Mathematics

Quantum Cohomology of a symplectic manifold X (or a smooth projective variety) is a family of deformations of its classical Cohomology ring H*(X), and it contains information about the enumerative geometry of X. After recalling basic notions of Gromov-Witten and Frobenius Manifolds Theories, we will focus on the locus of Small Quantum Cohomology of complex Grassmannians: the occurrence and frequency of a phenomenon of resonance (namely the coalescence of some Dubrovin canonical coordinates) will be studied. It will be shown that surprisingly this frequency is strictly subordinate and highly influenced by the distribution of prime numbers. Two equivalent formulations of the Riemann Hypothesis will be given in terms of numbers of non-coalescing complex Grassmannians.