We describe a relation between Arnold’s strange duality and a polar duality between the Newton polytopes which is mostly due to M. Kobayashi. We show that this relation continues to hold for the extension of Arnold’s strange duality found by C. T. C. Wall and the author. By a method of Ehlers-Varchenko, the characteristic polynomial of the monodromy of a hypersurface singularity can be computed...

Agency conflicts can arise when a fund manager also chairs the board of the fund. We examine the consequences of this fund manager duality using a broad sample of single managed US equity funds. We find that duality managers significantly underperform non-duality managers. This underperformance results from duality funds in the bottom performance quintile. This suggests that duality managers ca...

The p – q duality is a relation between the (p, q) model and the (q, p) model of two-dimensional quantum gravity. Geometrically this duality corresponds to a relation between the two relevant points of the Sato Grassmannian. Kharchev and Marshakov have expressed such a relation in terms of matrix integrals. Some explicit formulas for small p and q have been given in the work of Fukuma-Kawai-Nak...

In this paper we present a robust duality theory for generalized convex programming problems in the face of data uncertainty within the framework of robust optimization. We establish robust strong duality for an uncertain nonlinear programming primal problem and its uncertain Lagrangian dual by showing strong duality between the deterministic counterparts: robust counterpart of the primal model...

This paper explores relationships between many-valued logic and fuzzy topology from the viewpoint of duality theory. We first show a fuzzy topological duality for the algebras of Lukasiewicz n-valued logic with truth constants, which generalizes Stone duality for Boolean algebras to the n-valued case via fuzzy topology. Then, based on this duality, we show a fuzzy topological duality for the al...

We apply the framework developed in Target Space Duality I: General Theory. We show that both nonabelian duality and Poisson-Lie duality are examples of the general theory. We propose how the formalism leads to a systematic study of duality by studying few scenarios that lead to open questions in the theory of Lie algebras. We present evidence that there are probably new examples of irreducible...

In these expository notes derived categories and functors are gently introduced, and used along with Koszul complexes to develop the basics of local cohomology. Local duality and its far-reaching generalization, Greenlees-May duality, are treated. A canonical version of local duality, via differentials and residues, is outlined. Finally, the fundamental Residue Theorem, described here e.g., for...

We develop a systematic framework for studying target space duality at the classical level. We show that target space duality between manifolds M and M̃ arises because of the existence of a very special symplectic manifold. This manifold locally looks like M×M̃ and admits a double fibration. We analyze the local geometric requirements necessary for target space duality and prove that both manifol...

We generalize Priestley duality for distributive lattices to a duality for distributive meet-semilattices. On the one hand, our generalized Priestley spaces are easier to work with than Celani’s DS-spaces, and are similar to Hansoul’s Priestley structures. On the other hand, our generalized Priestley morphisms are similar to Celani’s meet-relations and are more general than Hansoul’s morphisms....