This paper presents a uni ed study of duality properties for the problem of minimizing a linear function over the intersection of an a ne space with a convex cone in nite dimension. Existing duality results are carefully surveyed and some new duality properties are established. Examples are given to illustrate these new properties. The topics covered in this paper include Gordon-Stiemke type th...

The paper presents general machinery for extending a duality between complete, cocomplete categories to a duality between corresponding categories of semilattice representations (i.e. sheaves over Alexandrov spaces). This enables known dualities to be regularized. Among the applications, regularized Lindenbaun-Tarski duality shows that the weak extension of Boolean logic (i.e. the semantics of ...

These are lecture notes, in progress, on monomial ideals. The point of view is that monomial ideals are best understood by drawing them and looking at their corners, and that a combinatorial duality satisfied by these corners, Alexander duality, is key to understanding the more algebraic duality theories at play in algebraic geometry and commutative algebra. Sections written so far cover Alexan...

We construct T-duality on K3 surfaces. The T-duality exchanges a 4-brane R-R charge and a 0-brane R-R charge. We study the action of the T-duality on the moduli space of 0-branes located at points of K3 and 4-branes wrapping it. We apply the construction to F-theory compactified on a Calabi-Yau 4-fold and study the duality of N = 2 SU(N c) gauge theories in four dimensions. We discuss the gener...

In this contribution we present the superfield T-duality rules relating type IIA and type IIB supergravity potentials for the case when both type IIA and type IIB superspaces have (at least) one isometry direction. We also give a brief review of T–duality and discuss the main steps of our approach to the derivation of the superfield T–duality rules, including the treatment of T-duality as an op...

In this work, we develop duality of the minimum volume circumscribed ellipsoid and the maximum volume inscribed ellipsoid problems. We present a unified treatment of both problems using convex semi–infinite programming. We establish the known duality relationship between the minimum volume circumscribed ellipsoid problem and the optimal experimental design problem in statistics. The duality res...

In this contribution we present the superfield T-duality rules relating type IIA and type IIB supergravity potentials for the case when both type IIA and type IIB superspaces have (at least) one isometry direction. We also give a brief review of T–duality and discuss the main steps of our approach to the derivation of the superfield T–duality rules, including the treatment of T-duality as an op...

The core of games arising from semi-infinite transportation situations with infinitely divisible goods is studied. In these situations one aims at maximizing the profit from transporting a good from a finite number of suppliers to an infinite number of demanders. This good is infinitely divisible. It is shown that the underlying primal and dual infinite programs have no duality gap. Further, th...

We study the corrections due to renormalons to the heavy hadron decay width. The renormalons contribution estimated in terms of finite gluon mass based on the assumption that the gluon mass represents the short distance nonperturbative effects in the standard OPE (and hence in the heavy quark expansion). We found that the corrections are about 10% of the leading decay rate. We point out the imp...

The Hamiltonian formalism offers a natural framework for discussing the notion of Poisson Lie T-duality. This is because the duality is inherent in the Poisson structures alone and exists regardless of the choice of Hamiltonian. Thus one can pose alternative dynamical systems possessing nonabelian T-duality. As an example, we find a dual Hamiltonian formulation of the O(3) nonlinear σ-model. In...