Related papers: The Berkovits Method for Conformally Invariant Non…

Building on the five-dimensional constructions in hep-th/0601177, we provide a unified description of four-dimensional N = 2 superconformal off-shell multiplets in projective superspace, including a realization in terms of N = 1…

For homogeneous reductive spaces G/H with reductive complements decomposable into an orthogonal sum \mathfrak{m}=\mathfrak{m}_1 \oplus \mathfrak{m}_2 \oplus \mathfrak{m}_3 of three Ad(H)-invariant irreducible mutually inequivalent…

We study a system of equations on a compact complex manifold, that couples the scalar curvature of a Kaehler metric with a spectral function of a first-order deformation of the complex structure. The system comes from an…

For a semisimple real Lie group $G$, we study topological properties of moduli spaces of polystable parabolic $G$-Higgs bundles over a Riemann surface with a divisor of finitely many distinct points. For a split real form of a complex…

We study the new case of the application of the JKLMR conjecture on the connection between the exact partition functions of $\mathcal{N}=(2,2)$ supersymmetric gauged linear sigma models (GLSM) on $S^2$ and special K\"ahler geometry on the…

We prove (under certain assumptions) the irreducibility of the limit $\sigma_2$ of a sequence of irreducible essentially self-dual Galois representations $\sigma_k: G_{\mathbf{Q}} \to \mathrm{GL}_4(\overline{\mathbf{Q}}_p)$ (as $k$…

The aim of the present paper is three folds. For a reproducing kernel Hilbert space $\mathcal{A}$ (R.K.H.S) and a $\sigma-$finite measure space $(M_{1},d\mu_{1})$ for which the corresponding $L^{2}-$space is a separable Hilbert space, we…

We study deformations of orbit closures for the action of a connected semisimple group $G$ on its Lie algebra $\mathfrak{g}$, especially when $G$ is the special linear group. The tools we use are on the one hand the invariant Hilbert scheme…

This work presents a novel class of metrics on a para-K\"{a}hler-Norden manifold $(M^{2m},F,g)$, derived from a conformal deformation of the Berger-type metric associated with the metric $g$. Initially, we examine the Levi-Civita link…

We consider a U(1) Gauged Linear Sigma Model (GLSM) with (2,2) supersymmetry, leading to a susy vacua of the resolved conifold. It possesses the non-Abelian global symmetry SU(2)xSU(2). A non-Abelian T-duality can be constructed which can…

In Batalin-Vilkovisky formalism a classical mechanical system is specified by means of a solution to the {\sl classical master equation}. Geometrically such a solution can be considered as a $QP$-manifold, i.e. a super\m equipped with an…

For nonrelativistic Hamiltonians which are shape invariant, analytic expressions for the eigenvalues and eigenvectors can be derived using the well known method of supersymmetric quantum mechanics. Most of these Hamiltonians also possess…

A consistent N=1 supersymmetric $\sigma$-model can be constructed, given a K\"ahler manifold by adding chiral matter multiplets. Their scalar components are covariant tensors on the underlying K\"ahler manifold. The K\"ahler U(1)-charges…

This article is an application of the author's paper about a construction method for discrete constant negative Gaussian curvature surfaces, the nonlinear d'Alembert formula. The heart of this formula is the Birkhoff decomposition, and we…

We introduce a semistability notion of the intrinsic reductions of a non-archimedean rational function at each non-classical point in the Berkovich projective line, which extends the potential GIT-semistability one defined at each type II…

We find the conditions under which a Riemannian manifold equipped with a closed three-form and a vector field define an on--shell N=(2,2) supersymmetric gauged sigma model. The conditions are that the manifold admits a twisted generalized…

We propose a universal method of relating the Calogero model to a set of decoupled particles on the real line, which can be uniformly applied to both the conformal and nonconformal versions as well as to supersymmetric extensions. For…

We give an irreducible decomposition of the so-called local representations (see arXiv:0707.2151) of the quantum Teichm\"uller space $\mathcal{T}_q(\Sigma)$ where $\Sigma$ is a punctured surface of genus $g>0$ and $q$ is a primitive $N$-th…

We prove mirror symmetry for supersymmetric sigma models on Kahler manifolds in 1+1 dimensions. The proof involves establishing the equivalence of the gauged linear sigma model, embedded in a theory with an enlarged gauge symmetry, with a…

Supersymmetric field theories of scalars and fermions in 4-D space-time can be cast in the formalism of Kaehler geometry. In these lectures I review Kaehler geometry and its application to the construction and analysis of supersymmetric…