It has recently been shown that infinite matroids can be axiomatized in a way that is very similar to finite matroids and permits duality. This was previously thought impossible, since finitary infinite matroids must have non-finitary duals. In this paper we illustrate the new theory by exhibiting its implications for the cycle and bond matroids of infinite graphs. We also describe their algebr...

A typed lambda calculus with categorical type constructors is introduced. It has a uniform category theoretic mechanism to declare new types. Its type structure includes categorical objects like products and coproducts as well as recursive types like natural numbers and lists. It also allows duals of recursive types, i.e. lazy types, like infinite lists. It has generalized iterators for recursi...

A class of non-canonical duals for the multiwindow Gabor scheme, incorporating both rational and integer oversampling of the Gaborian combined time-frequency space, is considered. Using properties of Gabor frame matrices, block Discrete Fourier transforms, and results from number theory, we establish existence conditions for the noncanonical duals for both integer and rational oversampling rate...

We develop tools to engineer de Sitter vacua with semi-holographic duals, using elliptic fibrations and orientifolds to uplift Freund-Rubin compactifications with CFT duals. The dual brane construction is compact and constitutes a microscopic realization of the dS/dS correspondence, realizing d-dimensional de Sitter space as a warped compactification down to (d− 1)-dimensional de Sitter gravity...

We discuss symplectic and hyperkahler implosion present candidates for the duals of universal various groups.

We argue that higher-curvature terms in the gravitational Lagrangian lead, via non-relativistic gauge-gravity duality, to finite renormalization of the dynamical exponent of the dual conformal field theory. Our argument includes a proof of the non-renormalization of the Schrödinger and Lifshitz metrics beyond rescalings of their parameters, directly generalizing the AdS case. We use this effect...

In this note we look at a number of infinite-dimensional R-vector spaces that arise in analysis, and we consider their dual and double dual spaces. As an application, we give an example of an infinite-dimensional vector space V for which the natural map η : V → V ∗∗ is not an isomorphism. In analysis, duals and double duals of vector spaces are often defined differently than in algebra, by cons...

Several stationary solutions of the low energy string equations are dualized with respect to their timelike symmetry. Many of the duals have simple physical interpretations. Those of the nonextremal three dimensional black hole and black string are negative mass black strings. The extremal cases of these, and extremal higher dimensional black strings also, give negative energy plane fronted wav...

Since many thermodynamic properties of black holes are universal, the thermodynamics of their holographic duals should be universal too. We show how this universality is exhibited in the example of symmetric orbifolds of general two dimensional CFTs. We discuss the free energies and phase diagrams of such theories and show that they are indeed universal in the large N limit. We also comment on ...