Research

Non-Commutative Function theory, Free Probability and Random Matrix Theory.
Spectrum of a random unitary linear pencil
Figure 1. Approximate spectrum of a random unitary linear pencil with coefficient matrices: \[ X_1 = \begin{bmatrix} 1 & 1 \\ 0 & 0 \end{bmatrix}, \quad X_2 = \begin{bmatrix} 0 & 1 \\ 1 & 2 \end{bmatrix}. \]

Reading That Inspired Research Interest

J. William Helton, Tobias Mai, Roland Speicher, Applications of realizations (aka linearizations) to free probability, Journal of Functional Analysis, 2018,
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Expository Writing

Framework for Commutative and Non-commutative Probability Theory

Zeros of Stable NC-Polynomials