Related papers: Generalisation of an IMO Geometry Problem
We present a brief overview of some key concepts in the theory of generalised complex manifolds. This new geometry interpolates, so to speak, between symplectic geometry and complex geometry. As such it provides an ideal framework to…
In this paper, by using analytical methods we obtain a generalization of the famous Kodaira embedding theorem.
This is an overview of math.AG/0310186, math.AG/0309290, math.AG/0501247, math.AG/0401002 and math.AG/0504584 written for the Proceedings of the AMS Meeting on Algebraic Geometry, Seattle, 2005.
So far, the most magnificent breakthrough in mathematics in the 21st century is the Geometrization Theorem, a bold conjecture by William Thurston (generalizing Poincar\'e's Conjecture) and proved by Grigory Perelman, based on the program…
Projective geometry provides the preferred framework for most implementations of Euclidean space in graphics applications. Translations and rotations are both linear transformations in projective geometry, which helps when it comes to…
We propose a robust and scalable procedure for general optimization and inference problems on manifolds leveraging the classical idea of `median-of-means' estimation. This is motivated by ubiquitous examples and applications in modern data…
The projective line over a field carries structure of a groupoid with a certain correspondence between objects and arrows. We discuss to what extent the field can be reconstructed from the groupoid.
Problem of global integration of geometric structures arising in the theory of dynamical systems admitting the normal shift is considered. In the case when such integration is possible the problem of globalization for shift maps is studied.
Open problems from the 15th Annual ACM Symposium on Computational Geometry.
The geometry of atomic arrangement underpins the structural understanding of molecules in many fields. However, no general framework of mathematical/computational theory for the geometry of atomic arrangement exists. Here we present…
Initial Orbit Determination (IOD) is the classical problem of estimating the orbit of a body in space without any presumed information about the orbit. The geometric formulation of the ''angles-only'' IOD in three-dimensional space: find a…
We address, through the automated reasoning tools in GeoGebra Discovery, a problem from a regional phase of the Austrian Mathematics Olympiad 2023. Trying to solve this problem gives rise to four different kind of feedback: the almost…
Many machine learning methods assume that the training and test data follow the same distribution. However, in the real world, this assumption is very often violated. In particular, the phenomenon that the marginal distribution of the data…
In this note, we present a refinement of the well-known AM-GM inequality. We use this improved inequalty to establish corresponding inequalities on Hilbert space. We also give some refinements of the Kantorovich inequality.
Cyclic polytopes have been studied since at least the early last century by Caratheodory and others.A generalization is a construction of a class of polytopes such that the polytopes have some of their properties.The best known example is…
This text serves as an introduction to $\mathbb{F}_1$-geometry for the general mathematician. We explain the initial motivations for $\mathbb{F}_1$-geometry in detail, provide an overview of the different approaches to $\mathbb{F}_1$ and…
An analogue of geometric quantization of Poisson algebras obtained by algebraic reduction of symmetries is developed. Interpretation of the obtained results and their application to the problem of commutativity of quantization and reduction…
We compute the depth and (give bounds for) the regularity of generalized binomial edge ideals associated with generalized block graphs.
One considers geometry with the intransitive equaivalence relation. Such a geometry is a physical geometry, i.e. it is described completely by the world function, which is a half of the squared distance function. The physical geometry…
In this paper we deal with a general type of integral formulas of the visual angle, among them those of Crofton, Hurwitz and Masotti, from the point of view of Integral Geometry. The purpose is twofold: to provide an interpretation of these…