**An Operad of Non-commutative Independences Defined by Trees.**

(with Weihua Liu)

Preprint written January 2019

PDF

arXiv 1901.09158**An Elementary Approach to Free Entropy Theory for Convex Potentials.**

Preprint submitted May 2018

arXiv 1805.08814

Talk Slides--shorter, less technical

Talk Slides--longer, more technical**Operator-valued Chordal Loewner Chains and Non-Commutative Probability.**

Preprint submitted November 2017, revised November 2018

arXiv 1711.02611

Talk Slides-
**Algebraic Properties of Generalized Graph Laplacians: Resistor Networks, Critical Groups, and Homological Algebra.**

(With Avi Levy, Will Dana, Austin Stromme, Collin Litterell)

SIAM J. Discrete Math 32-2 (2018), pp. 1040-1110.

Final Version PDF

arXiv 1604.07075

Operator-Valued Noncommutative Probability. (169 pages)

These notes are a systematic exposition / reference for results on free, boolean, and monotone independence, and they include a few new results as well. I welcome editorial feedback. Last updated November 19, 2018. Some material from these notes has been subsumed into the paper "Operad of Non-commutative Independences."

- Boolean Products of C* algebras preliminary research note
- Local and Spectral Convergence of Graph Laplacians Talk Slides
- (With Will Dana) note on Critical Groups of Graphs with Dihedral Symmetry
- 10-Minute Introduction to Free Probability
- Resources for Learning Free Probability
- .bib file of non-commutative probability papers--feel free to use.