## Math 1553 Exams and Recorded Lectures

I frequently coordinate Math 1553, Introduction to Linear Algebra. You can find past midterm exams for the course at the exam archive. In Spring 2022, I recorded most of my lectures, and they are available here.## Teaching

Fall 2024: Math 1553 and Math 6001.Spring 2024: Math 1553

Fall 2023: Math 1553 and Math 6001.

Spring 2023: Math 1553

Fall 2022: Office hours are Mondays 1:30-2:30 PM here and Tuesdays 1:00-2:00 PM here. I am teaching Math 6001.

Spring 2022: Math 1553.

Fall 2021: Math 1553 and Math 6001.

Spring 2021: Math 1553 A and D (click here for the common course calendar).

Fall 2020: Math 1551 and Math 6001.

Spring 2020: Math 1553

Fall 2019: Math 1553 and Math 6001.

Spring 2019: Math 1553 and Math 2550.

Fall 2018: Math 1553 and Math 6001

Spring 2018: Math 1553.

Fall 2017: Math 1553 and Math 6001

Spring 2017: Math 2550 (course information on T-Square).

Fall 2016: Math 1113 (along with its supplement, Math 0399) and Math 2603.

## 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. You can find
a portfolio with some other materials here.

## Papers

Classification of q-pure q-weight maps over finite dimensional Hilbert spaces(with Daniel Markiewicz and Robert T. Powers), J. Funct. Anal. 277 (2019), no. 6, 1763-1867.

Aligned CP-semigroups,

Int. Math. Res. Not. IMRN 2015, no. 15, 6639-6647 (with Daniel Markiewicz and Robert T. Powers)

Unital 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)

## About Me

Born and raised in Louisville, Kentucky, I have been a sports fan my entire coherent life. Most of my family currently resides in Louisville, including eight nephews and a niece (from whom I expect big things).

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