相关论文: Twisted symmetries of differential equations

We lay down the foundations for a systematic study of differentiable and algebraic supervarieties, with a special attention to supergroups.

Lie group theory was originally created more than 100 years ago as a tool for solving ordinary and partial differential equations. In this article we review the results of a much more recent program: the use of Lie groups to study…

In this paper, we develop differential twisted K-theory and define a twisted Chern character on twisted K-theory which depends on a choice of connection and curving on the twisting gerbe. We also establish the general Riemann-Roch theorem…

Recently, the theory of symmetric spaces has come to play an increased role in the physics of integrable systems and in quantum transport problems. In addition, it provides a classification of random matrix theories. In this paper we give a…

The problem of advancing coordinatization of mathematics is considered. The need to develop a theory for measuring value and complexity of mathematical implications and proofs is discussed including motivations, benefits and implementation…

In this talk, some aspects of duality symmetries are presented.

A review of recent developments in the analyses of supersymmetric dark matter is given.

We explain how a new type of fields called shadows and the use of twisted variables allow for a better description of Yang-Mills supersymmetric theories. (Based on lectures given in Cargese, June 2006.)

A speculative discussion on the role of various symmetries in physics.

It is argued that the twisted gauge theory is consistent provided it exhibits also the standard noncommutative gauge symmetry.

This is an introduction to the theory of disconjugacy for a second order linear differential equation. We give new proofs of some of basic results and obtain new sufficient conditions for disconjugacy (in particular, on the whole real…

A twisting system is one of the major tools to study graded algebras, however, it is often difficult to construct a (non-algebraic) twisting system if a graded algebra is given by generators and relations. In this paper, we show that a…

Generalized diffusion type equations are considered and point symmetry analysis is applied to them. The equations with extremal order point symmetry algebras are described. Some old geometrical results are rederived in connection with…

In this note, we review some of the recent developments in the well-posedness theory of nonlinear dispersive partial differential equations with random initial data.

Let X be a smooth algebraic variety over a field of characteristic 0. We introduce the notion of twisted associative (resp. Poisson) deformation of the structure sheaf O_X. These are stack-like versions of usual deformations. We prove that…

The common eigenfunctions of the twisted Cherednik operators can be first analyzed in the limit of $q\longrightarrow 1$. Then, the polynomial eigenfunctions form a simple set originating from the symmetric ground state of non-vanishing…

A likelihood function on a smooth very affine variety gives rise to a twisted de Rham complex. We show how its top cohomology vector space degenerates to the coordinate ring of the critical points defined by the likelihood equations. We…

The twisted Gaussian Schell Model describes a family of partially coherent beams that present several interesting characteristics, and as such have attracted attention in classical and quantum optics. Recent techniques have been…

Symmetry methods are by now recognized as one of the main tools to attack deterministic differential equations (both ODEs and PDEs); the situation is quite different for what concerns stochastic differential equations: here, symmetry…

Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal…