5 problems

Fix $Q=12$ and consider the Hessian of … where $\ell_Q$ is chosen so that the regular $N$-gon is a critical point. Restrict to eigenvectors orthogonal to the gradient of the area;…

Let $(X,\mathsf{d},\mathfrak{m})$ be a compact $\operatorname{RCD}(K,N)$ space with Hausdorff dimension $\beta$. Singular Weyl law conjecture. The limit … is the Hausdorff measure…

Annealed heat-kernel exponent conjecture. The lower-bound exponent is $\theta_1=\frac{d_w-1}{\kappa d_w-1}=\frac{32}{45}$, and this is also the correct value of the upper-bound exp…

In the holographic computation of the Weyl anomaly for four-dimensional conformal higher-spin fields, let $\hat{b}_4$ denote the third heat-kernel coefficient, and let the heat-ker…

Let $d=1$, let $t_0>0$, and take Gaussian initial data … Let $u_k(x,t)$ denote the approximation in one spatial dimension, and let $u(x,t)$ be the corresponding solution. Kim–Ni's…