Picture of Joshua A. Grochow Joshua A. Grochow
Omidyar Fellow
Santa Fe Institute

Office: C-4
Office phone: (505)-946-2789
Email: [first initial][lastname]@santafe.edu

About Me

I am an Omidyar Fellow at the interdisciplinary Santa Fe Institute; my "home discipline" is (theoretical) computer science. My research lies primarily at the intersection of theoretical computer science and mathematics—particularly algebraic geometry, representation theory, and group theory—but I am starting to branch out into more general complex systems and, thereby, more worldly pursuits such as biology, energy, and the environment (which I've been interested in for most of my career).

Prior to coming to the Santa Fe Institute, I was a postdoc in the University of Toronto CS Theory Group, and prior to that I got my Ph.D. at the University of Chicago.

What's new

(May 23, 2016) New paper posted: On cap sets and the group-theoretic approach to matrix multiplication. Joint with Jonah Blasiak, Thomas Church, Henry Cohn, and Chris Umans.

(May 11, 2016) Full version of Boundaries of VP and VNP now available as an arXiv preprint.

(April 27, 2016) "Boundaries of VP and VNP" accepted to ICALP 2016! Joint with Ketan Mulmuley and Youming Qiao.

(April 12, 2016) Story by Jennifer Ouellette on Dynamics of beneficial epidemics, and how we produced it in just 72 Hours of Science.

(April 12, 2016) Gave a CS colloquium at CU Boulder: "What makes individual problem instances hard? Computational complexity and complex systems." You can watch the video here.

(April 7, 2016) New paper posted: Dynamics of beneficial epidemics, joint with the Santa Fe Institute postdocs. This paper was the result of our "72 Hours of Science" event, in which we conceived, developed, executed, and wrote up an entire scientific project in only 72 hours (albeit with a team of 14 postdocs)! See the Appendix of the paper for a little more detail. Comments and suggestions are more than welcome.

(March 29, 2016) Gave a talk at the UW CS Theory Seminar: Combinatorial polytopes in algebraic and geometric complexity theory, about this paper and a forthcoming paper with Ketan Mulmuley and Youming Qiao.

(December 20, 2015) Quoted several times in a WIRED front-page article by Erica Klarreich about the recent breakthrough on Graph Isomorphism (reprinted from Quanta).

(November 3, 2015) Updated Monotone projection lower bounds from extended formulation lower bounds with new lower bound against reductions from perfect matchings in general graphs to perfect matchings in bipartite graphs.

(October 29, 2015) New paper posted: Network structure at multiple scales via a new network statistic: the onion decomposition, joint with Laurent Hébert-Dufresne and Antoine Allard.

(October 28, 2015) New paper posted: Monotone projection lower bounds from extended formulation lower bounds.

(October 12-16, 2015) Organized the SFI Workshop on Wildness in Computer Science, Physics, and Mathematics.

(October 8, 2015) New paper posted: Graph isomorphism and circuit size, joint with Eric Allender and Cris Moore.

(October 1, 2015) Eric Allender gave a great 15-minute talk at the Simons Institute for the Theory of Computing on our most recent joint work with Cris Moore, "Graph Isomorphism and Circuit Size."

(August 31, 2015) Polynomial-time isomorphism test of groups that are tame extensions accepted to ISAAC 2015 (the leading conference on algorithms in (East) Asia).

(July 14, 2015) You can listen to my interview by @Samuel_Hansen for the Strongly Connected Components podcast. My segment starts at 40:45, but you should also listen to the preceding interviews with my colleagues Yoav Kallus and Sid Redner!

(July 7, 2015) New paper posted: Polynomial-time isomorphism test of groups that are tame extensions (joint w/ Youming Qiao).