Abstract: We present our program of geometrizing cohomology on a totally disconnected space through the intrinsic Cantor function and the cohomological complex dimensions of the ternary Cantor set. The Cantor set is an uncountable, self-similar set of measure zero; yet beneath this apparent “dust” lies a remarkably rich geometry across scales. We show how cohomological […]

Abstract: Dirichlet’s 1837 proof of his theorem on primes in arithmetic progressions depended on the non-vanishing of L(1,\chi) for nonprincipal characters. The Birch and Swinnerton-Dyer conjecture relates the rank of an elliptic curve to the order of vanishing of its L-function at the central point. Determining whether an individual central value vanishes can be difficult, […]