# Colloquia/Fall18

# 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 12 | Botong Wang (Purdue) | Cohomology jump loci of algebraic varieties | Maxim | |

January 21 | Jun Kitagawa (Toronto) | TBA | Feldman | |

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

### January 12: Botong Wang (UC Santa Barbara)

#### Cohomology jump loci of algebraic varieties

In the moduli spaces of vector bundles (or local systems), cohomology jump loci are the algebraic sets where certain cohomology group has prescribed dimension. We will discuss some arithmetic and deformation theoretic aspects of cohomology jump loci. If time permits, we will also talk about some applications in algebraic statistics.

### 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]\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.