  A characteristic feature of a superconductor made of multiple condensates is
the possibility of the shape resonances in superconducting gaps. Shape
resonances belong to class of Fano resonances in configuration interaction
between open and closed scattering channels. The Shape resonances arise because
of the exchange interaction, a Josephson-like term, for transfer of pairs
between different condensates in different Fermi surface spots in the special
cases where at least one Fermi surface is near a 2.5 Lifshitz topological
transition. We show that tuning the shape resonances show first, the gap
suppression (like a Fano anti-resonance) driven by configuration interaction
between a BCS condensate and a BEC-like condensate, and second, the gap
amplification (like a Fano resonance) driven by configuration interaction
between BCS condensates in large and small Fermi surfaces. Shape resonances
usually occur in granular nanoscale complex matter (called superstripes)
because of the lattice instability near a 2.5 Lifshitz transition in presence
of interactions. Using a new imaging method, scanning nano-X-ray diffraction,
we have shown the generic formation in high temperature superconductors of a
granular superconducting networks made of striped puddles formed by ordered
oxygen interstitials or ordered local lattice distortions (like static short
range charge density waves). In the superconducting puddles the chemical
potential is tuned to a shape resonance in superconducting gaps and the maximum
Tc occurs where the puddles form scale free superconducting networks.
