The " Hodge strings " construction of solutions to associativity equations is proposed. From the topological string theory point of view this construction formalizes the " integration over the position of the marked point " procedure for computation of amplitudes. From the mathematical point of view the " Hodge strings " construction is just a composition of elements of harmonic theory (known a...

We propose a number of techniques for learning a global ranking from data that may be incomplete and imbalanced — characteristics that are almost universal to modern datasets coming from e-commerce and internet applications. We are primarily interested in cardinal data based on scores or ratings though our methods also give specific insights on ordinal data. From raw ranking data, we construct ...

We prove several formulas related to Hodge theory and the Kodaira-SpencerKuranishi deformation theory of Kähler manifolds. As applications, we present a construction of globally convergent power series of integrable Beltrami differentials on Calabi-Yau manifolds, and use an iteration method to construct global canonical families of holomorphic (n, 0)-forms on the deformation spaces of Kähler ma...

We initiate a new approach to relative p-adic Hodge theory based on systematic use of Witt vector constructions and nonarchimedean analytic geometry in the style of Berkovich. In this paper, we give a thorough development of φ-modules over a relative Robba ring associated to a perfect Banach ring of characteristic p, including the relationship between these objects and étale Zp-local systems an...

3 Construction of BdR 4 3.1 Witt Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3.2 Lifting to a Perfect Ring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.3 Carrying Out the Lifts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.4 Final Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....

Sasakian manifolds are odd-dimensional counterpart to Kähler manifolds. They can be defined as contact equipped with an invariant structure on their symplectic cone. The quotient of this cone by the homothety action is a complex manifold called Vaisman. We study harmonic forms and Hodge decomposition Vaisman construct Lie superalgebra associated in same way supersymmetry algebra manifold. use c...

In the present paper, which is the third in a series of four papers, we study the theory surrounding the log-theta-lattice, a highly noncommutative two-dimensional diagram of “miniature models of conventional scheme theory”, called Θ±ellNF-Hodge theaters, that were associated, in the first paper of the series, to certain data, called initial Θ-data, that includes an elliptic curve EF over a num...