Mathematical Sciences: Real Extremal Forms

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This project involves research on extremal forms. The principal investigator will study situations when positive semidefinite forms need not be sums of squares of forms. The principal investigator will also continue work on the multiplicative structure of extremal forms, the extremality of symmetric forms and the extremality of a class of forms which are closely related to agiforms. This research concerns the study of real positive semi-definite forms. It involves interplay among algebra, inequalities and geometry.