7 problems

Vanishing Einstein functional conjecture. The Einstein spectral functional vanishes.

Constant-term spectral-action conjecture. The constant term of the spectral action of $\mathcal{D}_A$ on the noncommutative $n$-torus is proportional to the constant term of the sp…

Let $L_{CM}={\mathbb Z}+\tau_D{\mathbb Z}$ be a lattice with complex multiplication by the ring of integers in the imaginary quadratic field ${\mathbb Q}(\sqrt{-D})$. Let…

Let $p$ be a prime with $p=3\pmod 4$, let ${\cal E}(p)={\cal E}_{CM}^{(-p,1)}$ be the associated $\mathbb Q$-curve, and let $h_K$ be the class number of the relevant imaginary quad…

Let ${\cal E}_{CM}^{(-D,f)}$ be an elliptic curve with complex multiplication by the order of conductor $f$ in the imaginary quadratic field, and let ${\cal A}_{RM}^{(D,f)}$ be the…

Let $A_\theta$ be a noncommutative torus with smooth subalgebra $A_\theta^\infty$, and let $\varphi_A$ be the $*$-automorphism defined by … where…

Let $E_{CM}$ be an elliptic curve with complex multiplication, let ${\theta}_{E_{CM}}$ be the real quadratic irrational associated with $E_{CM}$, and let…