Related papers: P versus NP and geometry
We develop a theory of complexity for numerical computations that takes into account the condition of the input data and allows for roundoff in the computations. We follow the lines of the theory developed by Blum, Shub, and Smale for…
Some basic notions and results in Topological Dynamics are extended to continuous groupoid actions in topological spaces. We focus mainly on recurrence properties. Besides results that are analogous to the classical case of group actions,…
The aim of this article is to present unifying proofs for results in geometric quantisation with real polarisations by exploring the existence of symplectic circle actions. It provides an extension of Rawnsley's results on the Kostant…
Triple factorisations of finite groups $G$ of the form $G=PQP$ are essential in the study of Lie theory as well as in geometry. Geometrically, each triple factorisation $G=PQP$ corresponds to a $G$-flag transitive point/line geometry such…
We describe quantizations on monoidal categories of modules over finite groups. They are given by quantizers which are elements of a group algebra. Over the complex numbers we find these explicitly. For modules over S3 and A4 we are given…
The goal of this paper is to consider some relations between varieties of representations of groups and varieties of associative algebras. The main emphasis is put on the varieties of representations of groups induced by the varieties of…
The vast majority of scientific community believes that P!=NP, with countless supporting arguments. The number of people who believe otherwise probably amounts to as few as those opposing the 2nd Law of Thermodynamics. But isn't nature…
Problems of dense and closed extension of actions of compact transformation groups are solved. The method developed in the paper is applied to problems of extension of equivariant maps and of construction of equivariant compactifications.
A generalization of recent group-theoretic matrix multiplication algorithms to an analogue of the theory of partial matrix multiplication is presented. We demonstrate that the added flexibility of this approach can in some cases improve…
We extend several techniques and theorems from geometric group theory so that they apply to geometric actions on arbitrary proper metric ARs (absolute retracts). A second way that we generalize earlier results is by eliminating freeness…
We define formal geometric quantisation for proper Hamiltonian actions by possibly noncompact groups on possibly noncompact, prequantised symplectic manifolds, generalising work of Weitsman and Paradan. We study the functorial properties of…
Computational complexity is examined using the principle of increasing entropy. To consider computation as a physical process from an initial instance to the final acceptance is motivated because many natural processes have been recognized…
This is a survey article devoted to the study of real structures on complex algebraic varieties endowed with a reductive group action.
In this talk, we'll present some recent results related to group actions in several complex variables. We'll not aim at giving a complete survey about the topic but giving some our own results and related ones. We'll divide the results into…
The purpose of this article is to examine and limit the conditions in which the P complexity class could be equivalent to the NP complexity class. Proof is provided by demonstrating that as the number of clauses in a NP-complete problem…
We present and discuss applications of the category of probabilistic morphisms, initially developed in \cite{Le2023}, as well as some geometric methods to several classes of problems in statistical, machine and manifold learning which shall…
We develop a complexity theory for approximate real computations. We first produce a theory for exact computations but with condition numbers. The input size depends on a condition number, which is not assumed known by the machine. The…
We present a general framework for reduction of symplectic Q-manifolds via graded group actions. In this framework, the homological structure on the acting group is a multiplicative multivector field.
Consider a finite group $G$ acting on a graded Noetherian $k$-algebra $S$, for some field $k$ of characteristic $p$; for example $S$ might be a polynomial ring. Regard $S$ as a $kG$-module and consider the multiplicity of a particular…
A full Lie point symmetry analysis of rational difference equations is performed. Non-trivial symmetries are derived and exact solutions using these symmetries are obtained.