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Journal articles on the topic 'Categorical spectral theory'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

Ben-Zvi, David, David Nadler, and Anatoly Preygel. "A spectral incarnation of affine character sheaves." Compositio Mathematica 153, no. 9 (2017): 1908–44. http://dx.doi.org/10.1112/s0010437x17007278.

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We present a Langlands dual realization of the putative category of affine character sheaves. Namely, we calculate the categorical center and trace (also known as the Drinfeld center and trace, or categorical Hochschild cohomology and homology) of the affine Hecke category starting from its spectral presentation. The resulting categories comprise coherent sheaves on the commuting stack of local systems on the two-torus satisfying prescribed support conditions, in particular singular support conditions, which appear in recent advances in the geometric Langlands program. The key technical tools

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2

Jamotton, Charlotte, Donatien Hainaut, and Thomas Hames. "Insurance Analytics with Clustering Techniques." Risks 12, no. 9 (2024): 141. http://dx.doi.org/10.3390/risks12090141.

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The K-means algorithm and its variants are well-known clustering techniques. In actuarial applications, these partitioning methods can identify clusters of policies with similar attributes. The resulting partitions provide an actuarial framework for creating maps of dominant risks and unsupervised pricing grids. This research article aims to adapt well-established clustering methods to complex insurance datasets containing both categorical and numerical variables. To achieve this, we propose a novel approach based on Burt distance. We begin by reviewing the K-means algorithm to establish the f

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3

Lin, Yen-Hwei. "PHONOLOGICAL KNOWLEDGE: CONCEPTUAL AND EMPIRICAL ISSUES. Noel Burton-Roberts, Philip Carr, and Gerard Docherty (Eds.). Oxford: Oxford University Press, 2001. Pp. x + 352. $85.00 cloth, $35.00 paper." Studies in Second Language Acquisition 25, no. 3 (2003): 460–61. http://dx.doi.org/10.1017/s0272263103230199.

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This book is a collection of papers dealing with the philosophical, conceptual, and empirical foundations of phonology, its position and relation with respect to syntax and phonetics in the theory of language, and the nature and acquisition of phonological knowledge. The introductory chapter by the editors provides a comprehensive discussion of the main themes presented in the following 11 chapters, in which diverse perspectives are represented. Bromberger and Halle open with a discussion of phonology within the context of the philosophy of language. Some chapters take a highly formal view of

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4

Hebestreit, Fabian, and Steffen Sagave. "Homotopical and operator algebraic twisted K-theory." Mathematische Annalen 378, no. 3-4 (2020): 1021–59. http://dx.doi.org/10.1007/s00208-020-02066-6.

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Abstract Using the framework for multiplicative parametrized homotopy theory introduced in joint work with C. Schlichtkrull, we produce a multiplicative comparison between the homotopical and operator algebraic constructions of twisted K-theory, both in the real and complex case. We also improve several comparison results about twisted K-theory of $$C^*$$ C ∗ -algebras to include multiplicative structures. Our results can also be interpreted in the $$\infty $$ ∞ -categorical setup for parametrized spectra.

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5

Yeshkeyev, A. R., A. R. Yarullina, and S. M. Amanbekov. "On categoricity questions for universal unars and undirected graphs under semantic Jonsson quasivariety." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 111, no. 3 (2023): 165–80. http://dx.doi.org/10.31489/2023m3/165-180.

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The article is devoted to the study of semantic Jonsson quasivarieties of universal unars and undirected graphs. The first section of the article consists of basic necessary concepts from Jonsson model theory. The following two sections are results of using new notions of semantic Jonsson quasivariety of Robinson unars JCU and semantic Jonsson quasivariety of Robinson undirected graphs JCG, its elementary theory and semantic model. In order to prove two main results of the paper, Robinson spectra RSp(JCU) and RSp(JCG) and their partition onto equivalence classes [∆]U and [∆]G by cosemanticness

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Guillou, Bertrand J., J. Peter May, Mona Merling, and Angélica M. Osorno. "SYMMETRIC MONOIDAL G-CATEGORIES AND THEIR STRICTIFICATION." Quarterly Journal of Mathematics 71, no. 1 (2019): 207–46. http://dx.doi.org/10.1093/qmathj/haz034.

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Abstract We give an operadic definition of a genuine symmetric monoidal $G$-category, and we prove that its classifying space is a genuine $E_\infty $$G$-space. We do this by developing some very general categorical coherence theory. We combine results of Corner and Gurski, Power and Lack to develop a strictification theory for pseudoalgebras over operads and monads. It specializes to strictify genuine symmetric monoidal $G$-categories to genuine permutative $G$-categories. All of our work takes place in a general internal categorical framework that has many quite different specializations. Wh

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7

Mahanta, Snigdhayan. "Noncommutative stable homotopy and stable infinity categories." Journal of Topology and Analysis 07, no. 01 (2014): 135–65. http://dx.doi.org/10.1142/s1793525315500077.

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The noncommutative stable homotopy category NSH is a triangulated category that is the universal receptacle for triangulated homology theories on separable C*-algebras. We show that the triangulated category NSH is topological as defined by Schwede using the formalism of (stable) infinity categories. More precisely, we construct a stable presentable infinity category of noncommutative spectra and show that NSHop sits inside its homotopy category as a full triangulated subcategory, from which the above result can be deduced. We also introduce a presentable infinity category of noncommutative po

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8

Yeshkeyev, A. R., I. O. Tungushbayeva, and S. M. Amanbekov. "Existentially prime Jonsson quasivarieties and their Jonsson spectra." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 108, no. 4 (2022): 117–24. http://dx.doi.org/10.31489/2022m4/117-124.

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This article is devoted to the study of Jonsson quasivarieties in a signature enriched with new predicate and constant symbols. New concepts of semantic Jonsson quasivariety and fragment-conservativeness of the center of the Jonsson theory are introduced. The cosemanticness classes of the Jonsson spectrum constructed for a semantic Jonsson quasvariety are considered. In this case, the Kaiser hull of the semantic Jonsson quasivariety is assumed to be existentially prime. By constructing a central type for classes of theories from the Jonsson spectrum, the following results are formulated and pr

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9

Jeeves, Malcolm A. "Why Science and Faith Belong Together: Stories of Mutual Enrichment." Perspectives on Science and Christian Faith 74, no. 1 (2022): 58–59. http://dx.doi.org/10.56315/pscf3-22jeeves.

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WHY SCIENCE AND FAITH BELONG TOGETHER: Stories of Mutual Enrichment by Malcolm A. Jeeves. Eugene, OR: Cascade Books, 2021. 294 pages. Paperback; $35.00. ISBN: 9781725286191. *Many sense tension between modern science and Christian faith. Malcolm Jeeves, however, intends to show how the two are quite complementary. As Emeritus Professor (University of St. Andrews), past-President of the Royal Society of Edinburgh, Fellow of both the Academy of Medical Sciences and the British Psychological Society, and a prolific author in the arena of science and faith, he is supremely qualified to write this

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10

Emmerson, Parker Yaohushuason. "Foundations of Categorical-Homotopical Operator Algebras, Daisy Network Dynamics, and Anterolateral Spectral Algebra." Journal of Liberated Mathematics, May 25, 2025. https://doi.org/10.5281/zenodo.15509974.

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This paper introduces and formalizes six novel mathematical frameworks synthesizing categorical, homotopical, operator-algebraic, and spectral constructs with emergent symmetry and criticality. We define \emph{ultranaut operators} as higher-categorical homotopy-enriched transitions; construct spectral decompositions over $\Sigma$-enriched matrices; develop integral operator algebra formalism; introduce the \emph{daisy network}, a self-similar symmetry-generating topological graph; analyze paradoxical scale-interaction criticality ($1 \ll Q \ll 1$); and establish \emph{anterolateral spectral al

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11

Bartsch, Thomas, Mathew Bullimore, Andrea E. V. Ferrari, and Jamie Pearson. "Non-invertible symmetries and higher representation theory II." SciPost Physics 17, no. 2 (2024). http://dx.doi.org/10.21468/scipostphys.17.2.067.

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In this paper we continue our investigation of the global categorical symmetries that arise when gauging finite higher groups and their higher subgroups with discrete torsion. The motivation is to provide a common perspective on the construction of non-invertible global symmetries in higher dimensions and a precise description of the associated symmetry categories. We propose that the symmetry categories obtained by gauging higher subgroups may be defined as higher group-theoretical fusion categories, which are built from the projective higher representations of higher groups. As concrete appl

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12

Mundey, Alexander, and Aidan Sims. "Homology and Twisted $$C^*$$-Algebras for Self-similar Actions and Zappa–Szép Products." Results in Mathematics 80, no. 1 (2024). https://doi.org/10.1007/s00025-024-02264-7.

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AbstractWe study the categorical homology of Zappa–Szép products of small categories, which include all self-similar actions. We prove that the categorical homology coincides with the homology of a double complex, and so can be computed via a spectral sequence involving homology groups of the constituent categories. We give explicit formulae for the isomorphisms involved, and compute the homology of a class of examples that generalise odometers. We define the $$C^*$$ C ∗ -algebras of self-similar groupoid actions on k-graphs twisted by 2-cocycles arising from this homology theory, and prove so

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13

Emmerson, Parker Yaohushuason. "Anterolateral Algebraic Chains and Methods." Journal of Liberated Mathematics, May 22, 2025. https://doi.org/10.5281/zenodo.15486968.

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This work develops a unified algebraic and geometric framework for analyzing anterolateral chains arising in spectral sequence mechanics, integrable systems, and quantum algebra. We introduce and systematically study anterolateral spectral chains—recursively defined sequences of heights and velocities—using explicit algebraic laws and case-based propagations across canonical parameter spaces. Utilizing cluster algebra mutations, symplectic geometry, and Lax pairs, we derive integrability properties and provide detailed transition mechanisms among cases via energy tags and discrimin

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14

Chang, Chi-Ming, and Ying-Hsuan Lin. "Lorentzian dynamics and factorization beyond rationality." Journal of High Energy Physics 2021, no. 10 (2021). http://dx.doi.org/10.1007/jhep10(2021)125.

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Abstract We investigate the emergence of topological defect lines in the conformal Regge limit of two-dimensional conformal field theory. We explain how a local operator can be factorized into a holomorphic and an anti-holomorphic defect operator connected through a topological defect line, and discuss implications on analyticity and Lorentzian dynamics including aspects of chaos. We derive a formula relating the infinite boost limit, which holographically encodes the “opacity” of bulk scattering, to the action of topological defect lines on local operators. Leveraging the unitary bound on the

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15

Shen, Che, and Mark D. Fairchild. "Individual color matching functions from cross‐media color‐matching experiment." Color Research & Application, October 21, 2024. http://dx.doi.org/10.1002/col.22960.

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AbstractHuman color vision exhibits substantial variability, challenging the accurate measurement and reproduction of individual color appearances. This paper introduces a novel cross‐media color‐matching experiment that combines physical pigments and digital displays, providing a practical and efficient solution to measure individual color matching functions (CMFs). By using the Kubelka–Munk theory to synthesize broadband spectral pigments, optimized metameric pairs can be created to significantly differentiate categorical observers. Psychophysical experiment results reveal the superiority of

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16

Emmerson, Parker. "Anterolateral Lite 2." Journal of Liberated Mathematics, May 25, 2025. https://doi.org/10.5281/zenodo.15510371.

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The \emph{Anterolateral Lite 2} formalism arises from a need to robustly track analytic and symbolic distinctions that are often lost in traditional algebraic and geometric frameworks, especially in contexts involving multi-branched solutions and subtle phase phenomena, such as Lorentzian and radical expressions. Classical algebraic structures, which treat coordinates as atomic or globally coherent entities, are prone to \emph{branch collapse}: the unwanted identification of distinct solution branches through singularities, degenerate loci, or insufficiently expressive type systems. Building o

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17

Gammage, Benjamin, Justin Hilburn, and Aaron Mazel-Gee. "Perverse schobers and 3d mirror symmetry." Journal of the European Mathematical Society, May 27, 2025. https://doi.org/10.4171/jems/1657.

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The proposed physical duality known as 3d mirror symmetry relates the geometries of dual pairs of holomorphic symplectic stacks. It has served in recent years as a guiding principle for developments in representation theory. However, due to the lack of definitions, thus far only small pieces of the subject have been mathematically accessible. In this paper, we formulate abelian 3d mirror symmetry as an equivalence between a pair of 2-categories constructed from the algebraic and symplectic geometry, respectively, of Gale dual toric cotangent stacks. In the simplest case, our theorem provides a

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18

HEBESTREIT, FABIAN, STEFFEN SAGAVE, and CHRISTIAN SCHLICHTKRULL. "MULTIPLICATIVE PARAMETRIZED HOMOTOPY THEORY VIA SYMMETRIC SPECTRA IN RETRACTIVE SPACES." Forum of Mathematics, Sigma 8 (2020). http://dx.doi.org/10.1017/fms.2020.11.

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In order to treat multiplicative phenomena in twisted (co)homology, we introduce a new point-set-level framework for parametrized homotopy theory. We provide a convolution smash product that descends to the corresponding $\infty$ -categorical product and allows for convenient constructions of commutative parametrized ring spectra. As an immediate application, we compare various models for generalized Thom spectra. In a companion paper, this approach is used to compare homotopical and operator algebraic models for twisted $K$ -theory.

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19

TAGGART, NIALL. "UNITARY FUNCTOR CALCULUS WITH REALITY." Glasgow Mathematical Journal, March 10, 2021, 1–34. http://dx.doi.org/10.1017/s0017089521000033.

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Abstract We construct a calculus of functors in the spirit of orthogonal calculus, which is designed to study ‘functors with reality’ such as the Real classifying space functor, $\BU_\Bbb{R}(-)$ . The calculus produces a Taylor tower, the n-th layer of which is classified by a spectrum with an action of $C_2 \ltimes \U(n)$ . We further give model categorical considerations, producing a zigzag of Quillen equivalences between spectra with an action of $C_2 \ltimes \U(n)$ and a model structure on the category of input functors which captures the homotopy theory of the n-th layer of the Taylor tow

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20

Cnossen, Bastiaan, Rune Haugseng, Tobias Lenz, and Sil Linskens. "Homotopical commutative rings and bispans." Journal of the London Mathematical Society 111, no. 6 (2025). https://doi.org/10.1112/jlms.70200.

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AbstractWe prove that commutative semirings in a cartesian closed presentable ‐category, as defined by Groth, Gepner, and Nikolaus, are equivalent to product‐preserving functors from the (2,1)‐category of bispans of finite sets. In other words, we identify the latter as the Lawvere theory for commutative semirings in the ‐categorical context. This implies that connective commutative ring spectra can be described as grouplike product‐preserving functors from bispans of finite sets to spaces. A key part of the proof is a localization result for ‐categories of spans, and more generally for ‐categ

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21

Escobedo-Morales, Alejandro, Lorenzo Tepech-Carrillo, Alejandro Bautista-Hernández, José Humberto Camacho-García, Diego Cortes-Arriagada, and Ernesto Chigo-Anota. "Effect of Chemical Order in the Structural Stability and Physicochemical Properties of B12N12 Fullerenes." Scientific Reports 9, no. 1 (2019). http://dx.doi.org/10.1038/s41598-019-52981-1.

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Abstract The effect of chemical order in the structural and physicochemical properties of B12N12 [4,6]-fullerene (BNF) isomers was evaluated using density functional theory and molecular dynamic calculations. The feasibility to find stable BNF isomers with atomic arrangement other than the well-known octahedral Th-symmetry was explored. In this study, the number of homonuclear bonds in the modeled nanostructures was used as categorical parameter to describe and quantify the degree of structural order. The BNF without homonuclear bonds was identified as the most energetically favorable isomer.

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