4 problems

The apparent-singularity conjecture for the associated third-order ODE
Apparent-singularity conjecture. The point $0$ is an apparent singularity if and only if $B=D_0=D=0$ ; equivalently, this polynomial system has only the trivial solution $B=D_0=D=0$ …
openFrom papersapparent-singularities ordinary-differential-equations toda-systems
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6
The non-degeneracy conjecture for solutions of the non-critical $SU(3)$ Toda system
Non-degeneracy conjecture. Except for finitely many $\tau$ modulo the $SL(2,\mathbb{Z})$ action, every solution of the Toda system is non-degenerate. If true, this would support th…
openFrom paperselliptic-pdes non-degeneracy toda-systems
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6
The Bruhat trajectory conjecture for non-split real forms
Bruhat trajectory conjecture. There exist trajectories connecting $w$ and $w'$ if and only if the corresponding elements are comparable in Bruhat order. In that case, the space of…
openFrom papersbruhat-order real-forms toda-systems
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8
The phase-portrait conjecture for generalized full symmetric Toda systems
Phase-portrait conjecture. The phase picture of the Toda system coincides with the Bruhat order on the corresponding Weyl group: stationary points correspond bijectively to Weyl-gr…
openFrom papersbruhat-order integrable-systems toda-systems
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3

The apparent-singularity conjecture for the associated third-order ODE