Joshua Grochow

  • Assistant Professor of Computer Science
  • Ph. D. University of Chicago, 2012

Research interests:

Theoretical computer science, group theory, representation theory, algebraic geometry

Research:

My research has two main thrusts (with deep underlying relations beneath):

  1. Interactions between theoretical computer science and mathematics (particularly algebraic geometry, representation theory, and group theory). In particular, this currently involves studying orbit closures of algebraic groups, using representations of finite groups and additive combinatorics to study algorithms for matrix multiplication, and studying representation theory and group cohomology in the context of algorithms for finite group (and graph, and other structures) isomorphism.
  2. Developing the rigorous mathematical theory of complex systems and complex networks, and applying this theory with my collaborators in a variety of fields, such as ecology, evolutionary biology, economics, climate, and beyond. I'm always looking for new problems that need new theory!

Select Publications:

  • Bull. AMS 56(1):29-64, 2019.
  • With T. Pitassi. Journal of the ACM, 65(6), Article No. 37, November 2018. Preliminary version in FOCS '14.
  •  With K. D. Mulmuley and Y. Qiao. Appeared in ICALP '16, submitted for journal publication. Preprint arXiv:1605.02815
  • . Open access. Computational Complexity, Special Issue, 24(2):393-475, 2015.
  •  With Y. Qiao. Preprint arXiv:1507.01917
  •  With J. Blasiak, T. Church, H. Cohn, and C. Umans. Preprint arXiv:1712.02302
  • . With J. Blasiak, T. Church, H. Cohn, E. Naslund, W. Sawin, and C. Umans. Discrete Analysis 2017:3.
  •  With C. Moore. Preprint arXiv:1612.01527