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 Cao, Daomin, 1963 author.
 New York : Cambridge University Press, 2020
 Description
 Book — 1 online resource
 Summary

 1. NonCompact Elliptic Problems
 2. Perturbation Methods
 3. Local Uniqueness of Solutions
 4. Construction of Infinitely Many Solutions
 5. A Compactness Theorem and Application
 6. The Appendix.
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 Muscalu, Camil.
 Cambridge : Cambridge University Press, ©2012.
 Description
 Book — 1 online resource
 Summary

 Preface Acknowledgements
 1. Leibniz rules and gKdV equations
 2. Classical paraproducts
 3. Paraproducts on polydiscs
 4. Calderon commutators and the Cauchy integral
 5. Iterated Fourier series and physical reality
 6. The bilinear Hilbert transform
 7. Almost everywhere convergence of Fourier series
 8. Flag paraproducts
 9. Appendix: multilinear interpolation Bibliography Index.
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 Goldfeld, D.
 Cambridge : Cambridge University Press, 2006.
 Description
 Book — 493 p.
 Summary

 Introduction
 1. Discrete group actions
 2. Invariant differential operators
 3. Automorphic forms and Lfunctions for SL(2, Z)
 4. Existence of Maass forms
 5. Maass forms and Whittaker functions for SL(n, Z)
 6. Automorphic forms and Lfunctions for SL(3, Z)
 7. The GelbertJacquet lift
 8. Bounds for Lfunctions and Siegel zeros
 9. The GodementJacquet Lfunction
 10. Langlands Eisenstein series
 11. Poincare series and Kloosterman sums
 12. RankinSelberg convolutions
 13. Langlands conjectures Appendix. The GL(n)pack manual References.
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 Bobrowski, Adam, author.
 Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2021
 Description
 Book — 1 online resource
 Summary

 A nontechnical introduction
 1. A guided tour through the land of operator semigroups
 2. Generators versus intensity matrices
 3. Boundary theory: core results
 4. Boundary theory continued
 5. The dual perspective Solutions and hints to selected exercises Commonly used notations References Index.
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 Geck, Meinolf, author.
 Cambridge, United Kingdom ; New York : Cambridge University Press, 2020
 Description
 Book — ix, 394 pages : illustrations ; 24 cm
 Summary

 1. Reductive groups and Steinberg maps
 2. Lusztig's classification of irreducible characters
 3. HarishChandra theories
 4. Unipotent characters Appendix. Further reading and open questions References Index.
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QA177 .G435 2020  Unknown 
 Geck, Meinolf, author.
 Cambridge, United Kingdom ; New York : Cambridge University Press, 2020
 Description
 Book — 1 online resource
 Summary

 1. Reductive groups and Steinberg maps
 2. Lusztig's classification of irreducible characters
 3. HarishChandra theories
 4. Unipotent characters Appendix. Further reading and open questions References Index.
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 Geck, Meinolf, author.
 Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2020
 Description
 Book — 1 online resource
 Summary

 1. Reductive groups and Steinberg maps
 2. Lusztig's classification of irreducible characters
 3. HarishChandra theories
 4. Unipotent characters Appendix. Further reading and open questions References Index.
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 Agrachev, Andrei A., author.
 Cambridge ; New York, NY : Cambridge University Press, 2020
 Description
 Book — xviii, 745 pages : illustrations ; 24 cm
 Summary

 Introduction
 1. Geometry of surfaces in R^3
 2. Vector fields
 3. SubRiemannian structures
 4. Pontryagin extremals: characterization and local minimality
 5. First integrals and integrable systems
 6. Chronological calculus
 7. Lie groups and leftinvariant subRiemannian structures
 8. Endpoint map and exponential map
 9. 2D almostRiemannian structures
 10. Nonholonomic tangent space
 11. Regularity of the subRiemannian distance
 12. Abnormal extremals and second variation
 13. Some model spaces
 14. Curves in the Lagrange Grassmannian
 15. Jacobi curves
 16. Riemannian curvature
 17. Curvature in 3D contact subRiemannian geometry
 18. Integrability of the subRiemannian geodesic flow on 3D Lie groups
 19. Asymptotic expansion of the 3D contact exponential map
 20. Volumes in subRiemannian geometry
 21. The subRiemannian heat equation Appendix. Geometry of parametrized curves in Lagrangian Grassmannians with Igor Zelenko References Index.
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QA671 .A47 2020  Unknown 
9. Derived categories [2020]
 Yekutiely, Amnon, author.
 Cambridge ; New York, NY : Cambridge University Press, 2020
 Description
 Book — xi, 607 pages : illustrations ; 24 cm
 Summary

 Introduction
 1. Basic facts on categories
 2. Abelian categories and additive functors
 3. Differential graded algebra
 4. Translations and standard triangles
 5. Triangulated categories and functors
 6. Localization of categories
 7. The derived category D(A, M)
 8. Derived functors
 9. DG and triangulated bifunctors
 10. Resolving subcategories of K(A, M)
 11. Existence of resolutions
 12. Adjunctions, equivalences and cohomological dimension
 13. Dualizing complexes over commutative rings
 14. Perfect and tilting DG modules over NC DG rings
 15. Algebraically graded noncommutative rings
 16. Derived torsion over NC graded rings
 17. Balanced dualizing complexes over NC graded rings
 18. Rigid noncommutative dualizing complexes References Index.
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10. Foundations of stable homotopy theory [2020]
 Barnes, David, 1981 author.
 Cambridge, United Kingdom ; New York, NY, USA : Cambridge University Press, 2020
 Description
 Book — 1 online resource
 Summary

 Introduction
 1. Basics of stable homotopy theory
 2. Sequential spectra and the stable homotopy category
 3. The suspension and loop functors
 4. Triangulated categories
 5. Modern categories of spectra
 6. Monoidal structures
 7. Left Bousfield localisation Appendix. Model categories References Index.
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11. Foundations of stable homotopy theory [2020]
 Barnes, David, 1981 author.
 Cambridge, United Kingdom ; New York, NY, USA : Cambridge University Press, 2020
 Description
 Book — vi, 423 pages : illustrations ; 24 cm
 Summary

 Introduction
 1. Basics of stable homotopy theory
 2. Sequential spectra and the stable homotopy category
 3. The suspension and loop functors
 4. Triangulated categories
 5. Modern categories of spectra
 6. Monoidal structures
 7. Left Bousfield localisation Appendix. Model categories References Index.
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QA612.7 .B375 2020  Unknown 
 Demeter, Ciprian, author.
 Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2020
 Description
 Book — xvi, 331 pages ; 24 cm
 Summary

 Background and notation
 1. Linear restriction theory
 2. Wave packets
 3. Bilinear restriction theory
 4. Parabolic rescaling and a bilineartolinear reduction
 5. Kakeya and square function estimates
 6. Multilinear Kakeya and restriction inequalities
 7. The BourgainGuth method
 8. The polynomial method
 9. An introduction to decoupling
 10. Decoupling for the elliptic paraboloid
 11. Decoupling for the moment curve
 12. Decouplings for other manifolds
 13. Applications of decoupling References Index.
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QA403.5 .D46 2020  Unknown 
13. From categories to homotopy theory [2020]
 Richter, Birgit, 1971 author.
 Cambridge ; New York, NY : Cambridge University Press, 2020
 Description
 Book — 1 online resource
 Summary

 Introduction Part I. Category Theory:
 1. Basic notions in category theory
 2. Natural transformations and the Yoneda lemma
 3. Colimits and limits
 4. Kan extensions
 5. Comma categories and the Grothendieck construction
 6. Monads and comonads
 7. Abelian categories
 8. Symmetric monoidal categories
 9. Enriched categories Part II. From Categories to Homotopy Theory:
 10. Simplicial objects
 11. The nerve and the classifying space of a small category
 12. A brief introduction to operads
 13. Classifying spaces of symmetric monoidal categories
 14. Approaches to iterated loop spaces via diagram categories
 15. Functor homology
 16. Homology and cohomology of small categories References Index.
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14. From categories to homotopy theory [2020]
 Richter, Birgit, 1971 author.
 Cambridge, United Kingdom ; New York, NY, USA : Cambridge University Press, 2020
 Description
 Book — x, 390 pages : illustrations ; 24 cm
 Summary

 Introduction Part I. Category Theory:
 1. Basic notions in category theory
 2. Natural transformations and the Yoneda lemma
 3. Colimits and limits
 4. Kan extensions
 5. Comma categories and the Grothendieck construction
 6. Monads and comonads
 7. Abelian categories
 8. Symmetric monoidal categories
 9. Enriched categories Part II. From Categories to Homotopy Theory:
 10. Simplicial objects
 11. The nerve and the classifying space of a small category
 12. A brief introduction to operads
 13. Classifying spaces of symmetric monoidal categories
 14. Approaches to iterated loop spaces via diagram categories
 15. Functor homology
 16. Homology and cohomology of small categories References Index.
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15. Toeplitz matrices and operators [2020]
 Matrices et opérateurs de Toeplitz. English
 Nikolʹskiĭ, N. K. (Nikolaĭ Kapitonovich), author.
 Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2020
 Description
 Book — xxii, 430 pages : illustrations ; 24 cm
 Summary

 1. Why ToeplitzHankel? Motivations and panorama
 2. Hankel and Toeplitz  brother operators on the space H2
 3. H2 theory of Toeplitz operators
 4. Applications: RiemannHilbert, WienerHopf, singular integral operators (SIO)
 5. Toeplitz matrices: moments, spectra, asymptotics Appendix A. Key notions of Banach spaces Appendix B. Key notions of Hilbert spaces Appendix C. An overview of Banach algebras Appendix D. Linear operators Appendix E. Fredholm operators and the Noether index Appendix F. A brief overview of Hardy spaces References Notation Index.
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QA188 .N5513 2020  Unknown 
16. Formal geometry and bordism operations [2019]
 Peterson, Eric, 1987 author.
 Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2019.
 Description
 Book — xiv, 405 pages ; 24 cm.
 Summary

 Foreword Matthew Ando Preface Introduction
 1. Unoriented bordism
 2. Complex bordism
 3. Finite spectra
 4. Unstable cooperations
 5. The orientation Appendix A. Power operations Appendix B. Loose ends References Index.
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QA613.2 .P48 2019  Unknown 
17. Hardy spaces [2019]
 Élements d'analyse avancée. 1, Espaces de Hardy. English
 Nikolʹskiĭ, N. K. (Nikolaĭ Kapitonovich) author.
 Cambridge ; New York : Cambridge University Press, 2019.
 Description
 Book — xviii, 277 pages : illustrations ; 24 cm.
 Summary

 The origins of the subject
 1. The space H^2(T). An archetypal invariant subspace
 2. The H^p(D) classes. Canonical factorization and first applications
 3. The Smirnov class D and the maximum principle
 4. An introduction to weighted Fourier analysis
 5. Harmonic analysis and stationary filtering
 6. The Riemann hypothesis, dilations, and H^2 in the Hilbert multidisk Appendix A. Key notions of integration Appendix B. Key notions of complex analysis Appendix C. Key notions of Hilbert spaces Appendix D. Key notions of Banach spaces Appendix E. Key notions of linear operators References Notation Index.
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QA331.7 .N5513 2019  Unknown 
18. Higher categories and homotopical algebra [2019]
 Cisinski, DenisCharles, author.
 Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2019
 Description
 Book — xviii, 430 pages ; 24 cm
 Summary

 Preface
 1. Prelude
 2. Basic homotopical algebra
 3. The homotopy theory of categories
 4. Presheaves: externally
 5. Presheaves: internally
 6. Adjoints, limits and Kan extensions
 7. Homotopical algebra References Notation Index.
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QA612.7 .C5645 2019  Unknown 
19. Character theory and the McKay conjecture [2018]
 Navarro, G. (Gabriel) author.
 Cambridge, United Kingdom ; New York, NY, USA : Cambridge University Press, 2018.
 Description
 Book — xviii, 234 pages ; 24 cm.
 Summary

 Preface Notation
 1. The basics
 2. Action on characters by automorphisms
 3. Galois action on characters
 4. Character values and identities
 5. Characters over a normal subgroup
 6. Extension of characters
 7. Degrees of characters
 8. The HowlettIsaacs theorem
 9. Globallocal counting conjectures
 10. A reduction theorem for the McKay conjecture Appendix Bibliographic notes References Index.
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QA177 .N383 2018  Unknown 
20. Discrete harmonic analysis : representations, number theory, expanders, and the Fourier transform [2018]
 CeccheriniSilberstein, Tullio, author.
 Cambridge, United Kingdom : Cambridge University Press, 2018.
 Description
 Book — xiii, 573 pages : illustrations ; 24 cm.
 Summary

 Part I. Finite Abelian Groups and the DFT:
 1. Finite Abelian groups
 2. The Fourier transform on finite Abelian groups
 3. Dirichlet's theorem on primes in arithmetic progressions
 4. Spectral analysis of the DFT and number theory
 5. The fast Fourier transform Part II. Finite Fields and Their Characters:
 6. Finite fields
 7. Character theory of finite fields Part III. Graphs and Expanders:
 8. Graphs and their products
 9. Expanders and Ramanujan graphs Part IV. Harmonic Analysis of Finite Linear Groups:
 10. Representation theory of finite groups
 11. Induced representations and Mackey theory
 12. Fourier analysis on finite affine groups and finite Heisenberg groups
 13. Hecke algebras and multiplicityfree triples
 14. Representation theory of GL(2, Fq).
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QA403 .C4285 2018  Unknown 
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