Related papers: Lagrangian correspondences and pullbacks of virtua…
The Langlands Program relates Galois representations and automorphic representations of reductive algebraic groups. The trace formula is a powerful tool in the study of this connection and the Langlands Functoriality Conjecture. After…
A complete understanding of physical systems requires models that are accurate and obeys natural conservation laws. Recent trends in representation learning involve learning Lagrangian from data rather than the direct discovery of governing…
This paper provides a description of an algebraic setting for the Lagrangian formalism over graded algebras and is intended as the necessary first step towards the noncommutative C-spectral sequence (variational bicomplex). A noncommutative…
I present a brief overview of the advantages of using a consistent effective Lagrangian approach in parameterizing virtual new physics effects. I then apply the formalism to certain top-quark processes.
We construct, for a second-order homogeneous Lagrangian in two independent variables, a differential 2-form with the property that it is closed precisely when the Lagrangian is null. This is similar to the property of the 'fundamental…
In general, a Kobayashi-Hitchin correspondence establishes an isomorphism between a moduli space of stable algebraic geometric objects and a moduli space of solutions of a certain (generalized) Hermite-Einstein equation. We believe that,…
These lecture notes give an overview of recent results in geometric Langlands correspondence which may yield applications to quantum field theory. We start with a motivated introduction to the Langlands Program, including its geometric…
Classical and quantum mechanical descriptions of physical world are seamlessly abridged within the framework of Lagrangian formalism which, besides revealing the essence of nonlocally correlated dynamic evolution, helps understanding abrupt…
We investigate an equivalence relation on Legendrian knots in the standard contact three-space defined by the existence of an interpolating zigzag of Lagrangian cobordisms. We compare this relation, restricted to genus-$0$ surfaces, to…
This paper explores the kinds of probabilistic relations that are important in syntactic disambiguation. It proposes that two widely used kinds of relations, lexical dependencies and structural relations, have complementary disambiguation…
The canonical structure of theories whose Lagrangian contains higher powers of time derivatives is often obscured by the nonlinear relationship between the velocities and momenta. We use the Dirac formalism and define a generalized Legendre…
This text is the English translation of a 1986 manuscript which gives the classification of the differential forms parametrizing the finite-dimensional Lie algebras of hamiltonian and contact Cartan types over fields of positive…
As part of the study of correspondence functors, the present paper investigates their tensor product and proves some of its main properties. In particular, the correspondence functor associated to a finite lattice has the structure of a…
We review recent progress concerning the analysis of Lagrangians on immersions into $\mathbb{R}^d$ depending on the first and second fundamental forms and their covariant derivatives.
In this paper we study the Lagrangian fibrations for projective irreducible symplectic fourfolds and exclude the case of non-smooth base. Our method could be extended to the higher-dimensional cases.
The classification of isoparametric hypersurfaces in spheres with four or six different principal curvatures is still not complete. In this paper we develop a structural approach that may be helpful for a classification. Instead of working…
We present a general Lagrangian formalism that allows the treatment of vorticity. We give solutions for the rotational perturbations up to the third-order in a flat background universe. We show how the primordial vorticity affects the…
We reconsider the construction of general derivative self-interactions for a massive Proca field. The constructed Lagrangian is such that the vector field propagates at most three degrees of freedom, thus avoiding the ghostly nature of a…
We analyze the relation between the concept of auxiliary variables and the Inverse problem of the calculus of variations to construct a Lagrangian from a given set of equations of motion. The problem of the construction of a consistent…
We propose a definition of symplectic 2-groupoid which includes integrations of Courant algebroids that have been recently constructed. We study in detail the simple but illustrative case of constant symplectic 2-groupoids. We show that the…