Publications

1. A Cuntz-Krieger uniqueness theorem for Cuntz-Pimsner algebras, with Menevşe Eryüzlü, submitted.

2. Recasting the Hazrat conjecture: Relating shift equivalence to graded Morita equivalence, with Gene Abrams and Efren Ruiz, Algebr. Represent. Theory 27 (2024), 1477--1511

3. Morita equivalence for graded rings, with Gene Abrams and Efren Ruiz, J. Algebra 617 (2023), 79--112

4. Matricial Archimedean order unit spaces and quantum correlations, with Roy Araiza and Travis Russell, Indiana Univ. Math. J., Indiana Univ. Math. J. 72 (2023), 2567--2591.

5. A universal representation for quantum commuting correlations, with Roy Araiza and Travis Russell, Ann. Henri Poincaré, Ann. Henri Poincaré 23 (2022), 4489--4520.

6. Reconstruction of groupoids and C*-rigidity of dynamical systems, with Toke Meier Carlsen, Efren Ruiz, and Aidan Sims, Adv. Math. 390 (2021), Paper No. 107923, 55 pp.

7. The extension problem for graph C*-algebras, with Søren Eilers, James Gabe, Takeshi Katsura, and Efren Ruiz, Ann. K-Theory 5 (2020), 295--315.
8. Naimark's problem for graph algebras, with Nishant Suri, Illinois J. Math, Illinois J. Math 61 (2017), 479--495.
9. Classification of graph algebras: A selective survey, Proceedings of the 2015 Abel Symposium (Eds. T.M. Carlsen, N.S. Larsen, S. Neshveyev, and C. Skau), Springer, (2016), 297--320.
10. Chaotic behavior in a forecast model (with Michael Boyle), Pi Mu Epsilon J. 14 (2016), 237--242.
11. The ranges of K-theoretic invariants for nonsimple graph algebras (with Søren Eilers, Takeshi Katsura, and James West), Trans. Amer. Math. Soc. 368 (2016), 3811--3847.
12. K-theory for Leavitt path algebras: computation and classification (with James Gabe, Efren Ruiz, and Tristan Whalen), J. Algebra 433 (2015), 35--72.
13. The nuclear dimension of graph C*-algebras (with Efren Ruiz and Aidan Sims), Adv. Math. 272 (2015), 96--123.
14. A class of C*-algebras that are prime but not primitive (with Gene Abrams), Münster J. Math. 7 (2014), 489--514.
15. The prime spectrum and the primitive ideal space of a graph C*-algebra (with Gene Abrams), Internat. J. Math. 25 no. 7 (2014), 1450070, 22 pp.
16. Identifying AF-algebras that are graph C*-algebras (with Søren Eilers, Takeshi Katsura, and Efren Ruiz), J. Funct. Anal. 266 (2014), 3968--3996.
17. One-sided shift spaces over infinite alphabets (with William Ott and Paulette Willis), New York Journal of Mathematics. NYJM Monographs 5. State University of New York, University at Albany, Albany, NY, 2014. 54 pp.
18. A groupoid generalization of Leavitt path algebras (with Lisa Orloff Clark, Cynthia Farthing, and Aidan Sims), Semigroup Forum 89 (2014), 501--517.
19. Ideals in graph algebras (with Efren Ruiz), Algebr. Represent. Theory 17 (2014), 849--861.
20. Classification of unital simple Leavitt path algebras of infinite graphs (with Efren Ruiz), J. Algebra 384 (2013), 45--83.
21. Ideal-related K-theory for Leavitt path algebras and graph C*-algebras (with Efren Ruiz), Indiana Univ. Math. J. 62 (2013), 1587--1620.
22. Quotients, exactness, and nuclearity in the operator system category (with Ali Kavruk, Ivan Todorov, and Vern Paulsen), Adv. Math. 235 (2013) 321--360.
23. Index maps in the K-theory of graph algebras (with Toke Carlsen and Søren Eilers), J. K-theory 9 (2012), 385--406.
24. Isomorphism and Morita equivalence of graph algebras (with Gene Abrams), Trans. Amer. Math. Soc. 363 (2011), 3733--3767.
25. Tensor products of operator systems (with Ali Kavruk, Ivan Todorov, and Vern Paulsen), J. Funct. Anal. 261 (2011), 267--299.
26. Leavitt path algebras with coefficients in a commutative ring, J. Pure Appl. Algebra 215 (2011), 471--484.
27. Operator system structures on ordered spaces (with Vern Paulsen and Ivan Todorov), Proc. London Math. Soc. 102 (2011), 25--49.
28. Frame theory for binary vector spaces (with Bernhard Bodmann, My Le, Letty Reza, and Matthew Tobin), Involve 2 (2010), 589--602.
29. On the classification of nonsimple graph C*-algebras (with Søren Eilers), Math. Ann. 346 (2010), 393--418.
30. Graph algebras, Exel-Laca algebras, and ultragraph algebras coincide up to Morita equivalence (with Takeshi Katsura, Paul S. Muhly, and Aidan Sims), J. Reine Angew. Math. 640 (2010), 135--165.
31. Realizations of AF-algebras as graph algebras, Exel-Laca algebras, and ultragraph algebras (with Takeshi Katsura and Aidan Sims), J. Funct. Anal. 257 (2009), 1589--1620.
32. Continuity of ring *-homomorphisms between C*-algebras, New York J. Math. 15 (2009), 1--7.
33. Equiangular tight frames from complex Seidel matrices containing cube roots of unity (with Bernhard Bodmann and Vern I. Paulsen), Linear Algebra Appl. 430 (2009), 396--417.
34. Vector spaces with an order unit (with Vern I. Paulsen), Indiana Univ. Math. J. 58 (2009), 1319--1360.
35. Ultragraph C*-algebras via topological quivers (with Takeshi Katsura, Paul S. Muhly, and Aidan Sims), Studia Math. 187 (2008), 137--155.
36. Strong Shift Equivalence of C*-correspondences (with Paul S. Muhly and David Pask), Israel J. Math. 167 (2008), 315--346.
37. Uniqueness theorems and ideal structure for Leavitt path algebras, J. Algebra 318 (2007), 270--299.
38. The structure of graph C*-algebras and generalizations, Chapter in the book "Graph Algebras: Bridging the gap between analysis and algebra", Eds. Gonzalo Aranda Pino, Francesc Perera Domenech, and Mercedes Siles Molina, Servicio de Publicaciones de la Universidad de Málaga, Málaga, Spain, (2006).
39. Strong Shift Equivalence in the C*-algebraic setting: Graphs and C*-correspondences, Contemporary Mathematics, Proceedings of the 25th Meeting of the Great Plains Operator Theory Symposium, American Mathematical Society, Providence, RI, (2006), 221--230.
40. Topological quivers (with Paul S. Muhly), Internat. J. Math. 16 (2005), 693--756.
41. The C*-algebras of arbitrary graphs (with Doug Drinen), Rocky Mountain J. Math. 35 (2005), 105--135.
42. Classification theorems for the C*-algebras of graphs with sinks (with Iain Raeburn and Dana P. Williams), Bull. Austral. Math. Soc. 70 (2004), 143--161.
43. Adding tails to C*-correspondences (with Paul S. Muhly), Documenta Math. 9 (2004), 79--106.
44. Stability of C*-algebras associated to graphs, Proc. Amer. Math. Soc. 132 (2004), 1787--1795.
45. A unified approach to Exel-Laca algebras and C*-algebras associated to graphs, J. Operator Theory 50 (2003), 345--368.
46. Simplicity of ultragraph algebras, Indiana Univ. Math. J. 52 (2003), 901--926.
47. Computing Ext for graph algebras, J. Operator Theory 49 (2003), 363--387.
48. The ordered K₀-group of a graph C*-algebra, C. R. Math. Acad. Sci. Soc. R. Can. 25 (2003), 19--25.
49. Computing K-theory and Ext for graph C*-algebras (with Doug Drinen), Illinois J. Math. 46 (2002), 81--91.
50. Ext classes and embeddings for C*-algebras of graphs with sinks, New York J. Math. 7 (2001), 233--256.

Books and Monographs

• The structure of graph C*-algebras and generalizations, Chapter in the book "Graph Algebras: Bridging the gap between analysis and algebra", Eds. Gonzalo Aranda Pino, Francesc Perera Domenech, and Mercedes Siles Molina, Servicio de Publicaciones de la Universidad de Málaga, Málaga, Spain, (2006).

Conference Proceedings and Non-Refereed Publications

• Classification of graph C*-algebras and Leavitt path algebras, summary of my talk given at the Endomorphisms, Semigroups and C*-algebras of Rings workshop held April 2012 at the Mathematisches Forschungsinstitut Oberwolfach in Oberwolfach, Germany. This appeared in the "Oberwolfach Report" (OWR) published by the Mathematisches Forschungsinstitut Oberwolfach.

Thesis

• Extensions of graph C*-algebras, Ph.D. thesis, Dartmouth College, 2002.

Notes and Talks

• In July 2010 I gave six lectures at the Master Class on Cuntz-Pimsner Algebras at the University of Copenhagen. Slides from my six talks are available here:
• Talk 1: An Introduction to Graph C*-algebras
• Talk 2: More on Graph C*-algebras
• Talk 3: Graph C*-algebras as Cuntz-Pimsner Algebras
• Talk 4: Classification of Nonsimple Graph C*-algebras
• Talk 5: Generalizations of Graph Algebras within the Cuntz-Pimsner Framework
• Talk 6: Leavitt Path Algebras