Related papers: Visualizing Poincar\'e Duality
We propose a duality between quiver gauge theories and the combinatorics of dimer models. The connection is via toric diagrams together with multiplicities associated to points in the diagram (which count multiplicities of fields in the…
We observe that for planar graphs, the geometric duality relation generates both 2-isomorphism and abstract duality. This observation has the surprising consequence that for links, the equivalence relation defined by isomorphisms of…
In this talk, some aspects of duality symmetries are presented.
We find a necessary and sufficient condition for a doubling metric space to carry a (1,p)-Poincare inequality. The condition involves discretizations of the metric space and Poincare inequalities on graphs.
Obtaining complete information about the shape of an object by looking at it from a single direction is impossible in general. In this paper, we theoretically study obtaining differential geometric information of an object from orthogonal…
Earlier it was described to which extent the Alexander polynomial in several variables of an algebraic link in the Poincar\'e sphere determines the topology of the link. It was shown that, except some explicitly described cases, the…
Quark-hadron duality and its potential applications are discussed. We focus on theoretical efforts to model duality.
2-stratifolds are a generalization of 2-manifolds in that there are disjoint simple closed curves where several sheets meet. They arise in the study of categorical invariants of 3-manifolds and may have applications to topological data…
We briefly review the main aspects of (Poincar\'e-Dulac) normal forms; we have a look at the non-uniqueness problem, and discuss one of the proposed ways to ``further reduce'' the normal forms. We also mention some convergence results.
In this paper, we give definitions and characterizations of normal and spherical curves in the dual space. We show that normal curves are also spherical curves in D^3.
The aim of this paper is to revisit some duality results in conic linear programming and to answer an open problem related to the duality gap function for Gale's example.
We continue our study of the variation of parabolic cohomology (math.AG/0310139) and derive an exact formula for the underlying Poincare duality. As an illustration of our methods, we compute the monodromy of the Picard-Euler system and its…
We give an elementary construction of homology of sheaves from Brown representability for the dual and see how its main properties are derived easily from the construction. Comparison with Poincar\'e-Verdier duality and with homology of…
Statistics of Poincar\' e recurrence for a class of circle maps, including sub-critical, critical, and super-critical cases, are studied. It is shown how the topological differences in the various types of the dynamics are manifested in the…
Pairs of metrics in a two-dimensional linear vector space are considered, one of which is a Minkowski type metric. Their simultaneous diagonalizability is studied and canonical presentations for them are suggested.
We show that for a system of two entangled particles, there is a dual description to the particle equations in terms of classical theory of conformally stretched spacetime. We also connect these entangled particle equations with Finsler…
We present a conceptually simple and intuitive method to calculate and to measure the dissimilarities among 2D shapes. Several methods to interpret and to visualize the resulting dissimilarity matrix are presented and compared.
A nonstandard application of bivariate polynomial interpolation is discussed: the implicitization of a rational algebraic curve given by its parametric equations. Three different approaches using the same interpolation space are considered,…
We give a combinatorial upper bound for the gonality of a curve that is defined by a bivariate Laurent polynomial with given Newton polygon. We conjecture that this bound is generically attained, and provide proofs in a considerable number…
We describe new relations among conformal block divisors in $\operatorname{Pic}(\bar{\operatorname{M}}_{0,n})$. These relations appear from various rank-level dualities of conformal blocks on $\mathbb{P}^1$ with $n$ marked points. We also…