Related papers: Virtual harmony
This paper aims to undertake an exploration of the behavior of the moduli space of line arrangements while establishing its combinatorial interplay with the incidence structure of the arrangement. In the first part, we investigate…
An approach to description of interactive psychoinformation systems, based on the concept of "virtualization" and essentially using the technique of the "secondary image synthesis" (adap-org/9409002), is sketched. The article has a rather…
We prove that, for any n, there are simply-connected four-manifolds which admit n-tuples of symplectic forms whose first Chern classes have pairwise different divisibilities in integral cohomology. It follows that the moduli space of…
Hybrid systems are complex dynamical systems that combine discrete and continuous components. Reachability questions, regarding whether a system can run into a certain subset of its state space, stand at the core of verification and…
In this thesis we study synchronization phenomena in natural and artificial coupled multi-component systems, applicable to the scalability of parallel discrete-event simulation for systems with asynchronous dynamics. We analyze the…
Motivated by counting pseudo-holomorphic curves in symplectic Calabi-Yau $3$-folds, this article studies a chamber structure in the space of real Cauchy-Riemann operators on a Riemann surface, and constructs three chambered invariants…
This survey paper addresses uniqueness questions for symplectic forms on closed manifolds, explains what is known in several examples, and reviews some open problems.
Virtual collaborative environment are 3D shared spaces in which people can work together. To collaborate through these systems, users must have a shared comprehension of the environment. The objective of this experimental study was to…
Kuranishi atlases were introduced by McDuff and Wehrheim to build a virtual fundamental class on moduli spaces of J-holomorphic curves and resolve some of the challenges in this field. This paper considers Gromov-Witten moduli spaces and…
In the first part of the present series of papers, we studied the moduli spaces of holomorphic discs and strips into an open symplectic manifold, isomorphic to the complement of a smooth divisor in a closed symplectic manifold. In…
Despite spectacular advances in defining invariants for simply connected smooth and symplectic 4-dimensional manifolds and the discovery of effective surgical techniques, we still have been unable to classify simply connected smooth…
Using a simplified version of Kuranishi perturbation theory that we call semi-global Kuranishi structures, we give a definition of the equivariant Lagrangian Floer cohomology of a pair of Lagrangian submanifolds that are fixed under a…
We review a geometric approach to classification and examination of quantum correlations in composite systems. Since quantum information tasks are usually achieved by manipulating spin and alike systems or, in general, systems with a finite…
If a one-phrase summary of the subject of this thesis were required, it would be something like: miscellaneous large (but finite) dimensional phenomena in quantum information theory. That said, it could nonetheless be helpful to briefly…
In this paper, we provide a geometric characterization of virtual nonlinear nonholonomic constraints from a symplectic perspective. Under a transversality assumption, there is a unique control law making the trajectories of the associated…
Processes are often viewed as coalgebras, with the structure maps specifying the state transitions. In the simplest case, the state spaces are discrete, and the structure map simply takes each state to the next states. But the coalgebraic…
Let $({\bf X},\omega_{\bf X}^*)$ be a separated, $-2$-shifted symplectic derived $\mathbb C$-scheme, in the sense of Pantev, Toen, Vezzosi and Vaquie arXiv:1111.3209, of complex virtual dimension ${\rm vdim}_{\mathbb C}{\bf X}=n\in\mathbb…
These informal lecture notes describe the progress in semiconductor spintronics in a historic perspective as well as in a comparison to achievements of spintronics of ferromagnetic metals. After outlining motivations behind spintronic…
We present a construction (and classification) of certain invariant 2-forms on the real symplectic group. They are used to define a symplectic form on the quotient by a maximal torus and to "lift" a symplectic structure from a symplectic…
In this expository manuscript, we review the construction of Gromov-Witten virtual fundamental class via FOOO's theory of Kuranishi structures for moduli spaces of pseudo-holomorphic maps defined on closed Riemann surfaces. We consider…