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Lie Algebras, Vertex Operator Algebras and Their Applications
The articles in this book are based on talks given at the international conference 'Lie algebras, vertex operator algebras and their applications'. The focus of the papers is mainly on Lie algebras, quantum groups, vertex operator algebras and their applications to number theory, combinatorics and conformal field theory.
Dualizable Tensor Categories
We investigate the relationship between the algebra of tensor categories and the topology of framed 3-manifolds. On the one hand, tensor categories with cer-tain algebraic properties determine topological invariants. We prove that fusion categories of nonzero global dimension are 3-dualizable, and therefore provide 3-dimensional 3-framed local field theories. We also show that all finite tensor cat-egories are 2-dualizable, and yield categorified 2-dimensional 3-framed local field theories. On the other hand, topological properties of 3-framed manifolds deter-mine algebraic equations among functors of tensor categories. We show that the 1-dimensional loop bordism, which exhibits a single...
Dirichlet Branes and Mirror Symmetry
Research in string theory has generated a rich interaction with algebraic geometry, with exciting work that includes the Strominger-Yau-Zaslow conjecture. This monograph builds on lectures at the 2002 Clay School on Geometry and String Theory that sought to bridge the gap between the languages of string theory and algebraic geometry.
Mathematical Reviews
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Lie Algebras, Vertex Operator Algebras, and Related Topics
This volume contains the proceedings of the conference on Lie Algebras, Vertex Operator Algebras, and Related Topics, celebrating the 70th birthday of James Lepowsky and Robert Wilson, held from August 14–18, 2015, at the University of Notre Dame, Notre Dame, Indiana. Since their seminal work in the 1970s, Lepowsky and Wilson, their collaborators, their students, and those inspired by their work, have developed an amazing body of work intertwining the fields of Lie algebras, vertex algebras, number theory, theoretical physics, quantum groups, the representation theory of finite simple groups, and more. The papers presented here include recent results and descriptions of ongoing research initiatives representing the broad influence and deep connections brought about by the work of Lepowsky and Wilson and include a contribution by Yi-Zhi Huang summarizing some major open problems in these areas, in particular as they pertain to two-dimensional conformal field theory.
Renormalization and Effective Field Theory
Quantum field theory has had a profound influence on mathematics, and on geometry in particular. However, the notorious difficulties of renormalization have made quantum field theory very inaccessible for mathematicians. This provides complete mathematical foundations for the theory of perturbative quantum field theory, based on Wilson's ideas of low-energy effective field theory and on the Batalin-Vilkovisky formalism.
2009
Every year, the Bibliography catalogues the most important new publications, historiographical monographs, and journal articles throughout the world, extending from prehistory and ancient history to the most recent contemporary historical studies. Within the systematic classification according to epoch, region, and historical discipline, works are also listed according to author's name and characteristic keywords in their title.
Proceedings of the Sixth International Scientific Conference “Intelligent Information Technologies for Industry” (IITI’22)
This book contains the works connected with the key advances in Intelligent Information Technologies for Industry presented in the main track of IITI 2022, the Sixth International Scientific Conference on Intelligent Information Technologies for Industry held on October 31 - November 6, 2022, in Istanbul, Turkey. The works were written by the experts in the field of artificial intelligence including topics such as machine learning, decision making intelligent systems, fuzzy logic, bioinspired systems and Bayesian networks. The following industrial application domains were touched: railway automation, intelligent medical systems, flexible socio-technical systems, navigation systems and energetic systems. The editors believe that this book will be helpful for all scientists and engineers interested in the modern state of applied artificial intelligence.
Applications of Topic Models
Describes recent academic and industrial applications of topic models with the goal of launching a young researcher capable of building their own applications of topic models.
USSR.
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