Related papers: Poincare duality in dimension 3
In this talk, some aspects of duality symmetries are presented.
The equations of motion that must be satisfied by fields that constitute realizations of the Poincare group algebra, for integral spin, and mass m, are obtained. For the case of massive spin 2 these equations are satisfied by the selfdual,…
In this sequel to earlier papers by three of the authors, we obtain a new bound on the complexity of a closed 3--manifold, as well as a characterisation of manifolds realising our complexity bounds. As an application, we obtain the first…
Previouly a possible extension of the complex number, together with its connected trigonometry was introduced. In this paper we focuss on the simplest case of ternary complex numbers. Then, some types of holomorphicity adapted to the…
Among Thurston maps (orientation-preserving, postcritically finite branched coverings of the 2-sphere to itself), those that arise as subdivision maps of a finite subdivision rule form a special family. For such maps, we investigate…
Two-dimensional N=1,2 supersymmetric chiral models and their dual extensions are introduced and canonically quantized. Working within a superspace formalism, the non-manifest invariance under 2D-superPoincare' transformations is proven. The…
The more recent paper "Generic strange duality for K3 surfaces" by the authors contains stronger results.
Thurston norms are invariants of 3-manifolds defined on their second homology vector spaces, and understanding the shape of their dual unit ball is a (widely) open problem. W. Thurston showed that every symmetric polygon in Z^2, whose…
In the setting of global geometric Langlands, we show that miraculous duality on the stack of principal bundles on a curve intertwines the functor of Poincare series with the dual functor to Whittaker coefficients. We construct, for…
In this paper the double-sided Talor's approximations are used to obtain generalisations and improvements of some trigonometric inequalities.
We discuss Poincar\'e duality complexes X and the question whether or not their Spivak normal fibration admits a reduction to a vector bundle in the case where the dimension of X is at most 4. We show that in dimensions less than 4 such a…
This survey discusses hyperbolicity properties of moduli stacks and generalisations of the Shafarevich Hyperbolicity Conjecture to higher dimensions. It concentrates on methods and results that relate moduli theory with recent progress in…
We establish a new homological lower bound for the Thurston norm on 1-cohomology of 3-manifolds. This generalizes previous results of C. McMullen, S. Harvey, and the author. We also establish an analogous lower bound for 1-cohomology of…
The Poincare function is a compact form of counting moduli in local geometric problems. We discuss its property in relation to V.Arnold's conjecture, and derive this conjecture in the case when the pseudogroup acts algebraically and…
This is a tutorial on duality properties of special functions, mainly of orthogonal polynomials in the ($q$-)Askey scheme. It is based on the first part of the 2017 R.P. Agarwal Memorial Lecture delivered by the author.
In this talk I present a review on the theoretical status of polarized fragmentation functions and the prospects for conceivable future semi-inclusive deep-inelastic scattering and proton-proton collision experiments to measure them.
Despite the non-convexity of most modern machine learning parameterizations, Lagrangian duality has become a popular tool for addressing constrained learning problems. We revisit Augmented Lagrangian methods, which aim to mitigate the…
The term Stone-type duality often refers to a dual equivalence between a category of lattices or other partially ordered structures on one side and a category of topological structures on the other. This paper is part of a larger endeavour…
In these expository notes we draw together and develop the ideas behind some recent progress in two directions: the treatment of finite type partial differential operators by prolongation, and a class of differential complexes known as…
We develop a systematic method to derive the Majorana representation of the Dirac equation in (1+3)-dimensions. We compare with similar approach in (2+2)-dimensions . We argue that our formalism can be useful to have a better understanding…