Research

My research interests lie in operator algebras and free probability, with a particular emphasis on operator-valued free probability. My recent work focuses on conjugate systems, free difference quotients, completely positive maps, and structural properties of von Neumann algebras. More broadly, I am interested in functional analysis, noncommutative probability, and random matrix theory. 

Publications:

• Irreducibility and weak spectral gap in free product von Neumann algebras, with Aldo Garcia Guinto, Fehmi Ekin Giritlioglu, Rahul Kumar R., Brent Nelson, preprint (2026)

• Strong convergence to operator-valued semicirculars, with David Jekel, Brent Nelon, Jennifer Pi, preprint (2025)

• On the genericity of irreducible subfactors, with Brent Nelson, to appear in the Journal of Operator Theory 

• On conjugate systems with respect to completely positive maps, preprint (2024)

• The operator equation AXB=X and the Fuglede-Putnam type property, with Eungil Ko, Operators and Matrices. 427-440. (2024)

• On solutions of operator equations satisfying the similarity of real and positive parts, with Eungil Ko, Linear and Multilinear Algebra (2020).

Invited talks :

• Functional Analysis Seminar, University of Oxford, Aug 4 2026

• Functional Analysis Seminar, Texas A&M University, Apr 13 2026

• Recent Development in Operator Algebras, Brin Mathematics Research Center, Feb 6 2026 

• AMS Special Session on Advances in Operator Algebras II, JMM, Jan 7 2026

• Kyoto University, Dec 12 2025

• Nagoya University, Dec 5 2025

• Brazos Analysis Seminar, University of Texas at Austin, Nov 15 2025

• Seminar in Operator Theory and Operator Algebras, University of Virginia, Nov 11 2025

• Subfactor Seminar, Vanderbilt University, Oct 3 2025

• Free Probability, Random Matrices and Finite-Dimensional Approximations workshop, CMO, Jun 3 2025

• Operator Theory Seminar, University of Iowa, Mar 11 2025

• Functional Analysis Seminar, UCSD, Mar 3 2025

• Free Entropy Theory and Random Matrices Workshop, IPAM, Feb 25 2025

• Operator Algebra Seminar, Purdue University, Feb 11 2025

• Abu Dhabi Stochastics Seminar, NYU Abu Dhabi (Online), Feb 5 2025

• Probalistic Operator Algebra Seminar, UC Berkely (Online), Jan 27 2025

Contributed talks :

• GPOTS, University of Iowa, May 25 2026

• GPOTS. Puerto Rico, Oct 21 2025

• Korean Mathematical Society Spring Meeting, Contributed talk (Online), Properties of operators with similar both real and positive parts, Jul 2020

• Joint Mathematics Meetings, Undergrad student poster session (San Diego), Three dimensional surface reconstruction from a single portrait based on supervised learning and optimization in Sobolev norm, Jan 2018