| Colby Math/Stats Colloquium |
| Spring 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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| February 16 |
Leo Livshits
Colby College |
If a square matrix is lower or upper triangular, then any linear algebra student can extract quite a bit of information about the behavior of the matrix from the numbers that appear on its diagonal, including, for example, complete information about the diagonals of the powers of the matrix (obtained by multiplying the matrix with itself a number of times). When a square matrix is not triangular, looking at its diagonal may not be enough to extract the same information. Yet it in many cases we can do well by examining the diagonals of the matrix itself as well as those of its powers. The answers are particularly pretty when the entries of the matrix are non-negative. |
| March 9 | Leon Harkleroad | In the mid-1800s, August Möbius gave us the Möbius strip and Hermann Grassmann laid the foundations for abstract linear algebra. But the two men also exchanged correspondence on different ways to tune a musical scale. We will examine their work and its relationship to other historical tuning methods. The mathematics is very simple, and I will explain the little bit of music necessary, so the talk will be accessible to everyone. |
| March 16 |
Aaron Luttman
Clarkson University |
Pictures taken by telescopes on the ground - like those at Kitt Peak in Arizona or Mauna Kea in Hawaii - suffer from two primary problems. The first is that the images are noisy. This means that random errors cause the picture to not look like the real scene. The second problem is that the pictures are blurry, which is a systematic (i.e. not random) phenomenon caused by the atmosphere. It turns out that we can mathematically "undo" the problems of noise and blur by using a mathematical model that looks a lot like a problem in linear algebra. In fact, some of the basic ideas of solving linear systems in linear algebra can be applied directly to find out what the picture would look like if there were no problems with noise and blur, given only a few basic assumptions about what the objects we're looking at really look like. |
| March 31 |
Tim Hesterberg
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I'll talk about some statistics jobs I've had:
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| April 20 |
Soule Sow Colby College |
TBA |
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April 22 Wednesday |
Ling Zhu Colby College |
TBA |
| April 27 |
Genevieve Walsh
Tufts University |
One way to understand groups is to look at their actions on certain "nice" spaces. ÊIn this talk we will look at some examples of this. In particular, we will look at group acting on a tree and a group acting on the hyperbolic plane. We will mention some current research being done in this area. |
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April 29 Wednesday |
Yilin Xu
Colby College |
TBA |
| May 4 |
Thomas Leung
Colby College |
TBA |
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May 6 Wednesday Olin 1 |
Jon McCammond
UC Santa Barbara |
We all know intuitively that doing things repeatedly can produce fundamental changes (an insight that cooks are well aware of). My talk will focus on a connected set of surprises and insights that arise through simple repetition and iteration: punching the [cos] button repeatedly on a calculator, continued fractions -- along with their connections to the golden ratio and the Fibonacci numbers, and continued square roots, with some mentions of Ramanujan, Chebyshev polynomials, and the Mandelbrot set thrown in along the way. I'll even mention the mathematics behind the software that creates realistic alien landscapes for movies. |
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