Related papers: Computing Special $L$-Values of Certain Modular Fo…

We establish several refined strong multiplicity one results for paramodular cusp forms by using automorphic and Galois-theoretic methods. We also give an application to distinguishing eigenforms by the twisted central values of the spinor…

Metrics on Calabi-Yau manifolds are used to derive a formula that finds the existence of integer solutions to polynomials. These metrics are derived from an associated algebraic curve, together with its anti-holomorphic counterpart. The…

We study the limit of Calabi-Yau modular forms, and in particular, those resulting in classical modular forms. We then study two parameter families of elliptically fibred Calabi-Yau fourfolds and describe the modular forms arising from the…

We describe a simple class of type IIA string compactifications on Calabi-Yau manifolds where background fluxes generate a potential for the complex structure moduli, the dilaton, and the K\"ahler moduli. This class of models corresponds to…

We study modules over the algebroid stack $\W[\stx]$ of deformation quantization on a complex symplectic manifold $\stx$ and recall some results: construction of an algebra for $\star$-products, existence of (twisted) simple modules along…

The aim of this note is to treat one distinguished example of a Calabi--Yau variety that appears as a small resolution of a Picard modular variety

In the previous papers \cite{L1, L2} the author constructed Mabuchi and Aubin-Yau functionals over any complex surfaces and three-folds, respectively. Using the method in \cite{L2}, we construct those functionals over any complex manifolds…

Black holes in string theory compactified on Calabi-Yau varieties a priori might be expected to have moduli dependent features. For example the entropy of the black hole might be expected to depend on the complex structure of the manifold.…

By applying the property of Ext-symmetry and the affine space structure of certain fibers, we introduce the notion of weighted quantum cluster functions and prove their multiplication formulas associated to abelian categories with…

The moduli space of multiply-connected Calabi-Yau threefolds is shown to contain codimension-one loci on which the corresponding variety develops a certain type of hyperquotient singularity. These have local descriptions as discrete…

In this work we study the analytic properties of the standard L-function attached to Siegel-Jacobi modular forms of higher index, generalizing previous results of Arakawa and Murase. Furthermore, we obtain algebraicity results on special…

Recently proposed mechanism of the black hole condensation at conifold singularity in type II string is an interesting idea from which we can interpret the phase of the universal moduli space of the string vacua. It might also be expected…

The proof of Serre's conjecture on Galois representations over finite fields allows us to show, using a method due to Serre himself, that all rigid Calabi-Yau threefolds defined over Q are modular.

We study the arithmetic aspects of the finite group of extensions of abelian varieties defined over a number field. In particular, we establish relations with special values of L-functions and congruences between modular forms.

We review the applications of mirror symmetry to the study of the moduli spaces of two-dimensional conformal field theories with $N{=}(2,2)$ supersymmetry, particularly those constructed from Calabi--Yau manifolds. (Lecture delivered at the…

We prove a formula for the $\infty$-adic special $L$-value of abelian $t$-modules. This gives function field analogues of the class number formula. We also express it in terms of the extension groups of shtukas.

The first part of this paper discusses general procedures for finding numerical approximations to distinguished Kahler metrics, such as Calabi-Yau metrics, on complex projective manifolds. These procedures are closely related to ideas from…

This is the extended version of the paper "Special Lagrangian conifolds, I: Moduli spaces", which discusses the deformation theory of special Lagrangian (SL) conifolds in complex space C^m. Conifolds are a key ingredient in the…

When we describe string propagation on non-compact or singular Calabi-Yau manifolds by CFT, continuous as well as discrete representations appear in the theory. These representations mix in an intricate way under the modular…

We prove that the 4-dimensional Galois representations associated with a certain Calabi-Yau threefold are reducible, with 2-dimensional composition factors coming from specific modular forms of weights 2 and 4, both level 14. This was…