## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

Friday, May 22, 2015 — 1:30 PM EDT

**Ehsaan Hossain, Department of Pure Mathematics, University of Waterloo **

“Classification of simple graph algebras”

Abstract

This summer we will be continuing our study of graph C*-algebras: to a directed graph E, one can associate a C*-algebra C∗(E) whose ∗-algebraic properties can be determined through graphical properties of E. For example, C∗(E) is an AF-algebra if and only if E is acyclic. Graph C*-algebras form a useful class of examples for C*-algebraists.

Through the famous and general classification results of Elliott and Kirchberg–Phillips, isomorphism of graph C*-algebras can be determined through a pair of groups known as K- theory (with some other data attached). We’ll start the summer by describing this classification theorem: defining the K-theory groups and the various hypotheses in the classification. Graph C*-algebras have sisters in ring theory called Leavitt path algebras, but there is no analogue of the Kirchberg–Phillips result — so there are still some algebraic open questions.

I hope this topic will be of interest to analysis and algebra students alike, and we’ll begin with a low prereq ceiling. Everyone is welcome!

MC 5417

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1

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