About me.

I’m a project scientist at Lawrence Berkeley National Laboratory and a principal investigator at the International Computer Science Institute. I work on randomized numerical linear algebra with Jim Demmel and Michael Mahoney.

In June of 2021, I completed my Ph.D. in Computing and Mathematical Sciences from the California Institute of Technology. My thesis work (in the vein of sums-of-squares certificates and moment relaxations for polynomial optimization) was supervised by Venkat Chandrasekaran and Adam Wierman. In 2016 I received my undergraduate degree from UC Berkeley in Industrial Engineering and Operations Research.

This website hosts information on my research and professional service activities. Navigate this website with the links at the top-right of each page.



  • February 22, 2023. A product of 19 months of postdoctoral work has now seen the light of day. I’m the first author of a new book on randomized linear algebra! This thing is the real deal; it’s joint work with Michael Mahoney, Jim Demmel, and Jack Dongarra, among many others.
  • August 31, 2022: a revised version of my paper, “Algebraic perspectives on signomial optimization,” has been accepted for publication in the SIAM Journal on Applied Algebra and Geometry. Our accepted version (sans SIAM copy editing) will go up on arXiv soon.
  • March 10, 2022: I led the release of CVXPY version 1.2.
  • Feb 9, 2022: Sublinear circuits and the constrained signomial nonnegativity problem, my joint work with Helen Naumann and Thorsten Theobald, has been published online by Mathematical Programming. (Open access.)
  • July 2nd, 2021: the last major component of my PhD work, “Algebraic perspectives on signomial optimization,” has gone live on arXiv!
  • June 11th, 2021: I received the Amori Doctoral Prize in Computing and Mathematical Sciences. You can find the final version of my thesis here (or jump straight to the PDF).
  • May 13th, 2021: I successfully defended my thesis!
  • January 2021: I’ve accepted an offer for a postdoc with Jim Demmel and Michael Mahoney. Starting in July I’ll have a dual appointment with UC Berkeley and ICSI, where I’ll be working on the randomized numerical linear algebra aspects of BALLISTIC.
  • December 20, 2020: my first journal submission in grad school, “Newton Polytopes and Relative Entropy Optimization,” has been accepted for publication in Foundations of Computational Mathematics.
  • November 9, 2020: my paper with Helen and Thorsten has been revised, and is available on arXiv under a new title “Sublinear Circuits and the Constrained Signomial Nonnegativity Problem.” This revision is more accessible, addresses insights for computational optimization, and improves one result.
  • August 19, 2020: I gave a remote presentation on “The X-circuits Behind Conditional SAGE Certificates” to the De Loera Group at UC Davis. Refer to my research page for slides.
  • August 11, 2020: my paper which introduced conditional SAGE certificates has been accepted to the  journal Mathematical Programming Computation.
  • June 15, 2020: Helen Naumann, Thorsten Theobald, and I have finished our paper “The X-circuits Behind Conditional SAGE Certificates.”
  • April 17, 2020: I gave a recorded talk on signomial optimization and “conditional SAGE relaxations” through MIT’s Virtual Seminar on Optimization and Related Areas. See the website’s research tab for more information.
  • December 2019: After two years of steady contributions, I’ve joined as the third member of CVXPY‘s core development team.
  • November 2019: my Facebook internship work on robust market equilibrium was accepted to AAAI 2020. Oral presentation given by coauthor Christian Kroer.
  • September – October 2019: I worked at the Max Planck Institute for Mathematics in the Sciences (MPI MiS) in Leipzig, Germany, as a visiting researcher in Bernd Sturmfels’ nonlinear algebra group.
  • August 2019: I organized ICCOPT sessions on sparse polynomial optimization (presentations by Venkat Chandrasekaran, Jie Wang, and Henning Seidler), and signomial optimization and log-log convexity (presentations by Berk Orztuk, myself, and Akshay Agarwal).
  • June 2019: as part of the SIAM Conference on Applied Algebraic Geometry, I presented my work on “conditional SAGE certificates” for signomial and polynomial nonnegativity.
  • May 2019: I gave a recorded talk on SAGE signomials and polynomials at the Banff International Research Station in Canada.
  • June – September 2019: I interned at Facebook’s division of Core Data Science, under the supervision of Parikshit Shah.

Riley Murray on ResearchGate

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