Related papers: Computing Schur complexes
We explain a Macaulay2 implementation of a construction, which appeared in [Holweck-Oeding arXiv:2206.13662], of a graded algebra structure on the direct sum of a Lie algebra $\mathfrak{g}$ (typically $\mathfrak{sl}_n$) and a…
Linear complexity is an important parameter for arrays that are used in applications related to information security. In this work we survey constructions of two and three dimensional arrays, and present new results on the multidimensional…
Plane partitions have been widely studied in Mathematics since MacMahon. See, for example, the works by Andrews, Macdonald, Stanley, Sagan and Krattenthaler. The Schur process approach, introduced by Okounkov and Reshetikhin, and further…
This paper is devoted to overview of the authors works for numerical solution of singular integral equations (SIE), polysingular integral equations and multi-dimensional singular integral equations of the second kind. The authors…
Here I present the 'clifford' package for working with Clifford algebras in the R programming language. The algebra is described and package idiom is given.
Basic elements of integral calculus over algebras of iterated differential forms, are presented. In particular, defining complexes for modules of integral forms are described and the corresponding berezinians and complexes of integral forms…
We construct the first, second and sophisticated non-linear and linear Spencer complexes for a differentiable Lie groupoid $G$. To do this, we extend the diagonal calculus, as applied by Malgrange to the groupoid $M\times M$, to the context…
We construct an Euler system attached to a weight 2 modular form twisted by a Groessencharacter of an imaginary quadratic field, and apply this to bounding Selmer groups.
We compute the cohomological Brauer groups of twists of weighted projective spaces and weighted projective stacks.
Package-X, a Mathematica package for the analytic computation of one-loop integrals dimensionally regulated near 4 spacetime dimensions is described. Package-X computes arbitrarily high rank tensor integrals with up to three propagators,…
We study dualizing complexes on algebraic stacks. In particular, we show their existence for (tame) Deligne--Mumford stacks of equicharacteristic in great generality.
We present here a new package to automatically generate a complete library of 2 to 2 squared amplitudes at leading order in any New Physics models. The package is written in C++ and based on the MARTY software. The numerical library…
We compute explicit formulas for the Euler characteristic of line bundles in the two exceptional examples of Hyperk\"ahler Manifolds introduced by O'Grady. In the Appendix Yalong Cao and Chen Jiang use our formulas to compute the Chern…
We introduce the Mathematica package SummerTime for arbitrary-precision computation of sums appearing in the results of DRA method. So far these results include the following families of the integrals: 3-loop onshell massless vertices,…
We present BSeries.jl, a Julia package for the computation and manipulation of B-series, which are a versatile theoretical tool for understanding and designing discretizations of differential equations. We give a short introduction to the…
In the previous papers \cite{L1, L2} the author constructed Mabuchi and Aubin-Yau functionals over any complex surfaces and three-folds, respectively. Using the method in \cite{L2}, we construct those functionals over any complex manifolds…
We establish upper bounds of bit complexity of computing solution operators for symmetric hyperbolic systems of PDEs. Here we continue the research started in in our revious publications where computability, in the rigorous sense of…
The singular chain complex of the iterated loop space is expressed in terms of the cobar construction. After that we consider the spectral sequence of the cobar construction and calculate its first term over Z/p-coefficients and over a…
NonlinearSchrodinger.jl is a Julia package with a simple interface for studying solutions of nonlinear Schr\"odinger equations (NLSEs). In approximately ten lines of code, one can perform a simulation of the cubic NLSE using one of 32…
A common challenge in scientific and technical domains is the quantitative description of geometries and shapes, e.g. in the analysis of microscope imagery or astronomical observation data. Frequently, it is desirable to go beyond scalar…