Gaussian noise sensitivity and Fourier tails

Guy Kindler*, Ryan O'Donnell

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

17 Scopus citations

Abstract

We study the problem of matrix isomorphism of matrix Lie algebras (MatIsoLie). Lie algebras arise centrally in areas as diverse as differential equations, particle physics, group theory, and the Mulmuley - Sohoni Geometric Complexity Theory program. A matrix Lie algebra is a set L of matrices that is closed under linear combinations and the operation [A, B] = AB - BA. Two matrix Lie algebras L, L' are matrix isomorphic if there is an invertible matrix M such that conjugating every matrix in L by M yields the set L'. We show that certain cases of MatIsoLie - for the wide and widely studied classes of semi simple and abelian Lie algebras - are equivalent to graph isomorphism and linear code equivalence, respectively. On the other hand, we give polynomial-time algorithms for other cases of MatIsoLie, which allow us to mostly derandomize a recent result of Kayal on affine equivalence of polynomials.

Original languageAmerican English
Title of host publicationProceedings - 2012 IEEE 27th Conference on Computational Complexity, CCC 2012
Pages137-147
Number of pages11
DOIs
StatePublished - 2012
EventIEEE Computer Society Technical Committee on Mathematical Foundations of Computing - Porto, Portugal
Duration: 26 Jun 201229 Jun 2012

Publication series

NameProceedings of the Annual IEEE Conference on Computational Complexity
ISSN (Print)1093-0159

Conference

ConferenceIEEE Computer Society Technical Committee on Mathematical Foundations of Computing
Country/TerritoryPortugal
CityPorto
Period26/06/1229/06/12

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