Related papers: Lagrangians, SO(3)-instantons and mixed equation

This expository article is an expanded version of talks given at the "Current Developments in Mathematics, 2002" conference. It gives an introduction to the (generalized) conjecture of Rapoport and Goresky-MacPherson which identifies the…

We extend some classical inequalities between the Dirichlet and Neumann eigenvalues of the Laplacian to the context of mixed Steklov--Dirichlet and Steklov--Neumann eigenvalue problems. The latter one is also known as the sloshing problem,…

In this work we study how nonminimally coupled theories of gravity modify the usual Friedmann equation, and develop two methods to treat these. The ambiguity in the form of the Lagrangian density of a perfect fluid is emphasized, and the…

For a bounded weak Lipschitz domain we show the so called `Maxwell compactness property', that is, the space of square integrable vector fields having square integrable weak rotation and divergence and satisfying mixed tangential and normal…

We study the Gromov-Hausdorff convergence of metric pairs and metric tuples and prove the equivalence of different natural definitions of this concept. We also prove embedding, completeness and compactness theorems in this setting. Finally,…

Given a bundle gerbe with connection on an oriented Riemannian manifold of dimension at least equal to 3, we formulate and study the associated Yang-Mills equations. When the Riemannian manifold is compact and oriented, we prove the…

The conformal symmetry on the instanton moduli space is discussed using the ADHM construction, where a viewpoint of "homogeneous coordinates" for both the spacetime and the moduli space turns out to be useful. It is shown that the conformal…

In this paper we define instanton Floer homology groups for a pair consisting of a compact oriented 3-manifold with boundary and a Lagrangian submanifold of the moduli space of flat SU(2)-connections over the boundary. We carry out the…

Consider the wrapped Fukaya category W of a collection of exact Lagrangians in a Liouville manifold. Under a non-degeneracy condition implying the existence of enough Lagrangians, we show that natural geometric maps from the Hochschild…

A concrete formulation of the Lehmann-Maehly-Goerisch method for semi-definite self-adjoint operators with compact resolvent is considered. Precise rates of convergence are determined in terms of how well the trial spaces capture the…

We prove the existence of perturbations for the PU(2) monopole equations, yielding transversality on the complement of the anti-self-dual or reducible solutions, and the existence of an Uhlenbeck compactification for the moduli space of…

We describe some L-infinity model for the local period map of a compact Kaehler manifold. Applications include the study of deformations with associated variation of Hodge structure constrained by certain closed strata of the Grassmannian…

We present new relations derived from Noether's identity that reveal the compatibility between the components of the Hessian matrix of the Lagrangian, the infinitesimal symmetry transformation of the configuration variables and time, and a…

We propose compactifications of the moduli space of Bridgeland stability conditions of a triangulated category. Our construction arises from a viewing a stability condition as a metric on the underlying category and is inspired by the…

Let $C\to M$ be the bundle of connections of a principal bundle on $M$. The solutions to Hamilton-Cartan equations for a gauge-invariant Lagrangian density $\Lambda $ on $C$ satisfying a weak condition of regularity, are shown to admit an…

The auto-parallel equation over spaces with affine connections and metrics is considered as a result of the application of the method of Lagrangians with covariant derivatives (MLCD) on a given Lagrangian density.

Outlined in this paper is a description of \emph{equivariance} in the world of 2-dimensional extended topological quantum field theories, under a topological action of compactLie groups. In physics language, I am gauging the theories ---…

We propose a model describing the scattering of hadrons as bound states of their constituent quarks. We analyze the role of simultaneity in measurements of the characteristics of different particles for the description of relativistic…

We provide fundamental properties of the first eigenpair for fractional $p$-Laplacian eigenvalue problems under singular weights, which is related to Hardy type inequality, and also show that the second eigenvalue is well-defined. We obtain…

We continue the study of symmetries in the Lagrangian formalism of arbitrary order with the help of the so-called Anderson-Duchamp-Krupka equations. For the case of second-order equations and arbitrary vector fields we are able to establish…