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]\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.