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A Chen generating series, along a path and with respect to $m$ differential forms,is a noncommutative series on $m$ letters and with coefficients which are holomorphic functionsover a simply connected manifold in other words a series with…
We use the moment method of Wood to study the distribution of random finite modules over a countable Dedekind domain with finite quotients, generated by taking cokernels of random $n\times n$ matrices with entries valued in the domain.…
In a recent paper we proposed the study of aggregation functions on lattices via clone theory approach. Observing that aggregation functions on lattices just correspond to $0,1$-monotone clones, we have shown that all aggregation functions…
We study generating series of torus integrals that contain all so-called modular graph forms relevant for massless one-loop closed-string amplitudes. By analysing the differential equation of the generating series we construct a solution…
We present a new type of equivalence for representable matroids that uses the automorphisms of the underlying matroid. Two $r\times n$ matrices $A$ and $A'$ representing the same matroid $M$ over a field $F$ are {\it geometrically…
This is the first in a series of two papers that study monogenicity of number rings from a moduli-theoretic perspective. Given an extension of algebras $B/A$, when is $B$ generated by a single element $\theta \in B$ over $A$? In this paper,…
Let $O_X$ (resp. $D_X$) be the sheaf of holomorphic functions (resp. the sheaf of linear differential operators with holomorphic coefficients) on $X$ (=the complex affine n-space). Let $Y$ be a locally weakly quasi-homogeneous free divisor…
In 2019, Butler, Choi, Kim, and Seo introduced a new type of juggling card that represents multiplex juggling patterns in a natural bijective way. They conjectured a formula for the generating function for the number of multiplex juggling…
We give a necessary condition of degeneration via matrix representations, and consider degenerations of indecomposable Cohen-Macaulay modules over hypersurface singularities of type ($A_\infty$). We also provide a method to construct…
Motivated by ideas from stable homotopy theory we study the space of strongly homotopy associative multiplications on a two-cell chain complex. In the simplest case this moduli space is isomorphic to the set of orbits of a group of…
K-theoretic Donaldson invariants are holomorphic Euler characteristics of determinant line bundles on moduli spaces of sheaves on surfaces. We compute generating functions of K-theoretic Donaldson invariants on the projective plane and…
We initiate the study of enumerating linear subspaces of alternating matrices over finite fields with explicit coordinates. We postulate that this study can be viewed as a linear algebraic analogue of the classical topic of enumerating…
Let $n$ be a natural number and $\mathcal{M}$ a set of $n \times n$-matrices over the nonnegative integers such that the joint spectral radius of $\mathcal{M}$ is at most one. We show that if the zero matrix $0$ is a product of matrices in…
We give a general formula for generators of the NL-cone, the cone of effective linear combinations of irreducible components of Noether-Lefschetz divisors, on an orthogonal modular variety. We then fully describe the NL-cone and its…
We give a purely algebraic construction of a cohomological field theory associated with a quasihomogeneous isolated hypersurface singularity W and a subgroup G of the diagonal group of symmetries of W. This theory can be viewed as an…
An $A$-module $E$ is said to be an \textit{annihilator multiplication module} if for each $e\in E$, there exists a finitely generated ideal $I$ of $A$ such that $ann(e)=ann(IE)$. This class of modules is quite large, as it contains…
Let $\mathbb{F}_q$ be a finite field with $q$ elements. M. Gerstenhaber and Irving Reiner has given two different methods to show the number of matrices with a given characteristic polynomial. In this talk, we will give another proof for…
The aim of this paper is to extend the structure theory for infinitely generated modules over tame hereditary algebras to the more general case of modules over concealed canonical algebras. Using tilting, we may assume that we deal with…
Let $\Lambda$ be a Legendrian in the jet space of some manifold $X$. To a generating family presentation of $\Lambda$, we associate a constructible sheaf on $X \times \mathbb{R}$ whose singular support at infinity is $\Lambda$, and such…
In this paper we use the results from the first part to compute the vanishing topology for matrix singularities based on certain spaces of matrices. We place the variety of singular matrices in a geometric configuration of free divisors…