Minimization of $L^4$-$L^2$ norms quotient for polarizations
After recalling some motivations from physics, I will present a
simple optimization problem for sections of ample line bundles on complex tori. It is naturally expressed in terms of theta functions and has connections with the geometry of modular forms in the Siegel upper half-space. Beside stating the general problem(s), some improvements of known results and new observations will be given.