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Fall 2009 schedule

Date Speaker Title
August 26 John Kerl Markov Jabberwocky: fesh, excenture, and the like
In Lewis Carroll’s Jabberwocky, and its translations, it’s clear that even nonsense words can look like they certainly belong to a particular language. Who could doubt the Englishness of ‘’Twas brillig, and the slithy toves did gyre and gimble in the wabe”, or the Frenchness of «Évite le frumieux Band-à-prend!»?
September 2 Enrique Acosta The Math Behind Escher's Print Gallery
Sure, there are mathematical aspects to the artwork of M.C. Escher; but just the amount of math hiding in Escher's litograph "Print Gallery" will come as a surprise for anyone who doesn't know the story. So come and enjoy some nice pictures and videos, and a story involving grids, conformal maps, fundamental groups, covering spaces, and one dimensional complex tori (a.k.a. complex elliptic curves). You will also get a real solid edible torus to enjoy while watching the talk.
September 9 Somnath Chakraborty Primes & Arithmetic Progression
We will discuss about Dirichlet's Theorem about primes in arithmetic progression. Given an arithmetic progression that is most likely to contain infinitely many primes, is it possible to make arithmetic progressions (finite/infinite) out of these primes only?
September 16 Dan Wanegar The Loewner Equation and Brownian Motion
The Riemann mapping theorem states that any two simply connected, open sets in the complex plane not equal to C are conformally isomorphic. It will turn out that the conformal map from upper half-plane to the upper half-plane without a loop-free trail that starts from the boundary will satisfy the Loewner Differential Equation. This in turn maps Brownian motion (the path) for a given driving function.
September 23 Casey Warmbrand Aztec diamonds, Aztec Pacmen, and the Essentially Arctic Tilings, and their common Typical Shapes
Once again, the definition of an Aztec diamond will be presented, briefly. We will then mention the shape of a typical tiling and define the set of essentially arctic tilings. A special modification to the boundary of the Aztec diamond will be looked at, where there is a unique extension from any tiling of this modified region to a tiling of the whole Aztec diamond. We will conclude the talk by showing how the space of modified tilings, when the modification is scaled appropriately, can be nested between the spaces of all tilings and the essentially arctic ones, thus implying the same typical arctic shapes to emerge in the modified tilings.
September 30 Alex Petrov Rigid Analysis
Rigid analysis is the analog of the complex analysis that we have grown to love in a non-archimedean situation . I will try to explain the challenges of setting up the theory in the first place. In the process we will see some major mathematical ideas from the last century: patching local data to get global data; weird topologies to support the patching; etc. If we have time I will finish by talking about the upper half plane in the rigid situation.
October 7 Cindy Phillips Complex Hyperbolic Plane in Cylindrical Coordinates about the Real Hyperbolic Plane
Based on my undergraduate research, we will review basics of the real hyperbolic plane, *RH*^2 , as it is contained in the complex hyperbolic plane, *CH*^2 . We see that special matrix groups from algebra will help us find the metric on a cylinder/tube which surrounds *RH*^2 . The talk will be an overview of the different relationships between the hyperbolic planes and the rotations/translations which lead to the algebra.
October 14 Michael Bishop On Streaks and Runs
Though simple to understand, the probability of getting a run (or streak) of r consecutive heads in n coin tosses is difficult to calculate. In this talk, we will discuss methods for calculating probabilities and use those tools to calculate the probability of getting a run of r consecutive heads. Using this probability, I will introduce a baseball statistic to provide yet another metric to compare great hitters (as if baseball needed more statistics). Time permitting, we will discuss the asymptotics of this probability.
October 21 Martin Leslie Lots of Zeros and Not Many Ones: the Search for Good Error Correcting Codes
In 1948, Claude Shannon proved that good error correcting codes exist. Unfortunately the beautiful algebraic codes that people talk about in math departments are not the ones he was referring to. Low-density parity-check (LDPC) codes, (re)invented in the 1990s, approach the theoretical limits of communication and have an efficient although non-optimal decoder that makes them usable in applications. I will give an introduction to error correcting codes and describe some of the interesting features of LDPC codes. I will assume little more than knowledge of basic linear algebra.
October 28 Tom Kennedy Meeting with Graduate Students
Tom Kennedy will be joining us to discuss the graduate program and answer any questions you may have.
November 4 Shane Passon Almost Surely the Self Avoiding Walk
This talk will introduce the probability spaces associated with self avoiding walks. Then it will go on to explore some of the predictions made about infinite self avoiding walks. We will explore some of the simulated results and the analytical tools used to prove a few known properties of the self avoiding walk. The events we will be exploring are events that happen 'almost surely'.
November 11 N/A N/A
Veteran's Day. Celebrate the end of WW1.
November 25 N/A N/A
There will be no colloquium because of the Thanksgiving Holiday.
December 2 Brad Weir Quasiconformal Mappings
The purpose of this talk is to introduce the basic theory of quasiconformal mappings, generalizations of conformal mappings, and give a tasting of their use. The topics include the measurable Riemann mapping theorem, an extension of the Riemann mapping theorem, Teichmuller's theorem about the relation of their extremal properties and analytic functions, and examples of their use in the study of elliptic partial differential equations.

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