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Pure MathematicsUniversity of Waterloo
200 University Avenue West
Waterloo, Ontario, Canada
N2L 3G1
Departmental office: MC 5304
Phone: 519 888 4567 x33484
Fax: 519 725 0160
Email: puremath@uwaterloo.ca
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Ehsaan Hossain, Pure Mathematics, University of Waterloo
"The Algebraic KirchbergPhillips Conjecture"
To a directed graph $E$, one can associate two algebras: the C*algebra $C^*(E)$, and the Leavitt path algebra $L(E)$. Remarkably many algebraic properties of $L(E)$ mirror C*algebraic properties of $C^*(E)$  in fact $L(E)$ is a dense subalgebra of $C^*(E)$. The famous KirchbergPhillips Theorem from C*algebras says that certain purely infinite simple C*algebras can be determined up to isomorphism from their Ktheory; this has nice implications for graph C*algebras because if $C^*(E)$ is simple then it is often purely infinite (as long as $E$ has at least one cycle). Since Leavitt path algebras mimic C*algebras in many ways, one may ask if they also satisfy a KirchbergPhillips classification: if $L(E)$ is purely infinite simple, can we recover its isomorphism class from its Ktheory? This remains an unresolved question, but many clues from symbolic dynamics hint that at a positive answer. The aim of this presentation is to give an overview of the stateofaffairs regarding the algebraic KirchbergPhillips question.
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Departmental office: MC 5304
Phone: 519 888 4567 x33484
Fax: 519 725 0160
Email: puremath@uwaterloo.ca
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