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06/28/2023
On the complexity of isomorphism problems for tensors, groups, and polynomials IV: linear-length reductions and their applications
Many isomorphism problems for tensors, groups, algebras, and polynomials...
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06/05/2023
On the complexity of isomorphism problems for tensors, groups, and polynomials III: actions by classical groups
We study the complexity of isomorphism problems for d-way arrays, or ten...
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12/26/2022
On linear-algebraic notions of expansion
A fundamental fact about bounded-degree graph expanders is that three no...
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06/09/2022
Connections between graphs and matrix spaces
Given a bipartite graph G, the graphical matrix space 𝒮_G consists of ma...
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10/03/2021
The isomorphism problem for plain groups is in Σ_3^𝖯
Testing isomorphism of infinite groups is a classical topic, but from th...
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09/14/2021
Symbolic determinant identity testing and non-commutative ranks of matrix Lie algebras
One approach to make progress on the symbolic determinant identity testi...
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12/02/2020
Average-case algorithms for testing isomorphism of polynomials, algebras, and multilinear forms
We study the problems of testing isomorphism of polynomials, algebras, a...
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06/30/2019
Isomorphism problems for tensors, groups, and cubic forms: completeness and reductions
In this paper we consider the problems of testing isomorphism of tensors...
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06/11/2019
General Linear Group Action on Tensors: A Candidate for Post-Quantum Cryptography
Starting from the one-way group action framework of Brassard and Yung (C...
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05/06/2019
Incorporating Weisfeiler-Leman into algorithms for group isomorphism
In this paper we combine many of the standard and more recent algebraic ...
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04/08/2019
From independent sets and vertex colorings to isotropic spaces and isotropic decompositions
In the 1970's, Lovász built a bridge between graphs and alternating matr...
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10/24/2017
On the Polynomial Parity Argument Complexity of the Combinatorial Nullstellensatz
The complexity class PPA consists of NP-search problems which are reduci...
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08/11/2017
Algorithms based on *-algebras, and their applications to isomorphism of polynomials with one secret, group isomorphism, and polynomial identity testing
We consider two basic algorithmic problems concerning tuples of (skew-)s...
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07/07/2017