相关论文: Geometry of symplectic intersections

Examples of nonformal simply connected symplectic manifolds are constructed.

In this article, we study the question of existence of leafwise intersection points for contact manifolds which are not necessarily of restricted contact type. Moreover we can find a leafwise intersection point on the symplectization for…

We obtain a coarse relationship between geometric intersection numbers of curves and the sum of their subsurface projection distances with explicit quasi-constants. By using this relationship, we give applications in the studies of the…

In recent work, we introduced topological notions of simple normal crossings symplectic divisor and variety, showed that they are equivalent, in a suitable sense, to the corresponding geometric notions, and established a topological…

Continuing from part (I), we develop properties of real intersection theory that turns out to be an extension of the well-established theory in algebraic geometry.

We present a new approach for constructing covariant symplectic structures for geometrical theories, based on the concept of adjoint operators. Such geometric structures emerge by direct exterior derivation of underlying symplectic…

In these memos, we define a pregeometry $\mathcal{T}_{\mathbb{S}} ^{alg}$ and a geometry $\mathcal{G}_{\mathbb{S}} ^{alg}$ which integrate symplectic manifolds with $E_{\infty}$-ring sheaves, enabling the construction of…

In this note we give simple symplecticity conditions for implicit schemes in the linear case. We consider implicit maps on generic symplectic manifold and we introduce the concept of consistent implicit maps, to generalize the symplecticity…

This paper first gives a brief overview over some interesting descriptions of conic sections, showing formulations in the three geometric algebras of Euclidean spaces, projective spaces, and the conformal model of Euclidean space. Second…

This is a survey on symplectic birational geometry. In arbitrary dimension, this subject is centered around the notion of uniruledness. In low dimensions, we will also discuss Kodaira dimension and minimality.

We study the local symplectic algebra of the 0-dimensional isolated complete intersection singularities. We use the method of algebraic restrictions to classify these symplectic singularities. We show that there are non-trivial symplectic…

The goal of this article is to survey recent developments in the theory of contact structures in dimension three.

A short survey on applications of algebraic geometry in topological data analysis.

In this article we study Ammann tilings from the perspective of symplectic geometry. Ammann tilings are nonperiodic tilings that are related to quasicrystals with icosahedral symmetry. We associate to each Ammann tiling two explicitly…

In this article, we are concerned with various aspects of arcs on surfaces. In the first part, we deal with topological aspects of arcs and their complements. We use this understanding, in the second part, to construct interesting actions…

A family of graphs optimized as the topologies for supercomputer interconnection networks is proposed. The special needs of such network topologies, minimal diameter and mean path length, are met by special constructions of the weight…

This is a survey of recent developments in combinatorics. The goal is to give a big picture of its many interactions with other areas of mathematics, such as: group theory, representation theory, commutative algebra, geometry (including…

This is a survey written in an expositional style on the topic of symplectic singularities and symplectic resolutions, which could also serve as an introduction to this subject.

The purpose of this paper is to present some results on the existence of homologous, nonisotopic symplectic or lagrangian surfaces embedded in a simply connected symplectic 4-dimensional manifold.

Systems of partial differential equations which appear in classical field theories can be studied geometrically using different geometrical structures, for example, k-symplectic geometry, k-cosymplectic geometry, multisymplectic geometry,…