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), particularly those of type II and index zero, 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 recently 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-semigroupsHouston J. Math., to appear
A family of non-cocycle conjugate E_0-semigroups obtained from boundary weight doubles
J. Operator Theory, to appear
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-semigroupsSubmitted (with Daniel Markiewicz and Robert T. Powers)
Slides of recent talks
Gauge groups of E_0-semigroupsA family of non-cocycle conjugate E_0-semigroups obtained from boundary weight doubles
Properties of q-positive maps and their relation to E_0-semigroups
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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