International Research Fellowship Program: Secant Varieties and Applications to Signal Processing

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0853000OedingThis award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).The International Research Fellowship Program enables U.S. scientists and engineers to conduct nine to twenty-four months of research abroad. The program's awards provide opportunities for joint research, and the use of unique or complementary facilities, expertise and experimental conditions abroad.This award will support a twenty-four-month research fellowship by Dr. Luke Oeding to work with Dr. Girogio Ottaviani at Universita degli Studi di Firenze in Italy.The primary goal of this project is to provide fundamental information to engineers in signal processing and to researchers in other disciplines that use varieties occurring in spaces of tensors in their work such as statistics (the study of dependence relations), computational complexity theory (bounding the complexity of algorithms via ranks of tensors) and physics (quantum information theory and measures of entanglement). The research is focused on solving questions about the decomposition of tensors and symmetric tensors posed by P. Comon (U. Nice at Sophia-Antipolis, electrical engineering) and questions about block decomposition of tensors posed by L. De Lathauwer (K.U.Leuven, electrical engineering). This fundamental information will be found via analyzing classical geometric objects known as secant varieties. Restated in geometric language, the goal of this project is to find new equations of secant varieties of Segre-Veronese varieties and secant varieties of subspace varieties. By studying these questions from the standpoint of classical algebraic geometry and representation theory, many classical and recent techniques can be used. The proposed research will combine theoretical and computational techniques for studying G-varieties used and developed in the PI's dissertation with the host scientist's expertise in classical algebraic geometry to solve questions in signal processing and further the PI's research in geometry and representation theory.This project will impact society by fostering international and cross-disciplinary collaboration between engineers and mathematicians. The findings of this research will also benefit areas such as statistics, computational complexity, and physics.