I am an Associate Professor in the Mathematics Department at the University of Houston and a member of the Analysis Research Group at UH. I have supervised a number of undergraduate students, graduate students, and postdocs, and published a number of papers.

Much of my work in Functional Analysis involves C*-algebras constructed from discrete and dynamical structures. This involves building C*-algebras from objects (e.g., graphs, matrices, bimodules, shift spaces) and then using the object to study properties of the associated C*-algebra. In these investigations one often considers the following questions: When can a known C*-algebra be modeled as the C*-algebra of an object? Can one translate well-known properties of the object into properties of the associated C*-algebra? Can invariants for the constructed C*-algebra be computed in terms of the object? Can the objects be used to classify the associated C*-algebras? At what level of generality can one use these methods to model well-known classes of C*-algebras?

My work in Algebra has been motivated by the recent development of Leavitt
path algebras, which are algebras constructed from graphs in a manner similar
to how graph C*-algebras are constructed. These Leavitt
path algebras are intimately related to graph C*-algebras, and both the
C*-algebraic and algebraic theories have guided, influenced, and assisted
each other. Indeed, each theory has had nontrivial applications to the
other, and together they have given a deeper understanding of
certain classes of algebras and C*-algebras. Much of my work in this area involves
describing the structure of Leavitt path algebras, classifying Leavitt path algebras in terms of K-theory,
examining the relationship between Leavitt path
algebras and graph C*-algebras, and using Functional Analysis results to
motivate the creation of new algebras from other objects besides graphs.

- The Wikipedia articles on Operator Algebras, C*-algebras, and von Neumann algebras.
- What are Operator Spaces?, available in both online and PDF versions.
- A survey article about graph C*-algebras.
- A survey article about the importance of C*-algebras.
- The Wikipedia article on Invariant Basis Number with a discussion of the Leavitt algebras, which are special cases of Leavitt path algebras.

- Operator Algebra Resources maintained by Chris Phillips
- The Graph Algebra Problem Page
- Counterexamples in Functional Analysis home page.
- The Noncommutative Geometry Resource Center.
- The K-book: An introduction to algebraic K-theory by Charles Weibel

- Applications of model theory to operator algebras , July 31--August 4, 2017
- Classification of C*-algebras, flow equivalence of shift spaces, and graph and Leavitt path algebras. , May 11--15, 2015
- Flow equivalence of graphs, shifts, and C*-algebras, Nov 18--22, 2013.
- Masterclass on Classification of non-simple purely infinite C*-algebras at the University of Copenhagen in August, 2013.
- Graph Algebras: Bridges between graph C*-algebras and Leavitt path algebras, held at the Banff International Research Station from April 21--26, 2013.
- Classification of amenable C*-algebras, held at the Banff International Research Station from September 19--24, 2010
- Lecture Notes from the Mathematical Institute of the Polish Academy of Sciences.

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