Related papers: Opers and nonabelian Hodge: numerical studies

In this paper, we consider compatible Hom-Leibniz algebra where the Hom map twists the operations in the compatible system. We consider a suitably graded Lie algebra whose Maurer-Cartan elements characterize the structure of compatible…

Using twistor methods we derive a generating function which leads to the hyperk\" ahler metric on a deformation of the Atiyah-Hitchin monopole moduli space. This deformation was first considered by Dancer through the quotient construction…

We conjecture an expression for the dimensions of the Khovanov-Rozansky HOMFLY homology groups of the link of a plane curve singularity in terms of the weight polynomials of Hilbert schemes of points scheme-theoretically supported on the…

It is observed that Kaygun's Hopf-Hochschild cochain complex for a module-algebra is a brace algebra with multiplication. As a result, (i) an analogue of Deligne's Conjecture holds for module-algebras, and (ii) the Hopf-Hochschild…

The algebraic conditions that specific gauged G/H-WZW model have to satisfy in order to give rise to Non-Abelian Toda models with singular metric with or without torsion are found. The classical algebras of symmetries corresponding to grade…

The universal enveloping algebra of any simple Lie algebra g contains a family of commutative subalgebras, called the quantum shift of argument subalgebras math.RT/0606380, math.QA/0612798. We prove that generically their action on…

We give a new proof of the Hodge conjecture for abelian fourfolds of Weil type with discriminant 1 and all of their powers. The Hodge conjecture for these abelian fourfolds was proven by Markman using hyperholomorphic sheaves on…

We make use of the cotangent complex formalism developed by Lurie to formulate Quillen cohomology of algebras over an enriched operad. Additionally, we introduce a spectral Hochschild cohomology theory for enriched operads and algebras over…

The Dirac-Dolbeault operator for a compact K\"ahler manifold is a special case of a Dirac operator. The Green function for the Dirac Laplacian over a Riemannian manifold with boundary allows to express the values of the sections of the…

First we argue that many BV and homotopy BV structures, including both familiar and new examples, arise from a common underlying construction. The input of this construction is a cyclic operad along with a cyclically invariant Maurer-Cartan…

Bialgebras and Hopf (bi)modules are typical algebraic structures with several interacting operations. Their structural and homological study is therefore quite involved. We develop the machinery of braided systems, tailored for handling…

We study homotopy-coherent commutative multiplicative structures on equivariant spaces and spectra. We define N-infinity operads, equivariant generalizations of E-infinity operads. Algebras in equivariant spectra over an N-infinity operad…

Linear non-compact operators are difficult to study because they do not exist in the finite dimensional world. Recently, Math\'{e} and Hofmann studied the singular values of the compact composition of the non-compact Hausdorff moment…

Let X=G/P be a homogeneous space of a complex semisimple Lie group G equipped with a hermitian metric. We study the action of the Hodge star operator on the space of harmonic differential forms on X. We obtain explicit combinatorial…

We introduce the theory of local and global monodromies of polynomials in cohomology groups in various geometric situations, focusing on its relations with toric geometry and motivic Milnor fibers, and moreover in the modern languages of…

Suppose $E$ is an elliptic curve over $\mathbb{Q}$ and $\chi$ is a Dirichlet character. We use statistical properties of modular symbols to estimate heuristically the probability that $L(E,\chi,1) = 0$. Via the Birch and Swinnerton-Dyer…

On an oriented 4-manifold, we examine the geometry that arises when the curvature operator of a Riemannian or Lorentzian metric $g$ commutes, not with its own Hodge star operator, but rather with that of another semi-Riemannian metric $h$…

We compute the Hodge numbers of the moduli space of semi-stable sheaves on the complex projective plane supported on quintic curves and having Euler characteristic 3. For this purpose we study the fixed-point set for a certain torus action…

We prove a criterion for the existence of harmonic metrics on Higgs bundles that are defined on smooth loci of klt varieties. As one application, we resolve the quasi-etale uniformisation problem for minimal varieties of general type to…

The arithmetic of Hilbert modular forms has been extensively studied under the assumption that the forms concerned are "paritious" -- all the components of the weight are congruent modulo 2. In contrast, non-paritious Hilbert modular forms…