This report documents the programme and outcomes of Dagstuhl Seminar 15441 ‘Duality in Computer Science’. This seminar served as a follow-up seminar to the seminar ‘Duality in Computer Science’ (Dagstuhl Seminar 13311). In this seminar, we focused on applications of duality to semantics for probability in computation, to algebra and coalgebra, and on applications in complexity theory. A key obj...

In this chapter we describe the pricing of Bermudan options by means of Fourier cosine expansions. We propose a technique to price early-exercise call options with the help of the (European) put-call parity and put–call duality relations. Direct pricing of call options with cosine expansions may give rise to some sensitivity regarding the choice of the size of the domain in which the Fourier ex...

We give a number of characterizations of structural entailment. In particular, we show that an alter ego M∼ structurally entails an algebraic relation s on a finite algebra M if and only if s can be obtained via a local construct from M∼ . We show, via a range of applications, that, whereas entailment is important in the study of dualisability, structural entailment is important in the study of...

In this paper we prove that the linear Koszul duality isomorphism for convolution algebras in K-homology of [MR3] and the Fourier transform isomorphism for convolution algebras in Borel– Moore homology of [EM] are related by the Chern character. So, Koszul duality appears as a categorical upgrade of Fourier transform of constructible sheaves. This result explains the connection between the cate...

Construction of integrable field theories in space with a boundary is extended to fermionic models. We obtain general forms of boundary interactions consistent with integrability of the massive Thirring model and study the duality equivalence of the MT model and the sine-Gordon model with boundary terms. We find a variety of integrable boundary interactions in the O(3) Gross-Neveu model from th...

Foundations should be designed for the needs of mathematics and not vice versa. We propose a technique for doing this that exploits the correspondence between category theory and logic and is potentially applicable to several mathematical disciplines. This method is applied to devising a new paradigm for general topology, called Abstract Stone Duality. We express the duality between algebra and...

Convex optimization is a branch of mathematics dealing with nonlinear optimization problems with additional geometric structure. This area has been the focus of considerable recent research due to the fact that convex optimization problems are scalable and can be efficiently solved by interior-point methods. Over the last ten years or so, convex optimization has found new applications in many a...

The main contribution of this paper is to present a canonical choice of a Hamiltonian theory corresponding to the theory of discrete Lagrangian mechanics. We make use of Lagrange duality and follow a path parallel to that used for construction of the Pontryagin principle in optimal control theory. We use duality results regarding sensitivity and separability to show the relationship between gen...

In this paper we analyse in the framework of constructive mathematics (BISH) validity Farkas' lemma and related propositions, namely Fredholm alternative for solvability systems linear equations, optimality criteria programming, Stiemke's Superhedging Duality from mathematical finance, von Neumann's minimax theorem with application to game theory.

The signature of the Poincaré duality of compact topological manifolds with local system of coefficients can be described as a natural invariant of nondegenerate symmetric quadratic forms defined on a category of infinite dimensional linear spaces. The objects of this category are linear spaces of the form W = V ⊕ V ∗ where V is abstarct linear space with countable base. The space W is consider...