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Property(T)
This package is concerned with sum of squares decompositions in group rings of finitely presented groups. Please have a look into e.g. this test 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
- M. Kaluba, P.W. Nowak and N. Ozawa
Aut(F₅)
has property (T) 1712.07167, and - M. Kaluba, D. Kielak and P.W. Nowak On property (T) for
Aut(Fₙ)
and $SLₙ(Z)$ 1812.03456.
The package depends on
Groups.jl
for computations with finitely presented groups,SymbolicWedderburn.jl
for symmetrizing the sum of squares relaxations of positivity problems,JuMP.jl
for formulating the optimization problems, andSCS.jl
wrapper for thescs
solver, orCOSMO.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