Related papers: On "two important theorems" in canonical duality t…
This paper has been withdrawn, as all conjectures (and one claim) have been proven incorrect. Some of what remains may eventually reappear in a different context.
We introduce a notion of Q-algebra that can be considered as a generalization of the notion of Q-manifold (a supermanifold equipped with an odd vector field obeying {Q,Q} =0). We develop the theory of connections on modules over Q-algebras…
The first part of this work established the foundations of a radial duality between nonnegative optimization problems, inspired by the work of (Renegar, 2016). Here we utilize our radial duality theory to design and analyze projection-free…
The purpose of this paper is to give two applications of Fourier transforms and generic vanishing theorems: - we give a cohomological characterization of principal polarizations - we prove that if $X$ an abelian variety and $\Theta $ a…
A class of two-dimensional globally scale-invariant, but not conformally invariant, theories is obtained. These systems are identified in the process of discussing global and local scaling properties of models related by duality…
An infinite number of topological conformal algebras with varying central charges are explicitly shown to be present in $2d$ gravity (treated both in the conformal gauge and in the light-cone gauge) coupled to minimal matter. The central…
The purpose of this paper was to give an algebraic analog of Poincare duality. But there is a mistake in the proof of the main theorem. It will be corrected as soon as possible.
A particular two-parameter class of little string theories can be described by $M$ parallel M5-branes probing a transverse affine $A_{N-1}$ singularity. We previously discussed the duality between the theories labelled by $(N,M)$ and…
We study in detail the space of perturbations of a pair of dual $N=1$ supersymmetric theories based on an $SU(N_c)$ gauge theory with an adjoint $X$ and fundamentals with a superpotential which is polynomial in $X$. The equivalence between…
We show that the main results of the expected utility and dual utility theories can be derived in a unified way from two fundamental mathematical ideas: the separation principle of convex analysis, and integral representations of continuous…
This is the third in a series of papers extending Martin-L\"of's meaning explanations of dependent type theory to a Cartesian cubical realizability framework that accounts for higher-dimensional types. We extend this framework to include a…
Recently the duality map between electric-like asymptotic charges of $p$-form gauge theories is studied. The outcome is an existence and uniqueness theorem and the topological nature of the duality map. The goal of this work is to extend…
This thesis is devoted to various questions connected with duality. It is composed of two parts. The first part discusses some aspects of timelike T-duality. We explore the possibility of compactification of supergravity theories with…
In this note we prove that the factorization theorem for dominated polynomials previously proved by the authors is equivalent to an alternative factorization scheme that uses classical linear techniques and a linearization process. However,…
We prove a duality theorem for certain graded algebras and show by various examples different kinds of failure of tameness of local cohomology.
A conventional wisdom often perpetuated in the literature states that: (i) a 3+1 decomposition of space-time into space and time is synonymous with the canonical treatment and this decomposition is essential for any Hamiltonian formulation…
Optimization problems with discrete decisions are nonconvex and thus lack strong duality, which limits the usefulness of tools such as shadow prices and the KKT conditions. It was shown in Burer(2009) that mixed-binary quadratic programs…
We establish a number of foundational results on Poincar\'e spaces which result in several applications. One application settles an old conjecture of C.T.C. Wall in the affirmative. Another result shows that for any natural number n, there…
We present a primal-dual algorithmic framework to obtain approximate solutions to a prototypical constrained convex optimization problem, and rigorously characterize how common structural assumptions affect the numerical efficiency. Our…
This is a general introduction to duality in field theories. The existence and breaking of global symmetries is used as a guideline to systematically prove duality between different field theories. Systems discussed include abelian and…