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Research

“It has always been a temptation for mathematicians to present the crystallized product of their thoughts as a deductive general theory and to relegate the individual mathematical phenomenon into the role of an example. The reader who submits to the dogmatic form will be easily indoctrinated. Enlightenment, however, must come from an understanding of motives; live mathematical development springs from specific natural problems which can be easily understood, but whose solutions are difficult and demand new methods of more general significance.”

– Richard Courant

I’m interested in probability theory and networks, bridging together structure, dynamics, and information. More broadly speaking, I would like to solve interesting and difficult problems in engineering and science while providing principled mathematical justifications.

Current projects include:

• limit theory for interacting particles on sparse graphs
• communication properties of biological signal transduction systems
• universal phenomena of high-dimensional projections

Below is a selected list of my published work, organized in terms on topics (topics and coauthors listed in alphabetical order). For a complete, chronological ordered (and automatically updated) list, see my Google Scholar profile.

Signal Processing

• Explicitly solvable continuous-time inference for partially-observed Markov processes (with Andrew W. Eckford, Alexander G. Strang, and Peter J. Thomas). IEEE Transactions on Signal Processing (2022). Journal. Arxiv.

Quantum Networks

• Inferring quantum network topology using local measurements (with Brian Doolittle, Eric Chitambar, Jeffrey Larson, and Zain H. Saleem). PRX Quantum (2023). Journal. Arxiv.

Quantum Algorithms

• Quantum circuit cutting for classical shadows (with Michael A. Perlin and Zain H. Saleem). ACM Transactions on Quantum Computing(2024). Journal. Arxiv

• Online detection of golden circuit cutting points (with Ethan Hansen, Shuai Xu, and others). IEEE Conference on Quantum Computing and Engineering (2023). Conference. Arxiv.