3 problems

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Treves' conjecture on analytic hypoellipticity of sums of squares
Treves' conjecture. The operator $P$ is analytic hypoelliptic if and only if every stratum in the above-described Poisson–Treves stratification is symplectic.
Conjectureopenanalytic-hypoellipticity partial-differential-equations sums-of-squaresarXiv posted 2 days ago
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Existence conjecture for nonlinear eigenvalues of homogeneous elliptic polynomials
Existence conjecture. The equation
Conjectureopenanalytic-hypoellipticity nonlinear-eigenvalue-problems semiclassical-analysisarXiv posted 2 days ago
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Treves' conjecture on characteristic curves and analytic hypoellipticity
Treves' characteristic-curve conjecture. If $\operatorname{Char}(P)$ contains such a smooth curve, then $P$ might not be analytic hypoelliptic.
Conjectureopenanalytic-hypoellipticity partial-differential-equations symplectic-geometryarXiv posted 2 days ago

Treves' conjecture on analytic hypoellipticity of sums of squares