Related papers: A factorization homology primer
The article shows how the factorization of an arbitrary Lorentz transformation is performed. That is, representation of an arbitrary Lorentz transformation as a sequence of spatial rotation and boost or boost and spatial rotation. Relations…
We overview some of theory and phenomenology aspects of high energy factorization. In the theory part we focus on basic equations of high energy factorization i.e. BFKL, CCFM, BK. In the phenomenology part we focus on forward-central jets…
In this note some recent developments in the study of homology in semi-abelian categories are briefly presented. In particular the role of protoadditive functors in the study of Hopf formulae for homology is explained.
We propose to study homomorphisms of connectome graphs. Homomorphisms can be studied as sequences of elementary homomorphisms - folds, which identify pairs of vertices. Several fold types are defined. Initial computation results for some…
An extension to the factorisation principle as suggested by Fermat is presented.We start from a symmetry of natural numbers and obtain the factorisation principle therefrom.Later it is extended further to test the primality of any natural…
The rational homology group of the order complex of non-even partitions of a finite set is calculated. A twisted version of the Goresky-MacPherson approach to similar homology calculations is proposed.
We define a relative version of contact homology for contact manifolds with convex boundary, and prove basic properties of this relative contact homology. Similar considerations also hold for embedded contact homology.
In this review the foundations of Geometric Quantization are explained and discussed. In particular, we want to clarify the mathematical aspects related to the geometrical structures involved in this theory: complex line bundles, hermitian…
We construct a pairing, which we call factorization homology, between framed manifolds and higher categories. The essential geometric notion is that of a vari-framing of a stratified manifold, which is a framing on each stratum together…
Mott noted a one-to-one correspondence between saturated multiplicatively closed subsets of a domain D and directed convex subgroups of the group of divisibility D. With this, we construct a functor between inclusions into saturated…
We develop a theory of equivariant factorization algebras on varieties with an action of a connected algebraic group $G$, extending the definitions of Francis-Gaitsgory [FG] and Beilinson-Drinfeld [BD1] to the equivariant setting. We define…
The present paper is mainly a survey of our work arXiv:0708.4221 and arXiv:0808.2440 but it also contains the announcement of some new results. Its main purpose is to present an accessible introduction to a technique allowing efficient…
Persistent homology is a topological feature used in a variety of applications such as generating features for data analysis and penalizing optimization problems. We develop an approach to accelerate persistent homology computations…
This paper addresses new results on the factorization of the general Heun's operator, extending the investigations performed in previous works [{\it Applied Mathematics and Computation} {\bf 141} (2003), 177 - 184 and {\bf 189} (2007), 816…
We summarize the standard factorization theorems for hard processes in QCD, and describe their proofs.
This is the first of two coupled papers estimating the mean values of multiplicative functions, of unknown support, on arithmetic progressions with large differences. Applications are made to the study of primes in arithmetic progression…
The contents of this 98-page paper have been subsumed into the 191-page paper "A colored sl(N)-homology for links in S^3" (arXiv:0907.0695v1 [math.GT]), in which we further develop the theory and use it to construct a colored link homology.
The chapter provides an introduction to the basic concepts of Algebraic Topology with an emphasis on motivation from applications in the physical sciences. It finishes with a brief review of computational work in algebraic topology,…
In this talk, I reviewed the role of factorization in diffraction hard scattering.
We introduce and consider a certain probability question involving elementary number theory and the likelihood that a fixed prime will appear in a certain recursively defined factorization of an integer. We derive several convergent…