Geometry and Analytic Theory of Semisimple Coalescent Frobenius Structures: an Isomonodromic approach to Quantum Cohomology and Helix structures in Derived Categories

In this Thesis we study geometrical and analytic aspects of semisimple points of Frobenius manifolds presenting a phenomenon of coalescence of canonical coordinates. Particular attention is given to the isomonodromic description of these resonances as well as to their (still conjectural) relationships with the derived geometry of Fano varieties.