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{\Large המחלקה למתמטיקה, בן-גוריון}

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{\Huge קולוקוויום}\\[0.2\baselineskip]

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\textbf{ב}\emph{יום שלישי, 14 במאי, 2019}
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\textbf{בשעה} \emph{14:30 -- 15:30}
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\textbf{ב}\emph{Math -101}

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ההרצאה

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{\Large\bfseries Dilation theory: fresh directions with new applications\par}
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תינתן על-ידי
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{\large\scshape Orr Shalit 
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  (Technion)
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\textbf{תקציר:}
  Dilation theory is a paradigm for understanding a general class of objects in terms of a better understood class of objects, by way of exhibiting every general object as ``a part of`` a special, well understood object. 
In the first part of this talk I will discuss both classical and contemporary results and applications of dilation theory in operator theory.  Then I will describe a dilation theoretic problem that we got interested in very recently: what is the optimal constant \$c = c\_\{\textbackslash{}theta,\textbackslash{}theta`\}\$, such that every pair of unitaries \$U,V\$ satisfying \$VU = e\^{}\{i\textbackslash{}theta\} UV\$ can be dilated to a pair of \$cU`, cV`\$, where \$U`,V`\$ are unitaries that satisfy the commutation relation  \$V`U` =e\^{}\{i\textbackslash{}theta`\} U`V`\$?

I will present the solution of this problem, as well as a new application (which came to us as a pleasant surprise) of dilation theory to the continuity of the spectrum of the almost Mathieu operator from mathematical physics.

Based on a joint work with Malte Gerhold.
  


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