Related papers: The Geometry of Supersymmetry / A concise introduc…
Quivers, gauge theories and singular geometries are of great interest in both mathematics and physics. In this note, we collect a few open questions which have arisen in various recent works at the intersection between gauge theories,…
This is a survey article on real algebra and geometry, and in particular on its recent applications in optimization and convexity. We first introduce basic notions and results from the classical theory. We then explain how these relate to…
Graph drawing research traditionally focuses on producing geometric embeddings of graphs satisfying various aesthetic constraints. After the geometric embedding is specified, there is an additional step that is often overlooked or ignored:…
This review aims to provide a very short and pedestrian introduction to some of the basics of extra-dimensional physics. The hope is to facilitate access and to be, in some respects, complementary to the many already existing reviews on…
These lecture notes are from a first course on the Minimal Supersymmetric Standard Model. The level of the notes is introductory and pedagogical. Standard Model, basic supersymmetry algebra and its representations are considered as…
This article is a very basic introduction to supersymmetry. It introduces the two kinds of superfields needed for supersymmetric extensions of the Standard Model, the chiral superfield and the vector superfield, and discusses in detail how…
A quick overview is provided on the current development of the WP metric geometry.
This is the introduction to the collection of review articles "Exact results on N=2 supersymmetric gauge theories". The first three sections are intended to give a general overview over the physical motivations behind this direction of…
A comparison on some facts concerning the geometric quantization of symplectic manifolds is presented here. Criticism, facts and improvements on the sophisticated theory of geometric quantization are presented touching briefly, all the…
Supersymmetry remains compelling theory over 30 years in spite of lack of its discovery. It could be already near the corner our days, therefore present and upcoming experiments are crucial for constraining or even discovery of the…
This is the first chapter of an introductory text under construction; further chapters are available via the authors' web pages. Our aim is to provide an elementary access to Cox rings and their applications in algebraic and arithmetic…
Weak-scale supersymmetry is one of the most favoured theories beyond the Standard Model of particle physics that elegantly solves various theoretical and observational problems in both particle physics and cosmology. In this thesis, I…
I give a short review of the theory of twisted symmetries of differential equations, emphasizing geometrical aspects. Some open problems are also mentioned.
In this text we expose basic cases of some fundamental ideas and methods of topology. Namely, of homotopy, degree, fundamental group, covering, Whitehead invariant, etc. This is done by considering the elementary example: closed polygonal…
We present an overview of the differential geometry of curves and surfaces using examples from soft matter as illustrations. The presentation requires a background only in vector calculus and is otherwise self-contained.
This paper focuses on a new approach to plane geometry and develops important concepts that can allow researchers to unite and observe plane geometry from a new, meaningful perspective.
Recent developments in supersymmetric unified theories are reviewed, with particular emphasis on supersymmetric grand unification and a brief discussion of recent ideas about extra dimensions.
Supersymmetry, a new symmetry that relates bosons and fermions in particle physics, still escapes observation. Search for SUSY is one of the main aims of the recently launched Large Hadron Collider. The other possible manifestation of SUSY…
These notes are an elementary introduction to supersymmetric quantum mechanics for students of mathematics. We start from the very basic concepts of quantum mechanics and proceed to construct a realization of Heisenberg's superalgebra as a…
In this paper we survey several intersection and non-intersection phenomena appearing in the realm of symplectic topology. We discuss their implications and finally outline some new relations of the subject to algebraic geometry.