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| [http://www.math.ucsb.edu/~mputinar/ Mihai Putinar] (UC Santa Barbara, Newcastle University) | | [http://www.math.ucsb.edu/~mputinar/ Mihai Putinar] (UC Santa Barbara, Newcastle University) | ||
| [[Quillen’s property of real algebraic varieties]] | | [[Colloquia#February 12: Mihai Putinar (UC Santa Barbara) | Quillen’s property of real algebraic varieties]] | ||
| Budišić | | Budišić | ||
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Revision as of 15:29, 6 January 2015
Mathematics Colloquium
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, unless otherwise indicated.
Spring 2015
| date | speaker | title | host(s) | |
|---|---|---|---|---|
| January 23 | Tentatively reserved for possible interview | |||
| January 30 | Tentatively reserved for possible interview | |||
| February 6 | Morris Hirsch (UC Berkeley and UW Madison) | Fixed points of Lie group actions | Stovall | |
| February 13 | Mihai Putinar (UC Santa Barbara, Newcastle University) | Quillen’s property of real algebraic varieties | Budišić | |
| February 20 | David Zureick-Brown (Emory University) | TBA | Ellenberg | |
| February 27 | Allan Greenleaf (University of Rochester) | TBA | Seeger | |
| March 6 | Larry Guth (MIT) | TBA | Stovall | |
| March 13 | Cameron Gordon (UT-Austin) | TBA | Maxim | |
| March 20 | Murad Banaji (University of Portsmouth) | TBA | Craciun | |
| March 27 | Kent Orr (Indiana University at Bloomigton) | TBA | Maxim | |
| April 3 | University holiday | |||
| April 10 | Jasmine Foo (University of Minnesota) | TBA | Roch, WIMAW | |
| April 17 | Kay Kirkpatrick (University of Illinois-Urbana Champaign) | TBA | Stovall | |
| April 24 | Marianna Csornyei (University of Chicago) | TBA | Seeger, Stovall | |
| May 1 | Bianca Viray (University of Washington) | TBA | Erman | |
| May 8 | Marcus Roper (UCLA) | TBA | Roch |
Abstracts
February 12: Mihai Putinar (UC Santa Barbara)
Quillen’s property of real algebraic varieties
A famous observation discovered by Fejer and Riesz a century ago is the quintessential algebraic component of every spectral decomposition result. It asserts that every non-negative polynomial on the unit circle is a hermitian square. About half a century ago, Quillen proved that a positive polynomial on an odd dimensional sphere is a sum of hermitian squares. Fact independently rediscovered much later by D’Angelo and Catlin, respectively Athavale. The main subject of the talk will be: on which real algebraic sub varieties of [math]\displaystyle{ \mathbb{C}^n }[/math] is Quillen theorem valid? An interlace between real algebraic geometry, quantization techniques and complex hermitian geometry will provide an answer to the above question, and more. Based a recent work with Claus Scheiderer and John D’Angelo.