Related papers: A factorization homology primer

This habilitation thesis summarizes the research that I have carried out from 2005 to 2019. It is organized in four chapters. The first three deal with random planar maps. Chapter 1 is about their metric properties: from a general…

We define a new cohomology for associative algebras which we compute for algebras with units.

We factorize harmonic maps with values in a semisimple Lie groups in a product of harmonic maps with values in the components of the Iwasawa decomposition. In particular, we use this factorization to study the harmonic maps from…

We show that any joint probability mass function (PMF) can be expressed as a product of parity check factors and factors of degree one with the help of some auxiliary variables, if the alphabet size is appropriate for defining a parity…

We survey earlier results on factorizations of extremal projectors and relative extremal projectors and present preliminary results on non-commutative factorizations of relative extremal projectors: we deduce the existence of such…

Using factorization homology, we realize the rational homology of the unordered configuration spaces of an arbitrary manifold $M$, possibly with boundary, as the homology of a Lie algebra constructed from the compactly supported cohomology…

Graph compositions generalize both integer compositions and partitions of a finite set. We develop formulas, generating functions and recurrence relations for composition counting functions for several families of graphs.

Another approach to constructing an upper bound for the Riemann-Farey sum is described.

Polynomial factorization and root finding are among the most standard themes of computational mathematics. Yet still, little has been done for polynomials over quaternion algebras, with the single exception of Hamiltonian quaternions for…

This paper provides an introduction to the basics of Heegaard Floer homology with some emphasis on the hat theory and to the contact geometric invariants in the theory. The exposition is designed to be comprehensible to people without any…

We construct linear operators factorizing the three bases of symmetric polynomials: monomial symmetric functions m(x), elementary symmetric polynomials E(x), and Schur functions s(x), into products of univariate polynomials.

We introduce and investigate the category of factorization of a multiplicative, commutative, cancellative, pre-ordered monoid $A$, which we denote $\mathcal{F}(A)$. The objects of $\mathcal{F}(A)$ are factorizations of elements of $A$, and…

We introduce twisted matrix factorizations for quantum complete intersections of codimension two. For such an algebra, we show that in a given dimension, almost all the indecomposable modules with bounded minimal projective resolutions…

All components of complements of discriminant varieties of simple real function singularities are explicitly listed. New invariants of such components (for not necessarily simple singularities) are introduced. A combinatorial algorithm…

This primer is intended as an introduction to differential forms, a central object in modern mathematical physics, for scientists and engineers.

This re-certifying paper describes the details of the Morse homology of manifolds with boundary, introduced by the author before, in terms of handlebody decompositions.

All ten symmetry classes of plane partitions that fit in a given box are known to be enumerated by simple product formulas, but there is still no unified proof for all of them. Progress towards this goal can be made by establishing…

A novel factorization for the sum of two single-pair matrices is established as product of lower-triangular, tridiagonal, and upper-triangular matrices, leading to semi-closed-form formulas for tridiagonal matrix inversion. Subsequent…

A brief review of checking the factorization hypothesis for matrix element of $B^0 - \bar B^0$ mixing within operator product expansion and QCD sum rules is given. Both perturbative and power corrections are considered.

This article investigates the homotopy theory of simplicial commutative algebras with a view to homological applications.