Related papers: Greenlees-May Duality in a Nutshell
A ring with an Auslander dualizing complex is a generalization of an Auslander-Gorenstein ring. We show that many results which hold for Auslander-Gorenstein rings also hold in the more general setting. On the other hand we give criteria…
Colour-kinematics duality is a remarkable property of Yang-Mills theory. Its validity implies a relation between gauge theory and gravity scattering amplitudes, known as double copy. Albeit fully established at the tree level, its extension…
In an earlier paper of the authors, a general family of instances of the relative Langlands duality of Ben-Zvi-Sakellaridis-Venkatesh [BZSV] were proposed and studied in the setting of branching problems for smooth representations. In this…
We discuss hidden symmetries of M-theory, its feedback on the construction of the M-theory effective action, and a response of the effective action when locality is preserved. In particular, the locality of special symmetries of the…
This is a talk given at YKIS '95, primarily to non-string theorists. I review the evidence for string duality, the principle that any string theory at strong coupling looks like another string theory at weak coupling. A postscript…
If k is an arbitrary field, we construct a category of k-1-motives in which every commutative algebraic k-group G has a dual object $G^{\vee}$. When k is a local field of arbitrary characteristic, we establish Pontryagin duality theorems…
Doubling a Yang-Mills field we apply the pattern which has been found to construct a "duality-symmetric" gravity with matter to the "duality-symmetric" Yang - Mills theory in five space-time dimensions. Constructing the action we conclude…
We introduce the space of parameters for the metaplectic Langlands theory as *factorization gerbes* on the affine Grassmannian, and develop metaplectic Langlands duality in the incarnation of the metaplectic geometric Satake functor. We…
We prove that double dualization into the generic algebra for an algebraic theory has some Gelfand- or Stone- duality properties
For a coherent filtered D-module we show that the dual of each graded piece over the structure sheaf is isomorphic to a certain graded piece of the ring-theoretic local cohomology complex of the graded quotient of the dual of the filtered…
In this letter we implement a recently proposed {\it spacetime duality} approach to dualize a two dimensional, Abelian, gauge field theory, which has no dual version under $p$--duality. Our result suggests that spacetime duality spans a…
I introduce new Langlands duality conjectures concerning skein modules of 3-manifolds, which we have made recently with David Ben-Zvi, Sam Gunningham, and Pavel Safronov. I recount some historical motivation and some recent special cases…
We review the notion of symplectic duality earlier introduced in the context of topological recursion. We show that the transformation of symplectic duality can be expressed as a composition of $x-y$ dualities in a broader context of log…
In his earlier work, the author introduced a group theory question that arises in the study of iterated Galois groups of post-critically finite quadratic polynomials. In this paper, we prove the first non-trivial results on this question.
We show that a derived bi-duality dg-module is quasi-isomorphic to the homotopy limit of a certain tautological functor. This is a simple observation, which seems to be true in wider context. From the view point of derived Gabriel topology,…
The notion of geometrical duality is discussed in the context of both Brans-Dicke theory and general relativity. It is shown that, in some particular solutions, the spacetime singularities that arise in usual Riemannian general relativity…
This paper generalizes Shelah's generic pair conjecture (now theorem) for the measurable cardinal case from first order theories to finite diagrams. We use homogeneous models in the place of saturated models.
We introduce bubbling diagrams and show that they compute the support of the Grothendieck polynomial of any vexillary permutation. Using these diagrams, we show that the support of the top homogeneous component of such a Grothendieck…
Mayer's theory of cluster integrals allows one to write the partition function of a gas model as a generating function of weighted graphs. Recently, Labelle, Leroux and Ducharme have studied the graph weights arising from the…
The main aim of this paper is to make a remark about the relation between (i) dualities between theories, as `duality' is understood in physics and (ii) equivalence of theories, as `equivalence' is understood in logic and philosophy. The…