Related papers: Geometry and Harmonic Superspace: some recent prog…
We summarize our work on spherically symmetric midi-superspaces in loop quantum gravity. Our approach is based on using inhomogeneous slicings that may penetrate the horizon in case there is one and on a redefinition of the constraints so…
The purpose of this paper is to provide a both comprehensive and summarizing account on recent results about analysis and geometry on configuration spaces $\Gamma_X$ over Riemannian manifolds $X$. Particular emphasis is given to a complete…
Previously, Pahlavan, Rouhani and Takook have introduced a novel $N=1$ super-symmetric algebra in de Sitter space-time. This paper is an attempt to build a proper $N=1$ super-symmetric field theory of classical level in the de Sitter space.…
In this short note, we hope to give a rapid induction for non-experts into the world of Differential Harnack inequalities, which have been so influential in geometric analysis and probability theory over the past few decades. At the…
Purely real space versions of the differential equations describing the kinematics of a dislocated crystalline medium are considered. The differential geometric structures associated with them are revealed.
In the past ten years, the ideas of supersymmetry have been profitably applied to many nonrelativistic quantum mechanical problems. In particular, there is now a much deeper understanding of why certain potentials are analytically solvable…
In the last decade, the development of new ideas in quantum theory, including geometric and deformation quantization, the non-Abelian Berry factor, super- and BRST symmetries, non-commutativity, has called into play the geometric techniques…
We present a geometric formulation of quantum mechanics based on the symplectic structure of the projective Hilbert space. Building upon the standard K\"ahler framework, we introduce an extension in which the symplectic structure is allowed…
This article deals with the existence of hypersurfaces minimizing general shape functionals under certain geometric constraints. We consider as admissible shapes orientable hypersurfaces satisfying a so-called reach condition, also known as…
The Yuri Golfand Memorial Volume commemorates Thirty Years of Supersymmetry. It will be published soon by World Scientific. The participants of the project are: D. Brace, L. Brink, S. Deser, G. Dvali, B. Feng, D. Freedman, G.-L. Gervais, G.…
We review some of the recent work on the dynamics of four dimensional, supersymmetric gauge theories. The kinematics are largely determined by holomorphy and the dynamics are governed by duality. The results shed light on the phases of…
Hyperbolic machine learning is an emerging field aimed at representing data with a hierarchical structure. However, there is a lack of tools for evaluation and analysis of the resulting hyperbolic data representations. To this end, we…
These notes are an expanded version of an introductory lecture on contact geometry given at the 2001 Georgia Topology Conference. They are intended to present some of the "topological" aspects of three dimensional contact geometry.
Recent work achieved impressive progress towards joint reconstruction of hands and manipulated objects from monocular color images. Existing methods focus on two alternative representations in terms of either parametric meshes or signed…
These notes are based on lectures given at the Clay School on Geometry and String Theory, Isaac Newton Institute, Cambridge, 25 March - 19 April 2002. They attempt to provide an elementary and somewhat self contained discussion of the…
These notes are for the author's lectures, "Integral Reduction and Applied Algebraic Geometry Techniques" in the School and Workshop on Amplitudes in Beijing 2016. I introduce the applications of algebraic geometry methods on multi-loop…
Physics in curved spacetime describes a multitude of phenomena, ranging from astrophysics to high energy physics. The last few years have witnessed further progress on several fronts, including the accurate numerical evolution of the…
We consider massive half-maximal supergravity in (d+3) dimensions and compactify it on a symmetric three space. We find that the static configurations of Minkowski X S^3, obtained by balancing the positive scalar potential for the dilaton…
The goal of this introduction to symmetries is to present some general ideas, to outline the fundamental concepts and results of the subject and to situate a bit the following lectures of this school. [These notes represent the write-up of…
This is a chapter for a planned collective volume entitled "New spaces in mathematics and physics" (M. Anel, G. Catren Eds.). The first part contains a short formal exposition of supergeometry as it is understood by mathematicians. The…