Related papers: On Algebraic-Geometry Approach to Ribaucour Transf…
A survey on recent developments in (algebraic) integral geometry is given. The main focus lies on algebraic structures on the space of translation invariant valuations and applications in integral geometry.
Tropical algebraic geometry is an active new field of mathematics that establishes and studies some very general principles to translate algebro-geometric problems into purely combinatorial ones. This expository paper gives an introduction…
A geometric approach is used to study the Abel first order differential equation of the first kind. The approach is based on the recently developed theory of quasi-Lie systems which allows us to characterise some particular examples of…
These lecture notes present a computation driven pathway from classical complex analysis to the theory of compact Riemann surfaces and their connections to algebraic geometry. The exposition follows a compute first then abstract philosophy,…
We develop a new framework of relative algebroids to address existence and classification problems of geometric structures subject to partial differential equations.
A short survey on applications of algebraic geometry in topological data analysis.
We introduce a new approach to constructing derived deformation groupoids, by considering them as parameter spaces for strong homotopy bialgebras. This allows them to be constructed for all classical deformation problems, such as…
In 1970s, a method was developed for integration of nonlinear equations by means of algebraic geometry. Starting from a Lax representation with spectral parameter, the algebro-geometric method allows to solve the system explicitly in terms…
This is the first paper in a series of eight where in the first three we develop a systematic approach to the geometric algebras of multivectors and extensors, followed by five papers where those algebraic concepts are used in a novel…
This article gives a classification scheme of algebraic transformations of Gauss hypergeometric functions, or pull-back transformations between hypergeometric differential equations. The classification recovers the classical transformations…
Every algebraic variety can be regarded as a symplectic manifold being equipped with a Kahler form. Therefore it is natural to study lagrangian geometry of any algebraic variety. We present two basic constructions which can be applied to a…
Numerical nonlinear algebra is a computational paradigm that uses numerical analysis to study polynomial equations. Its origins were methods to solve systems of polynomial equations based on the classical theorem of B\'ezout. This was…
We give a survey of algorithms for computing topological invariants of semi-algebraic sets with special emphasis on the more recent developments in designing algorithms for computing the Betti numbers of semi-algebraic sets. Aside from…
The main purpose of this paper is to lay the foundations of a general theory which encompasses the features of the classical Hough transform and extend them to general algebraic objects such as affine schemes. The main motivation comes from…
We survey the development of Clifford's geometric algebra and some of its engineering applications during the last 15 years. Several recently developed applications and their merits are discussed in some detail. We thus hope to clearly…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
Classical (Euclidean) Laguerre geometry studies oriented hyperplanes, oriented hyperspheres, and their oriented contact in Euclidean space. We describe how this can be generalized to arbitrary Cayley-Klein spaces, in particular hyperbolic…
The field of numerical algebraic geometry consists of algorithms for numerically solving systems of polynomial equations. When the system is exact, such as having rational coefficients, the solution set is well-defined. However, for a…
We study the Dirichlet problem for semilinear equations on general open sets with measure data on the right-hand side and irregular boundary data. For this purpose we develop the classical method of orthogonal projection. We treat in a…
A problem concerning the shift of roots of a system of homogeneous algebraic equations is investigated. Its conservation and decomposition of a multiple root into simple roots are discussed.