Research

I work in Operator Algebras. With Bob Powers as my advisor, I received my Ph.D. from the University of Pennsylvania in 2009. My main research interest lies in constructing and classifying E_0-semigroups (up to cocycle conjugacy) using the theory of CP-flows and boundary weight maps.

The comparison theory of a particular class of completely positive maps has been central to this research so far. In joint work, I have been working to compute a fundamental invariant (the gauge group) for a family of E_0-semigroups, and I have also become interested in various notions of subordination for CP-flows and E_0-semigroups.

Here is my CV.

Papers

Unital q-positive maps on M_2(C) and cocycle conjugacy of E_0-semigroups
Houston J. Math., to appear

A family of non-cocycle conjugate E_0-semigroups obtained from boundary weight doubles
J. Operator Theory 69 (2013), no. 1, 233-256.

E_0-semigroups and q-purity: boundary weight maps of range rank one and two
J. Funct. Anal. 262 (2012), no. 7, 3006-3061 (with Daniel Markiewicz and Robert T. Powers)

Gauge groups of E_0-semigroups obtained from Powers weights
Int. Math. Res. Not. IMRN (2011), in press (with Daniel Markiewicz)

On type II_0 E_0-semigroups induced by boundary weight doubles
J. Funct. Anal. 258 (2010), no. 10, 3413-3451

On K_*-ultrahomogeneous graphs
Ars. Combin. 82 (2007), 83-96 (with Daniel Isaksen and Stephanie Proctor)

Preprints

Aligned CP-semigroups
Submitted (with Daniel Markiewicz and Robert T. Powers)

About Me

Born and raised in Louisville, Kentucky, I have been a sports fan my entire coherent life. Aside of my oldest brother, who is an environmental engineer, I am the only member of my family who does not dislike math. Most of my family currently resides in Louisville, including five nephews (from whom I expect big things) and a noble dog.

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