Related papers: Modular Parametrization as Polyakov Path Integral:…
Highest-weight representations of infinite dimensional Lie algebras and Hilbert schemes of points are considered, together with the applications of these concepts to partition functions, which are most useful in physics. Partition functions…
Given a projective smooth curve $X$ over any field $k$, we discuss two notions of global $\mathbb{A}^1$ degree of a finite morphism of smooth curves $f: X \to \mathbb{P}^1_k$ satisfying certain conditions. One originates from computing the…
We say that a normalized modular form is of CM type modulo $\ell$ by an imaginary quadratic field $K$ if its Fourier coefficients $a_p$ are congruent to $0$ modulo a prime $\mathcal L\mid \ell$ for every prime $p$ that is inert in $K$. In…
We introduce a notion of generalized modular functors with Hilbert spaces of infinite dimension in general, and show that a generalized modular functor with data of conformal dimensions determines uniquely wave functions as its flat…
We study the holomorphic projection of mixed mock modular forms involving sesquiharmonic Maass forms. As a special case, we numerically express the holomorphic projection of a function involving real quadratic class numbers multiplied by a…
The authors have recently shown how direct limits of Hilbert spaces can be used to construct multi-resolution analyses and wavelets in $L^2(\R)$. Here they investigate similar constructions in the context of Hilbert modules over…
Let O_K be a discrete valuation ring with field of fractions K and perfect residue field. Let E be an elliptic curve over K, let L/K be a finite Galois extension and let O_L be the integral closure of O_K in L. Denote by X' the minimal…
We consider a variation of the Mahler measure where the defining integral is performed over a more general torus. We focus our investigation on two particular polynomials related to certain elliptic curve $E$ and we establish new formulas…
We construct symmetric square type $L$-series for vector-valued modular forms transforming under the Weil representation associated to a discriminant form. We study Hecke operators and integral representations to investigate their…
By employing the symmetries of the underlying conformal field theory, the tree-level K\"ahler potentials for untwisted moduli of the heterotic string compactifications on orbifolds with continuous Wilson lines are derived. These symmetries…
Given an orthogonal bundle $E$ over a smooth projective curve $X$ we define a Hecke transformation in the moduli space of orthogonal bundles by performing an elementary transformation with respect to a Lagrangian submodule $L \subset…
We present an algorithm to determine if the $L$-series associated to an automorphic representation and the one associated to an elliptic curve over an imaginary quadratic field agree. By the work of Harris-Soudry-Taylor, Taylor and…
The geometric Langlands correspondence for complex algebraic curves differs from the original Langlands correspondence for number fields in that it is formulated in terms of sheaves rather than functions (in the intermediate case of curves…
We first give an exposition of how the Polyakov path integral for the bosonic string produces a natural mapping class group invariant measure, $d(Poly)$, on the Teichm\"uller space of Riemann surfaces of each fixed genus. The description of…
Given a modular form f of even weight larger than two and an imaginary quadratic field K satisfying a relaxed Heegner hypothesis, we construct a collection of CM cycles on a Kuga-Sato variety over a suitable Shimura curve which gives rise…
Two dimensional adelic objects were introduced by I. Fesenko in his study of the Hasse zeta function associated to a regular model $\mathcal E$ of the elliptic curve $E$. The Hasse-Weil $L$-function $L(E,s)$ of $E$ appears in the…
The specializations of the motivic elliptic polylog are called motivic Eisenstein classes. For applications to special values of L-Functions, it is important to compute the realizations of these classes. In this paper, we prove that the…
We review a proof of the well know result stating that moduli spaces of stable sheaves with fixed Chern character on a polarized $K3$ surface are deformations of a hyperk\"ahler variety of Type $K3^{[n]}$ (if a suitable numerical hypothesis…
Given a curve $C$ over a number field $K$ equipped with the action of a finite group $G$ by $K$-automorphisms, one obtains a factorisation of $L(C,s)$ into a product of $L$-functions of `motivic pieces of curves' associated to irreducible…
We provide an angular parametrization of the special unitary group $\textrm{SU}(2^{n})$ generalizing Euler angles for $\textrm{SU}(2)$ by successively applying the KAK decomposition. We then determine constraint equations for the parametric…