# Difference between revisions of "Colloquia/Fall18"

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== Abstracts == | == Abstracts == | ||

+ | |||

+ | ===February 12: Mihai Putinar (UC Santa Barbara)=== | ||

+ | |||

+ | ====Geometry and counting in the Heisenberg group==== | ||

+ | |||

+ | 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>\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. | ||

== Past Colloquia == | == Past Colloquia == |

## Revision as of 10:25, 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) | TBA | 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)

#### Geometry and counting in the Heisenberg group

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]\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.