Algebraic Topology : Applications and New Directions.

Intro -- Preface -- Scientific Programme -- List of Participants and Conference Photo -- Representation stability in cohomology and asymptotics for families of varieties over finite fields -- 1. Introduction -- 2. The twisted Grothendieck-Lefschetz Formula -- 3. Hyperplane arrangements, their cohomology, and combinatorics of squarefree polynomials -- 4. Statistics of squarefree polynomials and the cohomology of the pure braid group -- 5. Maximal tori in \GL_{ }(\F_{ }) -- References -- A stability conjecture for the unstable cohomology of _{ }ℤ, mapping class groups, and ( _{ }) -- 1. Introduction -- 2. Stability in the unstable cohomology of _{ }ℤ -- 3. Stability in the unstable cohomology of mapping class groups -- 4. Stability in the unstable cohomology of ( _{ }) -- References -- The Boardman-Vogt tensor product of operadic bimodules -- Introduction -- 1. Lifting the Boardman-Vogt tensor product -- 2. The algebra of the divided powers functor -- Appendix A. Proofs of Proposition 1.20 and Theorem 1.22 -- References -- Detecting and realising characteristic classes of manifold bundles -- 1. Introduction and statement of results -- 2. Proof of Theorem 1.1 -- 3. Proof of Theorem 1.4 -- 4. Proof of Proposition 1.3 -- References -- Controlled Algebraic -theory, II -- 1. Introduction -- 2. Continuous Control for Filtered Modules -- 3. Continuously Controlled -theory -- 4. The Localization Homotopy Fibration -- 5. Controlled Excision Theorems -- References -- More examples of discrete co-compact group actions -- Introduction -- 1. Groups with periodic cohomology -- 2. Generalized cohomological dimension and Farrell cohomology -- 3. Co-compact actions on \bR^{ }× ⁿ -- 4. Involutions on the Klein bottle -- References -- On the -theory of planar cuspical curves and a new family of polytopes -- Introduction.

1. Big de Rham-Witt forms -- 2. The groups \TR_{ - }^{ }( ) -- 3. The cyclic bar-construction -- 4. Proof of Theorem A -- 5. Homology calculations -- 6. Stunted regular cyclic polytopes -- References -- Equivariant multiplicative closure -- Introduction -- 1. Localization of commutative rings -- 2. Homotopy theoretic commutative algebra -- 3. Extended powers and indexed monoidal products -- 4. Equivariant multiplicative closure -- References -- Topology of random simplicial complexes: a survey -- 1. Introduction -- 2. Random graphs -- 3. Random 2-complexes -- 4. Random flag complexes -- 5. Comments -- Acknowledgements -- References -- The definition of a non-commutative toric variety -- 1. Introduction -- 2. Classical Toric Varieties -- 3. Non-commutative Geometry -- 4. Variations on Diffeology -- 5. LVM-theory -- 6. Non-commutative Toric Varieties -- 7. Relation to Mirror Symmetry -- References -- The Stable Symplectic Category and Quantization -- 1. Introduction -- 2. Stabilized lagrangian immersions -- 3. The Stable Symplectic homotopy category -- 4. Internal structure of the stable symplectic homotopy category -- 5. The algebra of observables and the Sympletomorphism Group -- 6. The Stable Symplectic category as an _{∞}-category: Background -- 7. The Stable Symplectic category as an _{∞}-category: Morphisms -- 8. The Stable Metaplectic Category -- 9. Appendix: Some computations and Remarks -- References -- A geometric perspective on quantum field theory -- The compactness of _{ } -- The finite dimensionality of _{ } -- Quantum theory: waves and particles -- Noncommutative geometry -- Floer homotopy types -- References -- Sketches of a platypus: a survey of persistent homology and its algebraic foundations -- 1. Introduction -- 1.1. Foundations in use -- 2. Persistence barcodes and diagrams -- 3. Functions on a manifold.

3.1. A functional view of persistent homology -- 3.2. Filtered complexes -- 3.3. The stability meta-theorem -- 3.4. Vector spaces with ordered bases -- 3.5. Diagrams over (\R,≤) -- 3.6. Directly to diagrams -- 3.7. Measures on the real line -- 3.8. Categorification -- 4. Filtered topological spaces -- 4.1. Vector space with ordered basis -- 4.2. Graded modules over \kk[ ] -- 4.3. Modules over a quiver algebra -- 4.4. Diagrams of vector spaces over order categories -- 5. Shapes of theories, future directions -- 6. Conclusion -- 7. Acknowledgments -- References -- Cartier's first theorem for Witt vectors on ℤ_{≥0}ⁿ-0 -- 1. Introduction -- 2. Cartier's first theorem for Witt vectors on \Z_{≥0}ⁿ-0 -- Acknowledgements -- References.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.