In this paper, we relate Poisson’s summation formula to Heisenberg’s uncertainty 1 principle. They both express Fourier dualities within the space of tempered distributions and 2 these dualities are furthermore the inverses of one another. While Poisson’s summation 3 formula expresses a duality between discretization and periodization, Heisenberg’s 4 uncertainty principle expresses a duality be...

1.1 Duality is a frequently occurring principle for understanding a mathematical structure. The Fourier transformation is a classical example which leads to the Pontryagin duality of topological abelian groups. A more geometric example is the Fourier-Mukai ∗Mathematisches Institut, Universität Göttingen, Bunsenstr. 3-5, 37073 Göttingen, GERMANY, [email protected], [email protected] s...

We show that the numerical local Langlands duality for GLn and the T-duality of twodimensional quantum gravity arise from one and the same symmetry principle. The unifying theme is that the local Fourier transform in both its `-adic and complex incarnation gives rise to symmetries of arithmetic and geometric local Langlands parameters.

The purpose of this paper is to describe the appropriate mathematical framework for the study of the duality principle in option pricing. We consider models where prices evolve as general exponential semimartingales and provide a complete characterization of the dual process under the dual measure. Particular cases of these models are the ones driven by Brownian motions and by Lévy processes, w...

The classical random graph model G(n, λ/n) satisfies a ‘duality principle’, in that removing the giant component from a supercritical instance of the model leaves (essentially) a subcritical instance. Such principles have been proved for various models; they are useful since it is often much easier to study the subcritical model than to directly study small components in the supercritical model...

The main result in this paper characterizes those commutative rings R having the property that every linear dynamical system over R verifies the duality principle [i.e., the system 2 is observable (reachable) if and only if the dual system 8’ is reachable (observable)]. This characterization is given in terms of the finitely generated faithful ideals of R, and it generalizes a result due to Chi...

We study the optimal transport between two probability measures on the real line, where the transport plans are laws of one-step martingales. A quasi-sure formulation of the dual problem is introduced and shown to yield a complete duality theory for general marginals and measurable reward (cost) functions: absence of a duality gap and existence of dual optimizers. Both properties are shown to f...