Colloquiumhttps://www.math.umanitoba.ca/seminars/series/colloquium/en-usThu, 28 Feb 2019 20:56:11 +0000Adam Dor On - Operator Algebraic Graph Theoryhttps://www.math.umanitoba.ca/seminars/2019/3/22/adam-dor-on/Colloquium talk:<br>
Adam Dor On (University of Illinois at Urbana-Champaign)<br>
<i>Operator Algebraic Graph Theory</i><br>
Friday, March 22, 2019 at 14:30<br>
111 Armes<br>
<br>
<p>The Toeplitz algebra of a directed graph is the norm-closed \( {*} \)- algebra generated by concatenation operators on the inner-product space of square summable sequences indexed by finite paths of the graph. A canonical quotient of it is the celebrated Cuntz-Krieger algebra, which is deeply connected to the associated subshift of finite type and automata of the directed graph.</p>
<p>Understanding representations of such "reversible" operator algebras has become useful for producing wavelet on Cantor sets by Marcolli and Paolucci and in the study of semi-branching function systems by Bezuglyi and Jorgensen. Together with Davidson and Li, we provided an "irreversible" algebra perspective for such representations, which led to new invariants that distinguish them.</p>
<p>In this talk I will present a complete characterization of those finite directed graphs that admit weakly-closed "reversible" algebras that are generated only by represented concatenation operators (without their adjoints !). The first example of this counter-intuitive phenomenon was produced by Read in the case where the graph has a single vertex and two loops. I will explain how the Road Coloring theorem of Béal and Perrin from automata theory is used to solve the problem in general.</p>
<p>Based on joint work with Christopher Linden.</p>
Thu, 28 Feb 2019 20:56:11 +0000https://www.math.umanitoba.ca/seminars/2019/3/22/adam-dor-on/