Abstracts for Motivic structures on quantum cohomology and pencils of Calabi-Yau motives. Final reports

Subjects: Fano manifolds and their mirror dual pencils, maximally mutable Laurent polynomials, the first and second structure connections, gamma conjectures and the gamma class, drops in the images of monodromies in Landau-Ginzburg models, congruence Galois reps and congruence sheaves, Bloch-Kato classes and numerator/denominator of L-values, GSp_4 - Galois representations and paramodular non-lifts, hypergeometric families and weighted projective spaces, hypergeometric motives and their L-functions, extensions of Picard-Fuchs equations and subcritical L-valu

String theory amplitudes  are expressed as integral over a moduli
space of Riemann surface. The QFT is the degeneration limit of this.
I'll discuss how limitied Hodge structures are useful to bridge
between what we know in string theory and QFT.

Pencils of Calabi-Yau threefolds give rise to local systems and differential operators with very strong arithmetical properties. One interesting source of examples come from regularised quantum cohomology D-modules of Fano varieties. Although no classification is known, one may  hope to characerise and construct such operators  from  first principles.
I will describe joint work in progress with V. Golyshev and A.