Related papers: Mean field equations, hyperelliptic curves and mod…

Let $\mathcal{H}$ be a noncommutative regular projective curve over a perfect field $k$. We study global and local properties of the Auslander-Reiten translation $\tau$ and give an explicit description of the complete local rings, with the…

Modular symmetry offers the possibility to provide an origin of discrete flavour symmetry and to break it along particular symmetry preserving directions without introducing flavons or driving fields. It is also possible to use a weighton…

Let $H_k$ be the set of all normalized primitive holomorphic cusp forms of even integral weight $k\geq 2$ for the full modular group $SL(2, \mathbb{Z})$, and let $j\geq 3$ be any fixed integer. For $f\in H_k$, we write $\lambda_{{\rm{sym}^j…

Let $\eta$ be a closed real 1-form on a closed Riemannian $n$-manifold $(M,g)$. Let $d_z$, $\delta_z$ and $\Delta_z$ be the induced Witten's type perturbations of the de~Rham derivative and coderivative and the Laplacian, parametrized by…

In this paper we study the modular differential equation $y''+s\,E_4\, y=0$ where $E_4$ is the weight 4 Eisenstein series and $s=\pi^2r^2$ with $r=n/m$ being a rational number in reduced form such that $m\geq 7$. This study is carried out…

It is known that the L-function of an elliptic curve defined over Q is given by the Mellin transform of a modular form of weight 2. Does that modular form have anything to do with string theory? In this article, we address a question along…

Let $\bf{G}$ be the connected reductive group of type $E_{7,3}$ over $\mathbb{Q}$ and $\mathfrak{T}$ be the corresponding symmetric domain in $\mathbb{C}^{27}$. Let $\Gamma=\bf{G}(\mathbb{Z})$ be the arithmetic subgroup defined by Baily. In…

Let $K/\mathbf{Q}_p$ be a finite unramified extension, $\overline{\rho}:\mathrm{Gal}(\overline{\mathbf{Q}}_p/K)\rightarrow\mathrm{GL}_n(\overline{\mathbf{F}}_p)$ a continuous representation, and $\tau$ a tame inertial type of dimension $n$.…

We study M-theory on a Calabi-Yau fourfold with a smooth surface $S$ of $A_{N-1}$ singularities. The resulting three-dimensional theory has a $\mathcal{N}=2$ $SU(N)$ gauge theory sector, which we obtain from a twisted dimensional reduction…

Many rationally parametrized elliptic modular equations are derived. Each comes from a family of elliptic curves attached to a genus-zero congruence subgroup $\Gamma_0(N)$, as an algebraic transformation of elliptic curve periods,…

The main goal of this paper is to classify $\ast$-module categories for the $SO(3)_{2m}$ modular tensor category. This is done by classifying $SO(3)_{2m}$ nimrep graphs and cell systems, and in the process we also classify the $SO(3)$…

We build a bijection between the set $\sttilt\Lambda$ of isomorphism classes of basic support $\tau$-tilting modules over the Auslander algebra $\Lambda$ of $K[x]/(x^n)$ and the symmetric group $\mathfrak{S}_{n+1}$, which is an…

Mock modular forms have their origins in Ramanujan's pioneering work on mock theta functions. In a 1975 paper, Zagier proved certain transformation properties of the generating function of the Hurwitz class numbers $H(n)$ for the…

We examine extensions of the Standard Model (SM), basing our assumptions on what has already been observed; we don't consider anything fundamentally different, such as grand unification or supersymmetry, which is not directly suggested by…

The novel measurements of the $\gamma^\ast N \to \Delta(1232)$ Coulomb quadrupole form factor in the range $Q^2=0.04$--0.13 GeV$^2$ changed the trend of the previous data. With the new data the electric and Coulomb form factors are both in…

With the aid of the exponentiation functor and Fourier transform we introduce a class of modules $T(g,V,S)$ of $\mathfrak{sl} (n+1)$ of mixed tensor type. By varying the polynomial $g$, the $\mathfrak{gl}(n)$-module $V$, and the set $S$, we…

We study the semilinear elliptic equation --$\Delta$u + g(u)$\sigma$ = $\mu$ with Dirichlet boundary condition in a smooth bounded domain where $\sigma$ is a nonnegative Radon measure, $\mu$ a Radon measure and g is an absorbing…

We construct a new $N=4$ non-semisimple gauged supergravity in three dimensions with $E_{6(2)}/SU(6)\times SU(2)$ scalar manifold and $SO(4)\ltimes \mathbf{T}^6$ gauge group. Depending on the values of the gauge coupling constants, the…

The phase diagram at zero temperature of a lattice SU(2) scalar-fermion model in (2+1) dimensions is studied numerically and with Mean-Field methods. Special attention is devoted to the strong coupling regime. We have developed a new method…

For a flag manifold $M=G/B$ with the canonical torus action, the $T-$equivariant cohomology is generated by equivariant Schubert classes, with one class $\tau_u$ for every element $u$ of the Weyl group $W$. These classes are determined by…