For an up to date list of publications, check out my Google Scholar page. This page organizes my work into themes: numerical linear algebra, quantum computing, and mathematical optimization.
Numerical Linear Algebra
I primarily work on randomized numerical linear algebra.
Randomized Numerical Linear Algebra: A Perspective on the Field With an Eye to Software.
I’m the lead author of this 200-page monograph. It has a total of 13 authors, including Michael Mahoney, James Demmel, and Jack Dongarra. Check it out on arXiv!
Interface for sparse linear algebra operations.
With Ahmad Abdelfattah, Willow Ahrens, Hartwig Anzt, Chris Armstrong, Ben Brock, Aydin Buluc, Federico Busato, Terry Cojean, Tim Davis, Jim Demmel, Grace Dinh, David Gardener, Jan Fiala, Mark Gates, Azzam Haider, Toshiyuki Imamura, Pedro Valero Lara, Jose Moreira, Sherry Li, Piotr Luszczek, Maksim Melichenko, Jose Moeira, Yvan Mokwinski, Spencer Patty, Slaven Peles, Tobias Ribizel, Jason Riedy, Siva Rajamanickam, Piyush Sao, Manu Shantharam, Keita Teranishi, Stan Tomov, Yu-Hsiang Tsai, and Heiko Weichelt. [arXiv]
CholeskyQR with randomization and pivoting for tall matrices (CQRRPT).
With Maksim Melnichenko, Oleg Balabanov, Jim Demmel, Michael Mahoney, and Piotr Luszczek. [arXiv]
Fast multiplication of random dense matrices with fixed sparse matrices.
With Tianyu Liang, Aydın Buluç, and Jim Demmel. [arXiv]
Fast exact leverage score sampling from Khatri-Rao products with applications to tensor decomposition.
With Vivek Bharadwaj, Osman Asif Malik, Laura Grigori, Aydin Buluc, and Jim Demmel. Available at arXiv, and accepted to NeurIPS 2023.
Distributed-memory randomized algorithms for sparse tensor CP decomposition.
With Vivek Bharadwaj, Osman Asif Malik, Aydin Buluc, and Jim Demmel. [arXiv]
Sampling-based decomposition algorithms for arbitrary tensor networks.
With Vivek Bharadwaj and Osman Asif Malik. [arXiv]
Quantum computing
I’m a staff member in Sandia’s Quantum Performance Laboratory (QPL). We at the QPL develop state-of-the-art methods for quantum characterization, verification, and validation.
Randomized benchmarking with synthetic quantum circuits.
With Yale Fan, Thaddeous Ladd, Kevin Young, and Robin Blume-Kohout. [arXiv]
Certifying the quantumness of a nuclear spin qudit through its uniform precession.
With Arjen Vaartjes, Martin Nurizzo, Lin Htoo Zaw, Benjamin Wilhelm, Xi Yu, Danielle Holmes, Daniel Schwienbacher, Anders Kringhøj, Mark van Blankenstein, Alexander Jakob, Fay Hudson, Kohei Itoh, Robin Blume-Kohout, Namit Anand, Andrew Dzurak, David Jamieson, Valerio Scarani, and Andrea Morello. [arXiv]. To appear in Newton (Cell Press).
Schrödinger cat states of a nuclear spin qudit in silicon.
With Xi Yu, Benjamin Wilhelm, Danielle Holmes, Arjen Vaartjes, Daniel Schwienbacher, Martin Nurizzo, Anders Kringhøj, Mark van Blankenstein, Alexander Jakob, Pragati Gupta, Fay Hudson, Kohei Itoh, Robin Blume-Kohout, Thaddeus Ladd, Andrew Dzurak, Barry Sanders, David Jamieson, Andrea Morello. [arXiv]. To appear in Nature Physics.
Initially circulated under the title Creation and manipulation of Schrödinger cat states of a nuclear spin qudit in silicon.
Mathematical Optimization
I started contributing to CVXPY starting in January 2018. I now serve on the CVXPY steering committee and as one of its five project maintainers. Funnily enough, I’ve never been on a paper about the project! See below for some of my formal, academic work on optimization.
Applications of convex analysis to signomial and polynomial nonnegativity problems.
This thesis combines (and slightly expands upon) four papers I wrote in graduate school. The new content includes applications in chemical reaction networks and more discussion of the sageopt python package. There is also a chapter on preliminaries that covers generic ideas like nonnegativity cones, moment relaxations, and convex cone programming. This is an excellent on-boarding resource to learn about sums of arithmetic-geometric exponentials (SAGE) and related ideas such as sums of nonnegative circuits (SONC).
Received the Amori Doctoral Prize in Computing and Mathematical Sciences.
Algebraic perspectives on signomial optimization.
With Mareike Dressler. Published in the SIAM Journal on Applied Algebra and Geometry. A slightly older version is available on arXiv. An early-still version of this work appears as Chapter 6 of my PhD thesis.
Sublinear circuits and the constrained signomial nonnegativity problem.
With Helen Naumann and Thorsten Theobald. Currently available open-access at Mathematical Programming (2022). The same content is covered in a slightly more digestible way in Chapter 5 of my PhD thesis.
I mentioned this work towards the end of my MIT vsOPT talk. I also have slides from a 30-minute presentation focused on the paper (notation in slides is slightly different from the paper).
Signomial and polynomial optimization via relative entropy and partial dualization.
With Venkat Chandrasekaran and Adam Wierman. Available at Mathematical Programming Computation (2020) , with an earlier version on arXiv (2019). The mathematics described in this paper are implemented by the sageopt python package. I have two sets of slides that address the whole paper (MPI MiS 2019, ICCOPT 2019). On April 17 2020 I gave a recorded talk through MIT, which addressed the signomial parts of the paper in detail, along with other recent results in this area. Errata. The material in this paper appears (in expanded forms) throughout Chapters 4, 7, and 8 of my PhD thesis.
Newton polytopes and relative entropy optimization.
With Venkat Chandrasekaran and Adam Wierman. Available at Foundations of Computational Mathematics (2021). You can find a freely available read-only copy from Springer at this link (see also arXiv). In June 2019 I gave a recorded talk on this paper at the Banff International Research Station. Venkat gave a talk based on this work at ICERM in November 2018. The material in this paper appears in Chapter 3 of my PhD thesis.
Robust market equilibria with uncertain preferences.
With Christian Kroer, Alex Peysakhovich, and Parikshit Shah. [arXiv, AAAI 2020, blog post].
Structured state feedback for Metzler dynamics.
With James Anderson. [CDC 2018].
Scheduling distributed clusters of parallel machines : primal-dual and LP-Based algorithms.
With Samir Khuller and Megan Chao. [arXiv, ESA 2016, extended version in Algorithmica].
Riley Murray 