Related papers: Finite Generation of Canonical Ring by Analytic Me…
The article presents several methods for the arithmetic of finite abelian groups. We introduce a tool - already used by Delsarte in [1] as I found out later - analogous to Dirichlet's convolution to obtain combinatorial results on these…
Three elementary canonical transformations are shown both to have quantum implementations as finite transformations and to generate, classically and infinitesimally, the full canonical algebra. A general canonical transformation can, in…
As automated reasoning systems advance rapidly, there is a growing need for research-level formal mathematical problems to accurately evaluate their capabilities. To address this, we present Formal Conjectures, an evolving benchmark of…
We introduce the notion of radical preservation and prove that a radical-preserving homomorphism of left artinian rings of finite projective dimension with superfluous kernel reflects the finiteness of the little finitistic, big finitistic…
We construct finite coherent presentations of plactic monoids of type A. Such coherent presentations express a system of generators and relations for the monoid extended in a coherent way to give a family of generators of the relations…
We give a canonical construction of a balanced big Cohen-Macaulay algebra for a domain of finite type over $\mathbb C$ by taking ultraproducts of absolute integral closures in positive characteristic. This yields a new tight closure…
Ensemble control, an emerging research field focusing on the study of large populations of dynamical systems, has demonstrated great potential in numerous scientific and practical applications. Striking examples include pulse design for…
Full residual finiteness growth of a finitely generated group $G$ measures how efficiently word metric $n$-balls of $G$ inject into finite quotients of $G$. We initiate a study of this growth over the class of nilpotent groups. When the…
We give a new proof of the finiteness of B-representations. As a consequence of the finiteness of B-representations and Koll\'ar's gluing theory on lc centers, we prove that the (relative) abundance conjecture for slc pairs is implied by…
This paper develops a proof-theoretic framework for abstract interpretation by systematically associating logical systems with finite abstractions. Building on earlier work on the internal logics of abstractions, we propose a general…
On a complex symplectic manifold we prove a finiteness result for the global sections of solutions of holonomic DQ-modules in two cases: (a) by assuming that there exists a Poisson compactification (b) in the algebraic case. This extends…
We present a characterization of the completeness of the field of real numbers in the form of a \emph{collection of ten equivalent statements} borrowed from algebra, real analysis, general topology and non-standard analysis. We also discuss…
We sketch a simplification of proofs of old results on the arithmeticity of the group generated by opposing integral unipotent radicals in higher rank arithmetic groups
A group presentation is said to have rational growth if the generating series associated to its growth function represents a rational function. A long-standing open question asks whether the Heisenberg group has rational growth for all…
In this note, we will give an positive answer to Pan-Rong's conjecture that for an open manifold with nonnegative Ricci curvature, if its universal cover has Euclidean volume growth, then its fundamental group is finitely generated.…
Let ${\mathbf U}_q^-$ be the negative half of a quantum group of finite type. We construct the canonical basis of ${\mathbf U}_q^-$ by applying the folding theory of quantum groups, and piecewise linear parametrization of canonical basis.…
The purpose of this paper is to prove that the symbolic Rees rings of ideals defining certain finite sets of points in the projective plane over an algebraically closed field are finitely generated using a ring theoretical criterion which…
While Retrieval-Augmented Generation (RAG) mitigates hallucination and knowledge staleness in Large Language Models (LLMs), existing frameworks often falter on complex, multi-hop queries that require synthesizing information from disparate…
It is shown that the free energy associated to a finite dimensional Airy structure is an analytic function at each finite order of the $\hbar$ expansion. Semiclassical series itself is in general divergent. Calculations are facilitated by…
To use evolution algebras to model population dynamics that both allow extinction and introduction of certain gametes in finite generations, nilpotency must be built into the algebraic structures of these algebras with the entire algebras…