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On when the union of two algebraic sets is algebraic
In universal algebraic geometry, an algebra is called an equational domain if the union of two algebraic sets is algebraic. We characterize...
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Topology of closure systems in algebraic lattices
Algebraic lattices are spectral spaces for the coarse lower topology. Closure systems in algebraic lattices are studied as subspaces. Connections...
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LATTICE VERTEX ALGEBRAS AND LOOP GRASSMANNIANS
For an integral symmetric matrix κ we construct a new “nonabelian homology localization” of the lattice vertex algebra
L κ on the corresponding loop... -
Interactions with Lattice Polytopes Magdeburg, Germany, September 2017
This book collects together original research and survey articles highlighting the fertile interdisciplinary applications of convex lattice polytopes...
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Representing Distributive Dually Algebraic Lattices
We show that every distributive dually algebraic lattice can be represented as Sp(S, H) with S an algebraic lattice and H a monoid of operators. As a...
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Random Algebraic Numbers
A family of measures on a given set of real algebraic numbers of arbitrary fixed degree is considered. The paper presents a method for constructing a...
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Hodge similarities, algebraic classes, and Kuga–Satake varieties
We introduce in this paper the notion of Hodge similarities of transcendental lattices of hyperkähler manifolds and investigate the Hodge conjecture...
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Lattice-Based Cryptography: A Survey
Most of current public key cryptosystems would be vulnerable to the attacks of the future quantum computers. Post-quantum cryptography offers...
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Algebraic Preliminaries
In this chapter, we review some facts from abstract algebra. Since we assume that the reader is familiar with basic abstract algebra, we put the...
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Connected topological lattice-ordered groups
We answer two open problems about lattice-ordered groups that admit a connected lattice-ordered group topology. We show that, in the general case,...
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Algebraic Approaches to the Analysis of Social Networks
This chapter reviews the use of algebraic approaches for understanding the interconnected nature of social relationships. It outlines the algebraic...
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Algebraic Structures and Social Processes
There has long been an interest among social scientists in the use of algebraic structures to analyze social data. Many popular approaches are...
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Algebraic Machine Learning: Emphasis on Efficiency
AbstractA survey of the state of the art in research on algebraic machine learning is presented. The main emphasis is on computational complexity....
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Counting intrinsic Diophantine approximations in simple algebraic groups
We establish an explicit asymptotic formula for the number of rational solutions of intrinsic Diophantine inequalities on simply-connected simple...
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Pointed Lattice Subreducts of Varieties of Residuated Lattices
We study the pointed lattice subreducts of varieties of residuated lattices (RLs) and commutative residuated lattices (CRLs), i.e. lattice subreducts...
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Euclidean minima of algebraic number fields
In this paper, we use some of our previous results to improve an upper bound of Bayer–Fluckiger, Borello, and Jossen on the Euclidean minima of...
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Existence of moduli spaces for algebraic stacks
We provide necessary and sufficient conditions for when an algebraic stack admits a good moduli space and prove a semistable reduction theorem for...
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Compound Cubature Formulas on a Lattice
AbstractIn the present paper the lattice optimal cubature formulas are constructed by the variational method in the Sobolev space. In addition, the...