Research and Publications
Research
I am currently an assistant professor at the University of Houston, and a member of the
Analysis Research
Group in the Mathematics
Department there.
I work in the area of Functional Analysis and do research related to
Operator Algebras. Much of my work involves C*-algebras associated to
discrete and dynamical structures. This subject involves building
C*-algebras from objects (e.g., graphs, matrices, bimodules, shift spaces)
arising in discrete and dynamical systems in order to study the structure
of the C*-algebra and its relation to the defining system. It deals with the
questions: When can a given C*-algebra be modeled as the C*-algebra of
more than one type of discrete or dynamical system? Can one translate
well-known properties of the system into properties of the associated
C*-algebra? At what level of generality can one use these methods to
model classifiable C*-algebras?
I also have a growing interest in Frames, Operator Spaces and Operator
Systems, and the use algebraic techniques in Operator Algebra,
particularly in the context of Leavitt Path Algebras.
Publications
- Isomorphism and
Morita equivalence of graph algebras (with Gene Abrams),
submitted.
- Continuity of ring
*-homomorphisms between C*-algebras, submitted.
- Graph algebras, Exel-Laca
algebras, and ultragraph algebras coincide up to Morita
equivalence (with Takeshi Katsura, Paul S. Muhly, and Aidan Sims),
submitted.
-
Equiangular tight frames from complex Seidel matrices containing cube
roots of unity (with Bernhard Bodmann and Vern I. Paulsen),
Linear Algebra Appl., to appear.
-
Vector spaces with an order unit (with Vern I. Paulsen),
Indiana Univ. Math. J., to appear.
-
Ultragraph C*-algebras via topological quivers (with Takeshi
Katsura, Paul S. Muhly, and Aidan Sims), Studia Math. 187
(2008),
137--155.
-
Uniqueness theorems and ideal structure for Leavitt path algebras
, J. Algebra 318 (2007), 270--299.
- The structure of graph
C*-algebras and their 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 Malaga, Malaga, Spain, 2006.
-
Strong Shift Equivalence of C*-correspondences (with Paul S.
Muhly and David Pask), Israel J. Math 167 (2008), 315--346.
-
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, 221-230.
-
Topological quivers (with Paul S. Muhly), Internat. J. Math.
16 (2005), 693-756.
-
The C*-algebras of arbitrary graphs (with
Doug Drinen), Rocky Mountain J. Math. 35 (2005), 105-135.
-
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.
-
Adding tails to C*-correspondences (with Paul S. Muhly),
Documenta Math. 9 (2004), 79-106.
-
Stability of C*-algebras associated to graphs, Proc. Amer.
Math. Soc. 132 (2004), 1787-1795.
-
A unified approach to Exel-Laca algebras and C*-algebras associated to
graphs, J. Operator Theory 50 (2003), 345-368.
-
Simplicity of ultragraph algebras, Indiana Univ. Math. J.
52 (2003), 901-926.
-
Computing Ext for graph algebras, J. Operator Theory
49 (2003), 363-387.
- This paper was shortened considerably for publication. An unabridged
version appears here. [dvi] [pdf] [ps]
-
The ordered K0-group of a graph C*-algebra, C. R.
Math. Acad. Sci. Soc. R. Can. 25 (2003), 19-25.
-
Computing K-theory and Ext for graph C*-algebras (with
Doug Drinen), Illinois J. Math. 46 (2002), 81-91.
-
Ext classes and embeddings for C*-algebras of graphs with
sinks, New York J. Math. 7 (2001), 233-256.
Thesis
If you would like a copy of any of the above papers but are having
trouble downloading it, feel free to contact me.
Resources
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