Colloquia/Fall18

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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 (3PM) 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

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.

Past Colloquia

Fall 2014

Spring 2014

Fall 2013

Spring 2013

Fall 2012