Related papers: The Berkovits Method for Conformally Invariant Non…

Generalizing the method of Faltings-Serre, we rigorously verify that certain abelian surfaces without extra endomorphisms are paramodular. To compute the required Hecke eigenvalues, we develop a method of specialization of Siegel…

We introduce a general notion of a seminorm on sheaves of rings or modules and provide each sheaf of relative differential pluriforms on a Berkovich k-analytic space with a natural seminorm, called Kahler seminorm. If the residue field is…

We study the Z_5-orbifolding of the CHL string theory by explicitly constructing the modular form tilde{Phi}_2 generating the degeneracies of the 1/4-BPS states in the theory. Since the additive seed for the sum form is a weak Jacobi form…

We construct positive-genus analogues of Welschinger's invariants for many real symplectic manifolds, including the odd-dimensional projective spaces and the renowned quintic threefold. In some cases, our invariants provide lower bounds for…

When $G$ is a complex reductive algebraic group and $G/K$ is a reductive symmetric space, the decomposition of $\C[G/K]$ as a $K$-module was obtained (in a non-constructive way) by Richardson, generalizing the celebrated result of…

A general Lagrangian formulation of integrably deformed G/H-coset models is given. We consider the G/H-coset model in terms of the gauged Wess-Zumino-Witten action and obtain an integrable deformation by adding a potential energy term…

We proof existence theorems for the Dirichlet problem for hypersurfaces of constant special Lagrangian curvature in Hadamard manifolds. The first results are obtained using the continuity method and approximation and then refined using two…

A multidimensional gravitational model containing scalar fields and antisymmetric forms is considered. The manifold is chosen in the form $M = M_0 \times M_1 \times \cdots \times M_n$, where $M_i$ are Einstein spaces ($i \geq 1$). The…

We consider a two-fold problem: on the one hand, the classification of a family of solution-generating techniques in (modified) supergravity and, on the other hand, the classification of a family of canonical transformations of…

Recently, a gauged linear sigma model was proposed by Berkovits and Vafa which can be used to describe the AdS_5xS^5 superstring at finite and zero radius. In this paper we show that the model is classically integrable by constructing its…

Motivated by the principles of the conformal bootstrap, primarily the principle of Locality, simultaneously with the requirement of space-time supersymmetry, we reconsider constructions of compactified superstring models. Starting from…

We consider invariant Riemannian metrics on compact homogeneous spaces $G/H$ where an intermediate subgroup $K$ between $G$ and $H$ exists. In this case, the homogeneous space $G/H$ is the total space of a Riemannian submersion. The metrics…

Supersymmetry of the Wess-Zumino (N=1, D=4) multiplet allows field equations that determine a larger class of geometries than the familiar Kahler manifolds, in which covariantly holomorphic vectors rather than a scalar superpotential…

For a finite subgroup $\Gamma\subset \mathrm{SL}(2,\mathbb{C})$ and $n\geq 1$, we construct the (reduced scheme underlying the) Hilbert scheme of $n$ points on the Kleinian singularity $\mathbb{C}^2/\Gamma$ as a Nakajima quiver variety for…

Certain supersymmetric sigma models in 2+1 dimensions feature multi-soliton solutions, with and without scattering. We subject these systems to a non-anticommutative deformation by replacing the Grassmann algebra of the odd superspace…

This paper is a continuation of [2], where we complete our partial proof of the Deser-Schwimmer conjecture on the structure of ``global conformal invariants''. Our theorem deals with such invariants P(g^n) that locally depend only on the…

We use the method of group contractions to relate wavelets analysis and Gabor analysis. Wavelets analysis is associated with unitary irreducible representations of the affine group while Gabor analysis is associated with unitary irreducible…

Let $M$ be a compact irreducible hyperkahler manifold, from Bogomolov inequality [V1] we obtain forbidden values of the second Betti number $b_2$ in arbitrary dimension. UPD: Unfortunately, decomposition of dual to BBF-form is not right in…

We study invariant pseudo-K\"ahler structures on a solvmanifold $G$ such that the Lie algebra $\mathfrak{g}$ is almost abelian, that is $\mathfrak{g}=\mathfrak{h}\rtimes\mathbb{R}$, with $\mathfrak{h}$ abelian; comparing with the…

We study the integrability of gravity-matter systems in D=2 spatial dimensions with matter related to a symmetric space G/K using the well-known linear systems of Belinski-Zakharov (BZ) and Breitenlohner-Maison (BM). The linear system of BM…