Publications
5000 Years of Modern Programming
Online book
A Quarto e-book on the Curry-Howard-Lambek correspondence, logic, programs, and diagrams.
Linear Data
Online book
A free online textbook and course connecting linear algebra and data science.
Categorification of characteristic structures
Forum of Mathematics, Sigma (to appear)
Tensor Isomorphism by conjugacy of Lie algebras
J. Algebra 604 (2022) 790-807
Subgroups of simple groups are as diverse as possible
Bulletin LMS, 54 (1) 2022
Group isomorphism is nearly-linear time for most orders
Proc. IEEE Symp. on Found. Comp. Sci (FOCS) 2022, 457-467
Improved Algorithms for Alternating Matrix Space Isometry: from Theory to Practice
European Symposium on Algorithms (ESA2020)
The threshold for subgroup profiles to agree is log n-2
Theory of Computing, Vol. 15, pp. 1–25, 2019
Exact sequences of inner automorphisms of tensors
J. Algebra 545 (2019) 43-65
Isomorphism testing of groups of cube-free order
J. Algebra 545 (2019) 174-197
Isomorphism testing of Graded algebras
Trans. Amer. Math. Soc. 372 (11) 2019, 8067–8090
On automorphisms of groups, rings, and algebras
Comm. Algebra, 45 (2017) no. 4, 1452-1478
Earlier Works
More characteristic subgroups, Lie rings, and isomorphism tests for p-groups
J. Group Theory 16 6 (2013) 875-897
Division, adjoints, and dualities of bilinear maps
Communications in Algebra 41 11 (2013) 3989-4008
Optimal Gram-Schmidt type algorithms
Linear Algebra and Its Applications 438 (2013) 4573-4583
Existence, algorithms, and asymptotics of direct product decompositions, I
Groups - Complexity - Cryptology 4 (2012), 33-72
Isomorphism in expanding families of indistinguishable groups
Groups - Complexity - Cryptology 4 (2012) 73-110
On linear-size reductions and completeness
Preprints & arXiv Papers
Isomorphism Invariant Metrics
A spectral theory for transverse tensor operators
A Frobenius-Schreier-Sims Algorithm to tensor decompose algebras
Polynomial-time isomorphism testing of groups of most finite orders
Existence, algorithms, and asymptotics of direct product decompositions, II
Discovering tensor structures by non-associative algebra
Characteristic structure as splitting categories
Efficiently Computing with categories and high-order structures
Isomorphism Testing through higher categories
A representation theory of bilinear maps
Projects in Development
Group isomorphism is tied up in knots
NP-completeness as a method of counting
On indecomposable p-groups
Parallel algorithms for rings
Sylow subgroups in solvable matrix groups