Seminar Calendar
for Algebraic Geometry events the month of Monday, November 23, 2009.

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Questions regarding events or the calendar should be directed to Tori Corkery. 
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Tuesday, November 3, 2009

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, November 3, 2009
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Submitted by llpku.
Bruce Reznick (Department of Mathematics, University of Illinois)
Higher Laws of Inertia
Abstract: Newton's Law of Inertia says that if a real quadratic form is written as a linear combination of the squares of real linear forms, then there are computable lower bounds on the numbers of positive and negative coefficients. It seems natural to wonder what happens in higher (even) degree. It turns out that a similar law applies for binary forms in degree 4, but fails in degree 6 (and probably higher).

Tuesday, November 10, 2009

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, November 10, 2009
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Submitted by llpku.
Pramod N. Achar (Louisiana State University)
Positivity, coherent sheaves, and representation theory
Abstract: A number of questions in representation theory involve an endomorphism algebra endowed with a natural Z-grading; sometimes, deep consequences follow if it can be shown that the negative-degree components vanish. I will explain several instances of such "positivity phenomena" in derived categories of coherent sheaves, following work of Arkhipov, Bezrukavnikov, Ginzburg, and others. I will then discuss a new approach to proving positivity theorems, followed by some potential applications.

Tuesday, November 17, 2009

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, November 17, 2009
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Submitted by llpku.
Steven Bradlow (University of Illinois)
Sp(4,R)-Higgs bundles: a Higgs bundle case study
Abstract: Using G=Sp(4,R) as a special case, we will describe what G-Higgs bundles are and how they can be used to study maps from surface groups into non-compact real Lie groups.