4 problems

Conjecture. With an appropriate choice of local product codes, these complexes yield good locally testable codes (LTCs). Tensor products of projective Reed–Solomon codes are sugges…

Let $G$ be a definite Gross inner form, let $\mathcal{M}(G)$ be the set of $A$-shapes, and let $h(G,\varsigma;q)$ be the counting function defined from discrete global $A$-paramete…

Let $G$ be a definite Gross inner form and let $\mathfrak{p}$ be a finite place. Let $\{X_{\mathfrak{p}}(q)\}$ denote its family of congruence complexes. Density-Ramanujan conjectu…

Integer-cohomology conjecture. The dominant part of $H^1(\mathcal X;\bF_2)$ comes from the free part $\bZ^k\cong H^1(\mathcal X;\bZ)$ rather than the torsion part…