4 problems

Thin-shell conjecture. The thin-shell constant is universally bounded:

KLS conjecture. The KLS constant satisfies

Let $\{d_{\ell}(m)\}$ be the sequence described above, and define the operator … A sequence is infinitely logconcave if $\mathfrak{L}^j(\{x_k\})$ is nonnegative for every…

Let $A_n(x)$ be the polynomial defined earlier in the paper, and let a sequence be infinite logconcave when every iterate of the operator $\mathfrak{L}$ produces a positive sequenc…