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Thursday, April 24, 2008 Speaker: Alberto Damiano, assistant visiting professor of Mathematics Title: Syzygies, Antisyzygies, and how I defeated the Dirac system in a Singular way Abstract: Alberto Damiano, assistant visiting professor of Mathematics, will present an overview from this year’s collaboration with Daniele Struppa, Adrian Vajiac, and Mihaela Vajiac. He will introduce a new concept of “antisyzygies”, which constitutes a sort of inverse problem within the framework of algebraic analysis. Usually people start form a (non-homogeneous) system of PDEs, and hunt for the integrability conditions. Instead, they asked themselves the opposite question: Given the compatibility laws, how can the system be reconstructed in some canonical way? What properties can be obtained? In particular, he will mention the relation between the antisyzygy construction and Hartogs type of phenomena (removability of compact singularities from the solutions). On the computational side, he will present an idea shared by D. Eelbode. The goal is to construct the syzygies for the Dirac system in several vector variables. He will show how to use the computer algebra software, Singular, and the structure of the super Lie algebra osp (1/2) to get the (minimal) free resolution of the system, in just a few command lines. To read the full abstract and for more information, go to http://mathcs.chapman.edu/mathcs/index.php/MathCS_SeminarTuesday, April 29, 2008 Speaker: Hung-Jen (Stewart) Huang, Chapman University Title: Bayesian Analysis of Errors-in-Variables Growth Curves with Skewness in Models Abstract: Proposed to analyze model data 1) using errors-in-variables (EIV) model and 2) using the assumptions that the error random variables are subject to the influence of skewness through Bayesian approach. The use of EIV in model is necessary and realistic in studying many statistical problems, but their analysis usually mandate many simplifying and restrictive assumptions. Previous studies have shown the superiority of Bayesian approach in dealing with the complexity of these models… To read the full abstract and for more information, go to http://mathcs.chapman.edu/mathcs/index.php/MathCS_Seminar Thursday, May 1, 2008 Speaker: Professor Vincenzo Vespri, University of Firenze Title: Harnack inequalities for nonlinear parabolic equations Abstract: Vincenzo Vespri, professor at the University of Firenze, will discuss recent results obtained in collaboration with Emmanuele DiBenedetto and Ugo Gianazza. In the sixties Moser, using deep Nash ideas, proved Harnack inequalities for nonnegative solutions of linear praboilic equations. The approach, seems to not work in the nonlinear case (for instance in the case of p-Laplacean and porous medium equation). In recent papers published in Calc. Var., Acta Math and Duke Moser’s one based on DeGiori’s function classes. This approach is so flexible that it can be extended to the nonlinear case. To read the full abstract and for more information, go to http://mathcs.chapman.edu/mathcs/index.php/MathCS_Seminar Thursday, May 8, 2008 Speaker: Professor Alfonso Cariazzo (University of Sevilla) Title: Chen’s inequalities in generalized Sasakian-space-forms Professor Alfonso Cariazzo, University of Sevilla, will review the main facts about generalized Sasakian- space-forms, such as the existence of interesting examples in any dimension, or the possible structures for these spaces. Following, he will present sharp inequalities involving invariants for submanifolds in this setting, with arbitrary codimension and have proven to be a key tool in Submanifolds Theory, providing new very useful information concerning the immersion problem. To read the full abstract and for more information, go to http://mathcs.chapman.edu/mathcs/index.php/MathCS_Seminar |
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