Related papers: Geometry and Harmonic Superspace: some recent prog…

We explain in some detail the geometric structure of spheres in any dimension. Our approach may be helpful for other homogeneous spaces (with other signatures) such as the de Sitter and anti-de Sitter spaces. We apply the procedure to the…

We discuss the possible relationship between geodesic flow, integrability and supersymmetry, using fermionic extensions of the KdV equation, as well as the recently introduced supersymmetrisation of the Camassa-Holm equation, as…

This paper can be considered as an extension to our paper [On symplectically harmonic forms on six-dimensional nilmanifolds, Comment. Math. Helv. 76 (2001), n 1, 89-109]. Also, it contains a brief survey of recent results on symplectically…

These lectures, given at the Cargese Summer school in 2008, provide an introduction to dynamical supersymmetry breaking and gauge mediation, with emphasis on the recent appreciation of the possible role of metastable supersymmetry breaking,…

Recent one-loop calculations of certain supergravity-mediated quantum corrections in supersymmetric brane-world models employ either the component formulation (hep-th/0305184) or the superfield formalism with only half of the bulk…

We study the conditions under which N=(1,1) generalized sigma models support an extension to N=(2,2). The enhanced supersymmetry is related to the target space complex geometry. Concentrating on a simple situation, related to Poisson sigma…

This is the summary of a 90 minute introductory lecture on Supersymmetry presented at the Swiss Summer School on ``Hidden Symmetries and Higgs Phenomena'' at Zuoz, Engadin, in August 1998. I first review the hierarchy problem, and then…

The concept of synthetic dimensions has emerged as a powerful framework in photonics and atomic physics, enabling the exploration of high-dimensional physics beyond conventional spatial constraints. Originally developed for quantum…

This note is based on a lecture delivered by the author at the Second Conference on Differential Geometry, held in Fez in October 2024. It offers an accessible introduction to biharmonic and biconservative submanifolds, exploring the…

Higher dimensional super symmetry has been analyzed in terms of quaternion variables and the theory of quaternion harmonic oscillator has been analyzed. Supersymmertization of quaternion Dirac equation has been developed for…

In this thesis we study string compactifications on manifolds equipped with a $G$-structure, placing a special emphasis on the interplay between geometry and physics. We follow two complementary approaches. In the first part of the thesis…

After a brief chronological sketch of developments in non-perturbative canonical quantum gravity, some of the recent mathematical results are reviewed. These include: i) an explicit construction of the quantum counterpart of Wheeler's…

We extend superspace by introducing an antisymmetric tensorial coordinate. The resulting theory presents a supersymmetry with central charge. After integrating over the tensorial coordinate, an effective action describing massive bosons and…

We explain how a generic HKT geometry can be derived using the language of N = 4 supersymmetric quantum mechanics. To this end, one should consider a Lagrangian involving several (4,4,0) multiplets defined in harmonic superspace and subject…

We extend Tanaka theory to the context of supergeometry and obtain an upper bound on the supersymmetry dimension of geometric structures related to strongly regular bracket-generating distributions on supermanifolds and their structure…

This is a revised version of the notes from the week-long course I gave at the Centre de Recerca Matematica, Barcelona, in September of 2010. The aim is to give a working overview of recent methods and results in "Blaschkean integral…

On June 5, 2007 the second author delivered a talk at the Journees de l'Institut Elie Cartan entitled "Finite symmetry groups in complex geometry". This paper begins with an expanded version of that talk which, in the spirit of the…

With the help of the Penrose-Ward transform, which relates certain holomorphic vector bundles over the supertwistor space to the equations of motion of self-dual SYM theory in four dimensions, we construct hidden infinite-dimensional…

These are notes for a Ph.D.\ course I held at SISSA, Trieste, in the Winter 2025. We review well-known topics in Riemannian geometry where Lie groups play a fundamental role. Part of the theory of compact connected Lie groups, their…

The simplest supersymmetry algebra and superspace in three dimensional Euclidean (3dE) space is examined. Representations of the algebra are considered and the implications of restricting the space of states to states with positive definite…