Article
Mathematics
Mark Andrea A. de Cataldo
Summary: The study constructs a relative projective compactification, compatible with the Hitchin morphism, of Dolbeault moduli spaces of Higgs bundles for reductive algebraic groups on families of projective manifolds.
INTERNATIONAL MATHEMATICS RESEARCH NOTICES
(2021)
Article
Mathematics
Tomas Ibarlucia, Michael Megrelishvili
Summary: This study focuses on isometric G-spaces and their maximal equivariant compactifications in various spaces, such as the Urysohn sphere and related spaces. The research demonstrates the identification of compactifications with the space of 1-types over the metric structure M, and provides a unified understanding of previous examples. Additionally, a uniform version of Effros' Theorem for isometric actions of Roelcke precompact Polish groups is also established.
ADVANCES IN MATHEMATICS
(2021)
Article
Astronomy & Astrophysics
Satoshi Iso, Noriaki Kitazawa, Takao Suyama
Summary: This paper investigates the behavior of extra-dimensional components of gauge fields in higher-dimensional gauge theories after compactifications, revealing that in some models, although gauge symmetries are broken, they can be partially restored at the minimum of the Higgs potential.
Article
Mathematics
Nathaniel Adu, Piotr Mikusinski, Gary Richardson
Summary: This article investigates continuous partial actions and continuous enveloping actions in the category of convergence spaces. Product and quotient constructions are considered. Furthermore, it is shown that a continuous partial action on a convergence space can be extended to a continuous partial action on a compactification of the convergence space.
MATHEMATICA SLOVACA
(2022)
Article
Mathematics
Richard Pink
Summary: We constructed a compactification of the moduli space of Drinfeld modules, which involves A-reciprocal maps and technical assumptions on N. In a special case, a presentation for graded ideal of Drinfeld cusp forms and a dimension formula for the space of cusp forms were obtained. Similar results are expected in general, but the proof will require more ideas.
JOURNAL OF ALGEBRAIC GEOMETRY
(2021)
Article
Physics, Multidisciplinary
Stefano Gogioso, Maria E. Stasinou, Bob Coecke
Summary: The paper introduces a compositional algebraic framework to describe the evolution of quantum fields in discretised spacetimes, recovering familiar notions from Relativity and quantum causality purely through the causal order of events. By formulating theory-independent notions of fields and introducing concepts of symmetry and cellular automata, the framework shows potential for new developments in Algebraic Quantum Field Theory, Quantum Cellular Automata, and Quantum Field Theory in general.
FRONTIERS IN PHYSICS
(2021)
Article
Physics, Multidisciplinary
Anatoly Dymarsky, Alfred Shapere
Summary: Modular invariance imposes strict constraints on the partition functions of CFTs, leading to fundamental results. This study establishes a connection between a family of quantum error correcting codes and code CFI's, simplifying the modular invariance of 2D CFT partition functions.
PHYSICAL REVIEW LETTERS
(2021)
Article
Computer Science, Information Systems
F. Durante, J. Fernandez Sanchez, C. Ignazzi
Summary: In this study, operators defined on bounded functions on the power set of an infinite set X under finitely additive measures are reconsidered with an extended use of the concept of filter, offering new insights into the problem. The obtained results are then applied to the study of the aggregation of infinite sequences.
INFORMATION SCIENCES
(2021)
Article
Mathematics, Applied
Tadeu Zavistanovicz Almeida, Marcelo Sobottka
Summary: In this work, we introduce a new type of shift spaces, called blur shift spaces, where a single symbol can represent an entire set of infinite symbols. These shift spaces generalize previous ideas presented by Ott, Tomforde and Willis, and by Goncalves and Royer, and can be used as a compactification scheme for classical shift spaces.
BULLETIN DES SCIENCES MATHEMATIQUES
(2021)
Article
Mathematics
Christopher Daw, Alexander Gorodnik, Emmanuel Ullmo
Summary: The author conjectures that the set of homogeneous probability measures on the maximal Satake compactification of an arithmetic locally symmetric space is compact. They introduce several tools to study this conjecture and prove it in several cases, including when G = SL3(R) and Gamma = SL3(Z).
MATHEMATISCHE ZEITSCHRIFT
(2021)
Article
Mathematics, Applied
Lucia Lopez-Somoza, F. Adrian F. Tojo
Summary: In this article, the study of solutions of PDEs is combined with the study of asymptotic properties of the solutions through compactification of the domain. New spaces of functions are defined to study the equations, a version of the Ascoli-Arzela Theorem is proved, fixed point index results are developed to prove the existence and multiplicity of solutions in these spaces, and the applicability of the theory is illustrated with an example.
JOURNAL OF FIXED POINT THEORY AND APPLICATIONS
(2021)
Article
Mathematics, Applied
Pascal Lefevre, Daniel Li, Herve Queffelec, Luis Rodriguez-Piazza
Summary: We characterize the symbols phi that result in compact or bounded but not compact weighted composition operator MwC phi on the weighted Bergman space B-alpha(2). We also investigate the conditions for the existence of a weight w such that MwC phi is Hilbert-Schmidt on B-alpha(2).
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2022)
Correction
Mathematics
John R. Klein, Cary Malkiewich
Summary: We point out an error in the authors' earlier proof of the functoriality of the Becker-Gottlieb transfer. Due to this error, the question of functoriality is once again open.
ADVANCES IN MATHEMATICS
(2022)
Article
Computer Science, Information Systems
Amlan Jyoti Das, Navajit Saikia
Summary: This paper proposes new pedestrian detectors based on two types of classifiers, and utilizes multiple scale spaces and feature sets to improve the detection accuracy. The performance of the proposed detectors is evaluated through comparisons of miss rate and false positive rate, and compared with existing detectors of similar type.
JOURNAL OF KING SAUD UNIVERSITY-COMPUTER AND INFORMATION SCIENCES
(2022)
Article
Mathematics, Applied
Serge Bouc
Summary: The main theorem of this paper characterizes the cokernel of the natural injection from B-x in the dual Burnside functor (F2B)over cap, providing a set of generators Gs for the kernel L of the natural surjection F2B -> <(B-x)over cap>. This leads to a two terms projective resolution of <(B-x)over cap>, giving insight into extension functors Ext(1) (-, B-x). Additionally, the paper shows that the biset functor B-x is not finitely generated, while its dual <(B-x)over cap> is finitely generated but not finitely presented.
RESULTS IN MATHEMATICS
(2021)
Article
Mathematics
Chris Kottke
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY
(2015)
Article
Mathematics
Chris Kottke, Richard B. Melrose
MATHEMATICAL RESEARCH LETTERS
(2015)
Article
Mathematics
Chris Kottke
INTERNATIONAL MATHEMATICS RESEARCH NOTICES
(2018)
Article
Mathematics, Applied
Chris Kottke
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
(2015)
Article
Mathematics
Chris Kottke
JOURNAL OF K-THEORY
(2011)
Article
Physics, Fluids & Plasmas
Chris Kottke, Ardavan Farjadpour, Steven G. Johnson
Article
Physics, Mathematical
Chris Kottke, Frederic Rochon
Summary: We provide a pseudodifferential characterization of the limiting behavior of certain Dirac operators associated to a fibered boundary metric as k tends to 0, and use this characterization to derive a pseudodifferential characterization of the low energy limit of the resolvent of the operator. We also prove that the Dirac operator is Fredholm when acting on suitable weighted Sobolev spaces.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2022)
Article
Mathematics
Chris Kottke, Richard B. Melrose
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
(2015)
