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February 9, 2014

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We all know the Fundamental Theorem of Algebra (FTA), which says that a polynomial with real coefficients factors completely over the complex numbers or, equivalently, that it factors into linear and quadratic real factors. But if we do really know it, why could most of us not factor, say, a degree 6 polynomial? For that matter, why should we care about complex roots in the first place? I will …more

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Invariance problems of classical dependence measures like Pearson's classical correlation led me about ten years ago to introduce a new dependence measure, distance correlation, based on a generalization of Newton's gravitational potential energy. Distance covariance is the covariance of double centered distances between data in metric spaces. For random variables with finite expectation, the …more

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American University's Department of Mathematics and Statistics and Department of Physics present: "Mathematical Conversation Starters For the Rest of Us", an illustrated talk by Prof. John dePillis, Department of Mathematics, University of California Riverside. Dr. de Pillis is the author of "777 Mathematical Conversation Starters", and "Illustrated Special Relativity Through Its Paradoxes".
A …more

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There is a long standing conjecture of Arnol'd which says that we should be able to see invariants of the smooth topology of a manifold from looking at symplectic invariants of its cotangent bundle. The case that the manifold is of dimension 4 is particularly interesting due the existence of smooth manifolds which are homeomorphic but not diffeomorphic. Dr. Knapp will discuss exotic smooth …more

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In this talk, we present generalized generating functions for hypergeometric and q-hypergeometric orthogonal polynomials. These generalized expansions are obtained by re-expressing the polynomials in the generating functions using multi-parameter connection relations. The resulting multi-summation expressions are rearranged with justification in order to identify the coefficients of the …more

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