Higher Structures and Operadic Calculus by Bruno Vallette
This book presents the notes originating from five series of lectures given at the CRM Barcelona in 21-25 June, 2021, during the “Higher homotopical structures” programme.
Since their introduction 60 years ago, the notions of infinity algebras (Stasheff, Sugawara), higher categories (Boardman-Vogt), operads (May), and model categories (Quillen) have given rise to powerful new tools which made possible the resolution of open problems and prompted revolutions in many domains like algebraic topology (rational homotopy theory, faithful algebraic invariants of the homotopy type of spaces), deformation theory (formality theorems, formal moduli problems), and mathematical physics (quantization of Poisson manifolds, quantum field theories), to name but a few.
This theory of higher structures using operadic calculus is currently under rapid development. The aim of this book is to provide the community with an accessible state-of-the-art, while at the same time giving interested researchers and advanced students a brief overview on the subject.
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Harmonic and Geometric Analysis
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Integral Geometry and Valuations
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Operator Algebras and Dynamics: Groupoids, Crossed Products, and Rokhlin Dimension
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Mean Curvature Flow and Isoperimetric Inequalities
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Elliptic Curves, Hilbert Modular Forms and Galois Deformations
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Contemporary Cryptology
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The Geometry of the Word Problem for Finitely Generated Groups
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Simplicial Methods for Operads and Algebraic Geometry
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Combinatorial Number Theory and Additive Group Theory
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Compactifying Moduli Spaces
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Ramsey Methods in Analysis
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Group-based Cryptography
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Hyperbolic Cross Approximation
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Central Configurations, Periodic Orbits, and Hamiltonian Systems
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Crossed Products of C*-Algebras, Topological Dynamics, and Classification
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Numerical Solutions of Partial Differential Equations
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Proper Group Actions and the Baum-Connes Conjecture
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Homotopy Theoretic Methods in Group Cohomology
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An Introduction to Piecewise Smooth Dynamics
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Geometry and Dynamics of Integrable Systems
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Building Bridges Between Algebra and Topology
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Combinatorial Matrix Theory
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Lectures on Algebraic Quantum Groups
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Polynomial Identity Rings
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Kolmogorov Equations for Stochastic PDEs
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String Topology and Cyclic Homology
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Symplectic Geometry of Integrable Hamiltonian Systems
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Algorithmic and Geometric Topics Around Free Groups and Automorphisms
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Geometry and Quantization of Moduli Spaces
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From Levy-Type Processes to Parabolic SPDEs
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Variable Lebesgue Spaces and Hyperbolic Systems
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Advances in Poisson Geometry
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Analysis on h-Harmonics and Dunkl Transforms
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An Introduction to C*-Algebras and the Classification Program
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Global Riemannian Geometry: Curvature and Topology
Bruno Vallette is a mathematician at Université Sorbonne Paris Nord with main interests in operad theory, its generalizations and applications, including homotopy algebras and deformation theory. He co-authored the book 'Algebraic Operads' (2012).
| SKU | Unavailable |
| ISBN 13 | 9783031777783 |
| ISBN 10 | 3031777786 |
| Title | Higher Structures and Operadic Calculus |
| Author | Bruno Vallette |
| Series | Advanced Courses In Mathematics - Crm Barcelona |
| Condition | Unavailable |
| Binding Type | Paperback |
| Publisher | Birkhauser Verlag AG |
| Year published | 2025-04-18 |
| Number of pages | 341 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |