diff --git a/README.md b/README.md index 09be816..1a3356f 100644 --- a/README.md +++ b/README.md @@ -1,15 +1,20 @@ # Property(T) -[![Build Status](https://travis-ci.org/kalmarek/PropertyT.jl.svg?branch=master)](https://travis-ci.org/kalmarek/PropertyT.jl) +[![CI](https://github.com/kalmarek/PropertyT.jl/actions/workflows/ci.yml/badge.svg)](https://github.com/kalmarek/PropertyT.jl/actions/workflows/ci.yml) [![codecov](https://codecov.io/gh/kalmarek/PropertyT.jl/branch/master/graph/badge.svg)](https://codecov.io/gh/kalmarek/PropertyT.jl) This package is concerned with sum of squares decompositions in group rings of finitely presented groups. -Please have a look into [test](https://github.com/kalmarek/GroupRings.jl/blob/master/test/runtests.jl) directory to see how to use this package. For an example applications have a look at our papers: -[1703.09680](https://arxiv.org/abs/1703.09680), [1712.07167](https://arxiv.org/abs/1712.07167) and [1812.03456](https://arxiv.org/abs/1812.03456). +Please have a look into e.g. this [test](https://github.com/kalmarek/PropertyT.jl/blob/master/test/1712.07167.jl#L87) to see how this package can be used to prove Kazdhan Property (T) for a finitely presented group. For an example applications have a look at our papers: +* M. Kaluba and P.W. Nowak _Certifying numerical estimates for spectral gaps_ [1703.09680](https://arxiv.org/abs/1703.09680) +* M. Kaluba, P.W. Nowak and N. Ozawa *$Aut(F₅)$ has property (T)* [1712.07167](https://arxiv.org/abs/1712.07167), and +* M. Kaluba, D. Kielak and P.W. Nowak *On property (T) for $Aut(Fₙ)$ and $SLₙ(Z)$* [1812.03456](https://arxiv.org/abs/1812.03456). The package depends on - * [AbstractAlgebra](https://github.com/Nemocas/AbstractAlgebra.jl), - * [Groups](https://github.com/kalmarek/Groups.jl) - * [GroupRings](https://github.com/kalmarek/GroupRings.jl) - * [JuMP](https://github.com/JuliaOpt/JuMP.jl) - * [scs](https://github.com/JuliaOpt/SCS.jl) [solver](https://github.com/cvxgrp/scs) + * [`Groups.jl`](https://github.com/kalmarek/Groups.jl) for computations with finitely presented groups, + * [`SymbolicWedderburn.jl`](https://github.com/kalmarek/SymbolicWedderburn.jl) for symmetrizing the sum of squares relaxations of positivity problems, + * [`JuMP.jl`](https://github.com/JuliaOpt/JuMP.jl) for formulating the optimization problems, and + * [`SCS.jl`](https://github.com/JuliaOpt/SCS.jl) wrapper for the [`scs` solver](https://github.com/cvxgrp/scs), or + * [`COSMO.jl`](https://github.com/oxfordcontrol/COSMO.jl) solver to solve the problems. + + Certification of the results is done via `ℓ₁`-convexity of the sum-of-squares cone and our knowledge of its interior points. The certified computations use + * [`IntervalArithmetic.jl`](https://github.com/JuliaIntervals/IntervalArithmetic.jl)