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Department of Mathematics,
University of California San Diego

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Functional Analysis Seminar

Chris Nelson

UCSD

A Non-Commutative Nullstellensatz and Positivstellensatz

Abstract:

A natural question in real algebraic geometry is to ask, given polynomials $p$, $q$, and $r$, \begin{equation*} \tag{Q} \label{eq:quest} \mbox{Does} \quad q(x) \geq 0 \quad \mbox{and} \quad r(x) = 0 \quad \mbox{imply} \quad p(x) \geq 0\ \mbox{?} \end{equation*} In this talk I will focus on {\it free noncommutative} polynomials $p$, $q$, and $r$ and substitute matrices for the variables $x_j$. I will present an answer to a non-commutative version of (\ref{eq:quest}) which includes a non-commutative ``real nullstellensatz'' and ``positivstellensatz''.

Host: Bill Helton

February 20, 2013

12:00 PM

AP&M 5829

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