Five talks on this two-day programme sit directly on top of open questions in the dm³ work. Two of them — Landim and Faria — are closer to it than anything on the Bienal programme.
Interacting particle systems and the n-bonacci chains
The DNLS work builds discrete nonlinear Schrödinger chains on tribonacci and tetrabonacci substitution sequences, and measures a localisation transition by finite-size scaling — IPR against λ, α against N, saturation times against N. The whole apparatus is empirical: run the chain, fit the exponent.
Stability, delay, and the asymmetric basin
The dm³ inner boundary fails at r★ = 0.77594059 rather than at Grönwall's
2/3 because the coupling term 2(r−1)e⁻ᶻ is sign-aware: it behaves
differently above and below r = 1. A symmetric Lyapunov argument cannot see that.
Ricci flow and the curvature operator
The operator chain G = U ∘ F ∘ K ∘ C treats K as curvature: the stage that
constrains which configurations remain available, with a verified bound
κ* ≤ √(7/9) ≈ 0.882. The framework's claim is that curvature removes options rather
than supplying a drive — form is what the constraints permit.
Continued fractions, again — and a second chance
He speaks at both conferences. The tribonacci constant η ≈ 1.8393 anchors the
criticality threshold in the DNLS chapter; whether that threshold is really a statement about
rational approximation is the sharpest open question in the series.
Algebra and the operator chain
Volume I is an operator algebra: g-, L-, R- and U-operator families, a compositional grammar,
and a claim that G applied to itself has a fixed point. It was written by someone
doing dynamics, not representation theory.
Numerics
Everything sharp in this project rests on DOP853 integration at high precision, and everything symmetric rests on a PDE-style estimate that turns out to be blunt. Those are the two talks where the numerical-analysis and symmetry-breaking questions live respectively.
What is not claimed
dm³ is a toy system. It has an explicit closed form, one attracting limit cycle, and a basin whose inner edge has been located numerically to eight digits and not proved. The Lean development verifies the surrounding structure — eigenvalue, τ = 2, ε₀ = 1/3, the singularity classification — and states the basin result only as an existence claim over the interval (2/3, 1), which is far weaker than the number suggests. Nothing here needs to be taken on faith: the integrator, the Lean files and the failing cases are all public.