Problems

For an elliptic curve over the rational numbers, does the rank of its rational points equal the order of vanishing of its L-function at s = 1?

Must a simple directed graph with n vertices and minimum out-degree at least r ≥ 1 contain a directed cycle of length at most ⌈n/r⌉?

Can a fractional single-source flow be rounded to one path per terminal without increasing cost, while increasing each arc load by at most the largest demand?

Does every finite bridgeless loopless multigraph admit a collection of cycles that covers each edge exactly twice?

Is the maximum number of unit-distance pairs among n distinct planar points bounded by n^(1+o(1)) as n grows?

How small can P(S < E S + 1) be for a sum S of independent nonnegative random variables whose individual means are at most one?

If every positive power of a complex polynomial has zero Gaussian expectation, must its products with any fixed polynomial eventually have zero expectation?

On a smooth complex projective variety, is every rational Hodge class a rational linear combination of classes of algebraic cycles?

How small can gaps between consecutive primes be, infinitely often? In particular, is liminfₙ(pₙ₊₁ − pₙ) = 2?

Must every polynomial map F: ℂⁿ → ℂⁿ with a constant nonzero Jacobian determinant have a polynomial inverse?

Is there a universal upper bound on the Poincaré constant of every isotropic log-concave probability measure, independent of its dimension?

Is finding a best consensus ranking computationally hard even for exactly three voters?