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Poincaré's Little Gift

Abstract: The most important gifts of great mathematicians are often the questions that they ask but fail to answer. (Can you think of one?) At the dawn of the 20th century, Henri Poincaré asked two questions that have generated a wealth of mathematics in the ensuing 100 years. One of the questions was only recently answered (when Perelman solved the Poincaré Conjecture). We will focus on another a problem, Poincaré's Last Geometric Theorem, that was solved quickly (by Brouwer) but that spawned as-yet-unsolved generalizations. The theorem is easy to state and understand, and by proving a simplified version we will get a taste for the generalizations. Multivariable Calc. and/or Differential Eq. would make excellent background for this talk, but are not necessary. I will try to make all concepts accessible to anyone who has hd some calculus. Dr. Margaret Symington gave this presentation to the Math Club November 14, 2012. Thanks to Dr. Symington and to the Math Club for letting me capture the talk and to Dr. Jon Hanke for his technical support with this project.