Related papers: Efficient computation of BSD invariants in genus 2
Higher genus modular invariance of two-dimensional conformal field theories (CFTs) is a largely unexplored area. In this paper, we derive explicit expressions for the higher genus partition functions of a specific class of CFTs: code CFTs,…
We give an algorithm to compute a one-dimensional shape-constrained function that best fits given data in weighted-$L_{\infty}$ norm. We give a single algorithm that works for a variety of commonly studied shape constraints including…
Higher genus partition functions of two-dimensional conformal field theories have to be invariants under linear actions of mapping class groups. We illustrate recent results [4,6] on the construction of such invariants by concrete…
We introduce a new approach for computing the monodromy of the Hitchin map and use this to completely determine the monodromy for the moduli spaces of $L$-twisted $G$-Higgs bundles, for the groups $G = GL(2,\mathbb{C})$, $SL(2,\mathbb{C})$…
In this short note we organize a perturbation theory for the Bunch-Davies wavefunction in flat, accelerating cosmologies. The calculational technique avoids the in-in formalism and instead uses an analytic continuation from Euclidean…
In this paper we introduce a new class of extremal codes, namely the $i$-BMD codes. We show that for this family several of the invariants are determined by the parameters of the underlying code. We refine and extend the notion of an…
We conjecture a formula for the generating function of virtual $\chi_y$-genera of moduli spaces of rank 2 sheaves on arbitrary surfaces with holomorphic 2-form. Specializing the conjecture to minimal surfaces of general type and to virtual…
We give a complete factorization of the invariant factors of resultant matrices built from birational parameterizations of rational plane curves in terms of the singular points of the curve and their multiplicity graph. This allows us to…
Motivated by S-duality modularity conjectures in string theory, we define new invariants counting a restricted class of 2-dimensional torsion sheaves, enumerating pairs $Z\subset H$ in a Calabi-Yau threefold X. Here H is a member of a…
Braid monodromy is an important tool for computing invariants of curves and surfaces. In this paper, the \emph{rectangular braid diagram (RBD)} method is proposed to compute the braid monodromy of a completely reducible $n$-gonal curve,…
A novel algebraic method for finding invariant algebraic curves for a polynomial vector field in $\mathbb{C}^2$ is introduced. The structure of irreducible invariant algebraic curves for Li\'{e}nard dynamical systems $x_t=y$,…
In 1998 Don Zagier introduced the modified Bernoulli numbers $B_{n}^{*}$ and showed that they satisfy amusing variants of some properties of Bernoulli numbers. In particular, he studied the asymptotic behavior of $B_{2n}^{*}$, and also…
New Completely Integrable (2+1)-System is studied. It is based on the so-called L-A-B-triples $L_t=[H,L]-fL$ where L is a 2D Schrodinger Operator. This approach was invented by S.Manakov and B.Dubrovin, I.Krichever, S.Novikov(DKN) in the…
This paper presents the classification, over the fields of real and complex numbers, of the minimal ${\mathbb Z}_2\times{\mathbb Z}_2$-graded Lie algebras and Lie superalgebras spanned by $4$ generators and with no empty graded sector. The…
New methods for computing parametric local $b$-functions are introduced for $\mu$-constant deformations of semi-weighted homogeneous singularities. The keys of the methods are comprehensive Gr\"obner systems in Poincar\'e-Birkhoff-Witt…
We prove a substantial part of conjectures of Mazur and Tate that refine the conjecture of Birch and Swinnerton-Dyer. Our approach, which also leads to some results even finer than the predictions of Mazur and Tate, is via the `rank-zero…
For any arbitrary algebraic curve, we define an infinite sequence of invariants. We study their properties, in particular their variation under a variation of the curve, and their modular properties. We also study their limits when the…
The lambda calculus is a widely accepted computational model of higher-order functional pro- grams, yet there is not any direct and universally accepted cost model for it. As a consequence, the computational difficulty of reducing lambda…
We propose to generalize the work of R\'egis Dupont for computing modular polynomials in dimension $2$ to new invariants. We describe an algorithm to compute modular polynomials for invariants derived from theta constants and prove under…
In this article we develop a graphical calculus for stable invariants of Riemannian manifolds akin to the graphical calculus for Rozansky-Witten invariants for hyperk\"ahler manifolds; based on interpreting trivalent graphs with colored…