials, rational functions, and complex numbers. And for the students who remember me, they know there will be pretty and interesting graphs and electronic gadgetry. |
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