Related papers: Modular Zeros

This paper proves some results on negative gradient dynamics of Morse functions on Hilbert manifolds. It contains the compactness of flow lines, manifold structures of certain compacti- fied moduli spaces, orientation formulas, and CW…

We characterize all logarithmic, holomorphic vector-valued modular forms which can be analytically continued to a region strictly larger than the upper half-plane.

We consider compactifications of the space of triples of distinct points in projective $n$-space. One such space is a singular variety of configurations of points and lines; another is the smooth compactification of Fulton and MacPherson;…

We give an algebraic construction of the moduli space of irregular singular connections of generic ramified type on a smooth projective curve. We prove that the moduli space is smooth and give its dimension. Under the assumption that the…

We survey the theory of vector-valued modular forms and their connections with modular differential equations and Fuchsian equations over the three-punctured sphere. We present a number of numerical examples showing how the theory in…

The recent results of the Planck experiment put a stringent constraint on the sum of the light neutrino masses, m1+m2+m3 < 0.23 eV (95 % CL). On the other hand, two-zero Majorana mass matrix textures predict strong correlations among the…

Let $M_k^!(\Gamma_0^+(3))$ be the space of weakly holomorphic modular forms of weight $k$ for the Fricke group of level $3$. We introduce a natural basis for $M_k^!(\Gamma_0^+(3))$ and prove that for almost all basis elements, all of their…

There are many conceivable possibilities of embedding the MSSM in string theory. These proceedings describe an approach which is based on grand unification in higher dimensions. This allows one to obtain global string-derived models with…

We describe the moduli spaces of meromorphic connections on trivial holomorphic vector bundles over the Riemann sphere with at most one (unramified) irregular singularity and arbitrary number of simple poles as Nakajima's quiver varieties.…

Vacuum structure of a quantum field theory is a crucial property. In theories with extended symmetries, such as supersymmetric gauge theories, the vacuum is typically a continuous manifold, called the vacuum moduli space, parametrized by…

We discuss massless and massive neutrino zero modes in the background of an electroweak string. We argue that the eventual absence of the neutrino zero mode implies the existence of topologically stable strings where the required…

Composite rigging systems, involving membranes that meet on strings that meet on monopoles, arise naturally by the Kibble mechanism as topological defects in field theories involving spontaneous symmetry breaking. Such systems will tend to…

The zero-signature Killing metric of a new, real-valued, 8-dimensional gauging of the conformal group accounts for the complex character of quantum mechanics. The new gauge theory gives manifolds which generalize curved, relativistic phase…

In this paper, some properties on weighted modulation and Wiener amalgam spaces are characterized by the corresponding properties on weighted Lebesgue spaces. As applications, sharp conditions for product inequalities, convolution…

We introduce moduli spaces of colored graphs, defined as spaces of non-degenerate metrics on certain families of edge-colored graphs. Apart from fixing the rank and number of legs these families are determined by various conditions on the…

The dimming of Type Ia supernovae could be the result of Hubble-scale inhomogeneity in the matter and spatial curvature, rather than signaling the presence of a dark energy component. A key challenge for such models is to fit the detailed…

Let $M_k^\sharp(N)$ be the space of weakly holomorphic modular forms for $\Gamma_0(N)$ that are holomorphic at all cusps except possibly at $\infty$. We study a canonical basis for $M_k^\sharp(2)$ and $M_k^\sharp(3)$ and prove that almost…

We construct coarse moduli spaces of semiquasihomogeneous hypersurface singularities with respect to right equivalence and contact equivalence. We have to fix the principal part of the semiquasihomogeneous singularities. For the moduli…

Gradient vector fields are fundamental objects from both theoretical and practical perspectives, since various phenomena can be modeled within this framework. The ``moduli space'' of such vector fields provides the foundation for describing…

We show how to realize two-zero textures of the Majorana neutrino mass matrix $M_\nu$ based on modular $A_4$ invariant models without flavons. In these models, all matter fields are assigned to three inequivalent singlets, ${\bf 1}$, ${\bf…