相关论文: The Algebra and Geometry of Isometries

We examine relations between geometry and the associated curvature decompositions in Weyl geometry.

A unified description of the relationship between the Hamiltonian structure of a large class of integrable hierarchies of equations and W-algebras is discussed. The main result is an explicit formula showing that the former can be…

We provide the full classification of equidistant decomposition of a two-dimensional Euclidean plane and a two-dimensional sphere.

We investigate the SL(2,R) invariant geodesic curves with the as- sociated invariant distance function in parabolic geometry. Parabolic geom- etry naturally occurs in the study of SL(2,R) and is placed in between the elliptic and the…

A procedure for the algebraization of a $CR$-manifold and its holomorphic automorphisms is described. Examples of the application of algebraization are considered. Questions arising in connection with the algebraization of a $CR$-manifold…

A synaptic algebra is a generalization of the Jordan algebra of selfadjoint elements of a von Neumann algebra. We study symmetries in synaptic algebras, i.e., elements whose square is the unit element, and we investigate the equivalence…

Part I: The geometric algebra of space is derived by extending the real number system to include three mutually anticommuting square roots of plus one. The resulting geometric algebra is isomorphic to the algebra of complex 2x2 matrices,…

Geometrization of physical theories have always played an important role in their analysis and development. In this contribution we discuss various aspects concerning the geometrization of physical theories: from classical mechanics to…

In this work we propose a geometric view of the azeotropy problem, using some simplified models. We demonstrate that the occurrence of azeotropes in binary mixtures can be viewed-geometrically-as the intersection of curves in the plane (for…

This a slightly expended version of my habilitation thesis, which is an overview of my research activities during the last 4 years, written in a rather informal style.

The first part of the book is devoted to the symmetry approach to classification of scalar integrable evolution PDEs with two independent variables. In the second part systems of evolution equations with polynomial homogeneous right-hand…

We apply the notion of 2-extensions of algebras to the deformation theory of algebras. After standard results on butterflies between 2-extensions, we use this (2, 0)-category to give three perspectives on the deformation theory of algebras.…

Distance Geometry is based on the inverse problem that asks to find the positions of points, in a Euclidean space of given dimension, that are compatible with a given set of distances. We briefly introduce the field, and discuss some open…

The relations between integrable Poisson algebras with three generators and two-dimensional manifolds are investigated. Poisson algebraic maps are also discussed.

We introduce the notions of mixed resolutions and simplicial sections, and prove a theorem relating them. This result is used (in another paper) to study deformation quantization in algebraic geometry.

Visual insights into a wide variety of statistical methods, for both didactic and data analytic purposes, can often be achieved through geometric diagrams and geometrically based statistical graphs. This paper extols and illustrates the…

We investigate the quasisymmetric uniformization of a special class of metric surfaces known as paper surfaces, constructed as quotients of planar multipolygons via segment pairings, including infinite Type W identifications. These spaces,…

The development of computational techniques in the last decade has made possible to attack some classical problems of algebraic geometry. In this survey, we briefly describe some open problems related to algebraic curves which can be…

A short introduction to the mathematical methods and technics of differential algebras and modules adapted to the problems of mathematical and theoretical physics is presented.

This is an expository introduction to tropical algebraic geometry based on my lectures at the Workshop on Tropical Geometry and Integrable Systems in Glasgow, July 4-8, 2011, and at the ELGA 2011 school on Algebraic Geometry and…