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.
PapersUnital q-positive maps on M_2(C) and cocycle conjugacy of E_0-semigroups
Houston J. Math. 39 (2013), 1233-1266.
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 (2012), no. 14, 3278-3310 (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)
Int. Math. Res. Not. IMRN, to appear (with Daniel Markiewicz and Robert T. Powers)
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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