6 problems

Koch–Tataru endpoint conjecture. The natural bound

For each randomly distributed $N\times N$ matrix, let $P_n$ denote its spectral projections and consider the logarithms of their norms, sorted increasingly. Form the covariance mat…

For randomly generated tridiagonal $N\times N$ matrices, let ${\cal P}_{50}$ denote the value below which $50\%$ of the instability indices lie, where the instability index is the…

Hermite spectral projection estimate. For $(1/p,1/q)\in {\mathlarger{\square}}$, the estimate

Let $(M,omega)$ be a closed quantizable symplectic manifold, let $(\mathcal H_n,T_n)$ be a BerezinToeplitz quantization with $\dim \mathcal H_n\to\infty$, and let…

Let $T$ be a self-adjoint operator and let $D(\lambda)$ denote the difference of the spectral projections associated with $T$ and a rank-one perturbation, as in Proposition 3. The…