### interests

Operator theory, weighted composition operators, Bloch functions, functional analysis, pattern formation in PDEs, mathematical biology, Lie algebras, operator algebras.

### current projects

** Operators on Spaces of Holomorphic Functions **

I investigate weighted composition operators on spaces of holomorphic functions defined by $W_{\psi,\varphi} f = \psi(f\circ\varphi)$. I study these operators on spaces such as the Bloch space, Hardy spaces $H^p$, Bergman and weighted Bergman spaces, and Dirichlet and weighted Dirichlet spaces. I study these spaces in the unit disk $\mathbb{D}$ and the unit ball and polydisk $\mathbb{B}_n$ and $\mathbb{D}^n$. I also study equivalent spaces on discrete structures such as trees. (with Flavia Colonna, Katherine Heller, and Matthew Pons)

** Embeddings of Discrete Structures in the Hyperbolic Ball **

We are defining discrete structures such as trees to embed into the unit ball in $\mathbb{R}^n$ under the hyperbolic geometry. We are attempting to use this embedding to solve an interpolation problem: if we define a function on the vertices of the structure, can we find a function on the unit ball which agrees on the vertices? (with Tushar Das and Eddie Kim)

** Mathematical Biology and Sociology**

We are looking at how SIR models can be modified with nonlinear mass-action and stochasticity to describe various situations in biology and sociology. These topics include the spread of disease and rumors through populations. (with Eric Eager)

### journal articles

- Composition operators on the Lipschitz space of a Tree (with Flavia Colonna and Glenn R. Easley), Mediterranean Journal of Mathematics, to appear.
- Multiplication operators on the weighted Lipschitz space on a tree (with Flavia Colonna and Glenn R. Easley), Journal of Operator Theory
**69**(2013), 209-231. - Multiplication operators on the iterated logarithmic Lipschitz spaces of a tree (with Flavia Colonna and Glenn R. Easley), Mediterranean Journal of Mathematics
**9**(2012), 575-600. - Multiplication operators between Lipschitz-type spaces of a tree (with Flavia Colonna and Glenn R. Easley), International Journal of Mathematics and Mathematical Sciences, 2011, Art. ID 47495, 33pp.
- Weighted composition operators between \(H^\infty\) and the Bloch space of a bounded homogeneous domain (with Flavia Colonna), Integral Equations and Operator Theory
**66**(2010), 21-40. - Weighted composition operators on the Bloch space of a bounded homogeneous domain (with Flavia Colonna), Topics in Operator Theory Volume 1: Operators, Matrices and Analytic Functions, ISBN:978-3-0346-0157-3, 2010, 11-38.
- Multiplication operators on the Bloch space of a bounded homogeneous domain (with Flavia Colonna), Computational Methods and Function Theory
**9**(2009), 679-693. - On the isometric composition operators on the Bloch space in \(\mathbb{C}^n\) (with Flavia Colonna), Journal of Mathematical Analysis and Applications
**355**(2009), 675-688. - Isometries and spectra of multiplication operators on the Bloch space (with Flavia Colonna), Bulletin of the Australian Mathematical Society
**79**(2009), 147-160.

### manuscripts under review

- Isometric composition operators on the analytic Besov spaces (with Katherine Heller and Matthew A. Pons), submitted to Journal of Mathematical Analysis and Applications.
- Multiplication operators on $S^2(\mathbb{D})$ (with Katherine Heller and Matthew A. Pons), submitted to Computational Methods and Function Theory.
- Compact differences of composition operators on weighted Dirichlet spaces (with Katherine Heller and Matthew A. Pons), submitted to Central European Journal of Mathematics.
- Weighted composition operators from the Bloch space to \(H_\mu^\infty\) of a bounded homogeneous domain, submitted to Complex Variables and Operator Theory.

### manuscripts in progress

- Weighted composition operators between $S^p$ spaces (with Katherine Heller and Matthew A. Pons).
- Surviving an outbreak of zombiism (with Cassandra Jens and Theodore Wendt).

### dissertations and theses

- A class of operators with symbol on the Bloch space of a bounded homogeneous domain, Ph.D. dissertation, George Mason University.
- Turing instabilities with spatial pattern formation in one-dimension, Honors theses, George Mason University.
- The C-- programming language, Undergraduate thesis, University of Virginia.

### talks

**Conferences**

- "Surviving an Outbreak of Zombiism", MAA-DC/MD/VA Sectional Meeting, Salisbury MD, April 2013
- "Mass-Action in Action: From Zombiism to Undergraduate Research", MAA-WI Sectional Meeting, Baraboo, WI, April 2013.
- "Zombies, Ecology, and Epidemiology...Oh My!", MAA MathFest 2012, Sesson on Undergraduate Research in Mathematical and Computational Biology, MAA MathFest, Madison, WI, August 2012.
- "Surviving an Outbreak of Zombiism", MAA-WI Sectional Meeting, Milwaukee, WI, April 2012.
- "Using WeBWorK in Mathematics and Statistics Courses", Best Practices in Science, Math, and Engineering Teaching Conference, Baraboo, WI, August 2011.
- "Mathematical Modeling Meets Pop Culture", MAA MathFest 2011, Session on Mathematical Modeling Projects that Matter, MAA MathFest, Lexington, KY, August 2011.
- "Functional Analysis and Operator Theory for Undergraduates", MAA-WI Sectional Meeting, Menomonie, WI, April 2011.
- "Using WeBWorK in Mathematics and Statistics Courses", MAA-WI Sectional Meeting, Menomonie, WI, April 2011.
- "Multiplication Operators Between Lipschitz-Type Spaces of a Tree", Joint AMS/MAA Mathematics Meeting, Session on Operator Theory, New Orleans, LA, January 2011.
- "Motivating Class Participation and Cooperation Through Pop Culture", Best Practices in Science, Math, and Engineering Teaching Conference, Baraboo, WI, August 2010.
- "Isometries on the Bloch Space"', MAA-WI Sectional Meeting, Oshkosh, WI, April 2010.
- "Weighted Composition Operators from \(H^\infty\) to the Bloch Space of a Bounded Homogeneous Domain", Joint AMS/MAA Mathematics Meeting, Session on Functional Analysis and Operator Theory, San Francisco, CA, January 2010.
- "Multiplication Operators on the Bloch Space of a Bounded Homogeneous Domain", Joint AMS/MAA Mathematics Meeting, Special Session on Function Theoretic Operator Theory, Washington, D.C., January 2009.
- "Weighted Composition Operators on the Bloch Space on a Bounded Homogeneous Domain", International Workshop on Operator Theory and its Applications XIX, Special Session on Composition Operators, College of William & Mary, July 2008.
- "On the Spectrum of an Isometric Composition Operator on the Bloch Space of the Polydisk", South Eastern Analysis Meeting XXIII, University of Richmond, March 2007.

**Seminars and Colloquia**

- "Surviving an Outbreak of Zombiism", MSCP Lecture Series, Roanoke College, March 2012.
- "Composition Operators: Something for Everyone", Mathematics Colloquium, George Mason University, March 2012.
- "Surviving an Outbreak of Zombiism", Pi Mu Epsilon Prime Time Mathematics Colloquium, North Central College, October 2011.
- "Multipliers on Lipschitz-Type Spaces of a Tree", Mathematics Department Colloquium, University of Wisconsin-La Crosse, September 2010.
- "Turing Instabilities in Reaction-Diffusion Equations: A Model for the Formation of Mammalian Coat Patterns", Mathematics Research Seminar, University of Wisconsin-La Crosse, March 2010.
- "Isometries on the Bloch Space", Mathematics Research Seminar, University of Wisconsin-La Crosse, February 2010.
- "Analysis on Discrete Structures", Mathematics Research Seminar, University of Wisconsin-La Crosse, October 2009.
- "Classical and Modern Operator Theory on the Bloch Space", Mathematics Research Seminar, University of Wisconsin-La Crosse, September 2009.
- "Why I Should Have Paid More Attention in Linear Algebra", Math Department Colloquium, University of Wisconsin-La Crosse, February 2009.
- "An Introduction to Lie Algebras and their Cohomology", Combinatorics, Algebra and Geometry Seminar, George Mason University, November 2008.
- "Turing Instabilities in Reaction-Diffusion Equations: A Model for the Formation of Mammalian Coat Patterns", Applied & Computational Math Seminar, George Mason University, September 2008.
- "Isometries on the Bloch Space", Graduate Student Seminar, George Washington University, April 2008.
- "Isometric Composition Operators on the Bloch Space of the Unit Disk", Complex Analysis & Potential Theory Seminar, George Mason University, November 2007.
- "Embeddings of Trees in the Hyperbolic Disk", Graduate Seminar, University of Virginia, November 2004.

**Panel Discussions**

- "The Academic Job Talk", George Mason University, Fairfax VA, March 2012.
- "Effective Use of Online Homework to Enhance Student Learning and Retention", Project NeXT Panel, Lexington KY, August 2011.