Prof. Dr. Gregory G. Smith (Queen's University Kingston, Kanada): Nonnegative Sections and Sums of Squares |
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| Startdatum/-zeit: | 03.07.2013 17:15 |
| Enddatum/-zeit: | 03.07.2013 |
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| Adresse: | Fachbereich Mathematik/ Informatik, Institut für Mathematik Prof. Dr. Winfried Bruns Albrechtstr. 28a 49076 Osnabrück |
| Telefon: | 0541 - 969 - 2485 |
| Telefax: | 0541 - 969 - 2770 |
| E-Mail: | wbruns@uni-osnabrueck.de |
| Homepage: | http://www.mathematik.uni-osnabrueck.de/index.php?controller=kolloquium |
Veranstaltungsort: |
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| Adresse: | Institut für Mathematik Albrechtstr. 28a, Geb. 69/ Raum 125 49076 Osnabrück |
| Karte: | Bei Google Maps anzeigen |
| Beschreibung: | A polynomial with real coefficients is nonnegative if it takes on only nonnegative values. For example, any sum of squares is obviously nonnegative. For a homogeneous polynomial with respect to the standard grading, Hilbert famously characterized when the converse statement hold, i.e. when every nonnegative homogeneous polynomial is a sum of squares. After reviewing the history of this problem, we will examine this converse for homogenous polynomials with respect to a positive multigrading (or more generally global sections of a line bundle). In particular, we will provide many new examples in which every nonnegative homogeneous polynomial is a sum of squares. The new results in this talk are based on joint work with Grigoriy Blekherman and Mauricio Velasco. |
| Kategorie: | Mathematisches Kolloquium |
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