MathCS Seminar

Title: Positive Polynomials and Varieties of Minimal Degree
Seminar: Algebra
Speaker: Daniel Plaumann of Universitat Konstanz
Contact: David Zureick-Brown,
Date: 2016-09-06 at 4:00PM
Venue: W306
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A celebrated result by Hilbert says that every real nonnegative ternary quartic is a sum of three squares of quadratic forms. We show more generally that every nonnegative quadratic form on a real projective variety X of minimal degree is a sum of dim(X) + 1 squares of linear forms. This provides a new proof for one direction of a recent result due to Blekherman, Smith, and Velasco. We explain the geometry behind this generalization and discuss what is known about the number of equivalence classes of sum-of-squares representations. (Joint work with G. Blekherman, R. Sinn, and C. Vinzant)

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