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 Ammari, Habib.
 Providence, R.I. : American Mathematical Society, c2009.
 Description
 Book — vi, 202 p. : ill. ; 26 cm.
 Summary

Since the early part of the twentieth century, the use of integral equations has developed into a range of tools for the study of partial differential equations. This includes the use of single and doublelayer potentials to treat classical boundary value problems. The aim of this book is to give a selfcontained presentation of an asymptotic theory for eigenvalue problems using layer potential techniques with applications in the fields of inverse problems, band gap structures, and optimal design, in particular the optimal design of photonic and phononic crystals. Throughout this book, it is shown how powerful the layer potentials techniques are for solving not only boundary value problems but also eigenvalue problems if they are combined with the elegant theory of Gohberg and Sigal on meromorphic operatorvalued functions. The general approach in this book is developed in detail for eigenvalue problems for the Laplacian and the Lame system in the following two situations: one under variation of domains or boundary conditions and the other due to the presence of inclusions. The book will be of interest to researchers and graduate students working in the fields of partial differential equations, integral equations, and inverse problems. Researchers in engineering and physics may also find this book helpful.
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QA3 .A4 V.153  Unknown 
 Hjorth, Greg, 1963
 Providence, R.I. : American Mathematical Society, c2000.
 Description
 Book — xvii, 195 p. : ill. ; 27 cm.
 Summary

 An outline Definitions and technicalities Turbulence Classifying homeomorphisms Infinite dimensional group representations A generalized Scott analysis GE groups The dark side Beyond Borel Looking ahead Ordinals Notation Bibliography Index.
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QA3 .A4 NO.75  Unknown 
 Bortolan, Matheus C. (Matheus Cheque), 1985 author.
 Providence, Rhode Island : American Mathematical Society, [2020]
 Description
 Book — ix, 246 pages : illustrations ; 27 cm
 Summary

 Autonomous theory: Semigroups and global attractors Upper and lower semicontinuity Topological structural stability of attractors Neighborhood of a critical element MorseSmale semigroups Nonautonomous theory: Nonautonomous dynamical systems and their attractors Upper and lower semicontinuity Topological structural stability Neighborhood of a global hyperbolic solution Nonautonomous MorseSmale dynamical systems Bibliography List of figures Index.
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QA3 .A4 V.246  Unknown 
 Adrianov, Nikolai M., 1973 author.
 Providence, Rhode Island : American Mathematical Society, [2020]
 Description
 Book — xi, 187 pages : illustrations ; 26 cm
 Summary

 Introduction. Dessins d'enfants: From polynomials through Belyi functions to weighted trees. Existence theorem. Recapitulation and perspective. Classification of unitrees. Computation of DavenportZannier pairs for unitrees. Primitive monodromy groups of weighted trees. Trees with primitive monodromy groups. A zoo of examples and constructions. Diophantine invariants. Enumeration. What remains to be done. Bibliography. Index.
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QA3 .A4 V.249  Unknown 
5. Geometric set theory [2020]
 Larson, Paul B. (Paul Bradley), 1970 author.
 Providence, Rhode Island : American Mathematical Society, [2020]
 Description
 Book — ix, 330 pages : illustrations ; 26 cm
 Summary

 Introduction. Equivalence relations: The virtual realm. Turbulence. Nested sequences of models. Balanced extensions of the Solovay model: Balanced Suslin forcing. Simplicial complex forcings. Ultrafilter forcings. Other forcings. Preserving cardinalities. Uniformization. Locally countable structures. The Silver divide. The arity divide. Other combinatorics. Bibliography. Index.
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QA3 .A4 V.248  Unknown 
6. Hopf algebras and root systems [2020]
 Heckenberger, István, 1969 author.
 Providence, Rhode Island : American Mathematical Society, [2020]
 Description
 Book — xix, 582 pages : illustrations ; 27 cm
 Summary

 Hopf algebras, Nichols algebras, braided monoidal categories, and quantized enveloping algebras: A quick introduction to Nichols algebras Basic Hopf algebra theory Braided monoidal categories YetterDrinfeld modules over Hopf algebras Gradings and filtrations Braided structures Nichols algebras Quantized enveloping algebras and generalizations Cartan graphs, Weyl groupoids, and root systems: Cartan graphs and Weyl groupoids The structure of Cartan graphs and root systems Cartan graphs of Lie superalgebras Weyl groupoids and root systems of Nichols algebras: A braided monoidal isomorphism of YetterDrinfeld modules Nichols systems, and semiCartan graph of Nichols algebras Right coideal subalgebras of Nichols systems, and Cartan graph of Nichols algebras Applications: Nichols algebras of diagonal type Nichols algebras of Cartan type Nichols algebras over nonabelian groups Bibliography Index of symbols Subject index.
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QA3 .A4 V.247  Unknown 
 Tsfasman, M. A. (Michael A.), 1954 author.
 Providence, Rhode Island : American Mathematical Society, [2019]
 Description
 Book — x, 453 pages : illustration ; 27 cm.
 Summary

 Curves with many points. I: Modular curves Class field theory Curves with many points. II Infinite global fields Decoding: Some examples Sphere packings Codes from multidimensional varieties Applications Appendix: Some basic facts from Volume 1 Bibliography List of names Index.
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QA3 .A4 V.238  Unknown 
 Arcozzi, N. (Nicola), 1963 author.
 Providence, Rhode Island : American Mathematical Society, [2019]
 Description
 Book — xix, 536 pages ; 27 cm.
 Summary

 The Dirichlet space Foundations: Geometry and analysis on the disk Hilbert spaces of holomorphic functions Intermezzo: Hardy spaces Carleson measures Analysis on trees The Pick property Interpolation The Dirichlet space Selected topics: Onto interpolation Boundary values Alternative norms and applications Shift operators and invariant subspaces Invariant subspaces of the Dirichlet shift Bilinear forms on $\mathcal{D}$ Besov spaces on the ball: Besov spaces on balls and trees Interpolating sequences Spaces on trees Corona theorems for Besov spaces in $\mathbb{C}^n$ Some functional analysis Schur's test Bibliography Index.
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QA3 .A4 V.239  Unknown 
9. Jordan structures in Lie algebras [2019]
 López, Antonio Fernández, 1952 author.
 Providence, Rhode Island : American Mathematical Society, [2019]
 Description
 Book — xi, 299 pages : illustrations ; 26 cm.
 Summary

 Preface
 Introducton
 Chapter 1. Nonassociative algebras
 Chapter 2. General facts on Lie algebras
 Chapter 3. Absolute zero divisors
 Chapter 4. Jordan elements
 Chapter 5. Von Neumann regular elements
 Chapter 6. Extremal elements
 Chapter 7. A characterization of strong primeness
 Chapter 8. From Lie algebras to Jordan algebras
 Chapter 9. The Kostrikin radical
 Chapter 10. Algebraic Lie algebras and local finiteness
 Chapter 11. From Lie algebras to Jordan pairs
 Chapter 12. An Artinian theory for Lie algebras
 Chapter 13. Inner ideal structure of Lie algebras
 Chapter 14. Classical infinitedimensional Lie algebras
 Chapter 15. Classical BanachLie algebras.
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QA3 .A4 V.240  Unknown 
 Isidro, José M., author.
 [Providence, Rhode Island] : American Mathematical Society, [2019]
 Description
 Book — xiii, 560 pages ; 26 cm
 Summary

 JB$^*$triples in dual Banach spaces From bounded domains to symmetric Banach manifolds: Analytic manifolds and their automorphism groups Uniform manifolds and their automorphism groups The semigroup $\mathcal{O}_c(X)$ of holomorphic contractions Manifolds with a compatible invariant metrics Manifolds with a compatible tangent norm Symmetric normed manifolds J$^*$triples and their related Lie algebras The J$^*$triple associated with a symmetric manifold The symmetric manifold associated with a J$^*$triple Finite Rank J$^*$triples and JH$^*$triples: Algebraic study of J$^*$triples Atomic J$^*$triples and JH$^*$triples From symmetric Banach manifolds to JB$^*$triples: Spectral properties and bounded J$^*$triples The Riemann mapping theorem for JB$^*$triples The category of JB$^*$triples Automorphisms of bounded symmetric domains Tripotents in JB$^*$triples Functional calculus in a JB$^*$triple. Applications Automorphisms of BanachGrassmann manifolds Symmetric Grassmann manifolds over Hilbert spaces Affine structure of the unit ball in a JB$^*$triple JB$^*$triples in dual Banach spaces or JBW$^*$triples: Structure theory for JBW$^*$triples and their preduals Facial structure in JBW$^*$triples and in JB$^*$triples The strong and strong* topologies in JBW$^*$triples Derivations of JB$^*$triples Some results on functional analysis Lists of symbols and their meanings Bibliography Index.
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QA3 .A4 V.243  Unknown 
 Boussaïd, Nabile, 1978 author.
 Providence, Rhode Island : American Mathematical Society, [2019]
 Description
 Book — vi, 297 pages ; 27 cm.
 Summary

 Introduction Distributions and function spaces Spectral theory of nonselfadjoint operators Linear stability of NLS solitary waves Solitary waves of nonlinear Schrodinger equation Limiting absorption principle CarlemanBerthierGeorgescu estimates The Dirac matrices The Soler model Bifrequency solitary waves Bifurcations of eigenvalues from the essential spectrum Nonrelativistic asymptotics of solitary waves Spectral stability in the nonrelativistic limit Bibliography Index List of symbols.
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QA3 .A4 V.244  Unknown 
12. Ordinary differential operators [2019]
 Wang, Aiping, 1977 author.
 Providence, Rhode Island : American Mathematical Society, [2019]
 Description
 Book — xv, 250 pages ; 27 cm
 Summary

 Differential equations and expressions: First order systems Quasidifferential expressions and equations The Lagrange identity and maximal and minimal operators Deficiency indices Symmetric, selfadjoint, and dissipative operators: Regular symmetric operators Singular symmetric operators Selfadjoint operators Selfadjoint and symmetric boundary conditions Solutions and spectrum Coefficients, the deficiency index, spectrum Dissipative operators Twointerval problems: Twointerval symmetric domains Twointerval symmetric domain characterization with maximal domain functions Other topics: Green's function and adjoint problems Notation Topics not covered and open problems Bibliography Index.
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QA3 .A4 V.245  Unknown 
 Arizona Winter School on Perfectoid Spaces (20th : 2017 : Tucson, Ariz.), author.
 Providence, Rhode Island : American Mathematical Society, [2019]
 Description
 Book — xii, 297 pages : illustrations ; 27 cm.
 Summary

 Preface / by Bryden Cais
 Introduction / by Peter Scholze
 Adic spaces / by Jared Weinstein
 Sheaves, stacks, and shtukas / by Kiran S. Kedlaya
 The HodgeTate decomposition via perfectoid spaces / by Bhargav Bhatt
 Perfectoid Shimura varieties / by Ana Caraiani.
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QA3 .A4 V.242  Unknown 
14. A tool kit for groupoid C*algebras [2019]
 Williams, Dana P., 1952 author.
 Providence, Rhode Island : American Mathematical Society, [2019]
 Description
 Book — xv, 398 pages : illustrations ; 27 cm.
 Summary

 From groupoid to algebra
 Groupoid actions and equivalence
 Measure theory
 Proof of the equivalence theorem
 Basic representation theory
 The existence and uniqueness of Haar systems
 Unitary representations
 Renault's Disintegration Theorem
 Amenability for groupoids
 Measurewise amenability for groupoids
 Comments on simplicity
 Duals and topological vector spaces.
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QA3 .A4 V.241  Unknown 
 Providence, Rhode Island : American Mathematical Society ; [Stony Brook, New York] : Simons Center for Geometry and Physics, [2019]
 Description
 Book — xv, 298 pages : illustrations ; 27 cm.
 Summary

 Introduction / by John W. Morgan
 Notes on Kuranishi atlases / by Dusa McDuff
 GromovWitten theory via Kuranishi structures /rby Mohammad F. Tehrani and Kenji Fukaya
 Kuranishi spaces as a 2category / by Dominic Joyce.
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QA3 .A4 V.237  Unknown 
 Smith, Stephen D., 1948 author.
 Providence, Rhode Island : American Mathematical Society, [2018]
 Description
 Book — xiii, 231 pages ; 27 cm.
 Summary

 Background: Simple groups and their properties Outline of the proof of the CFSG: Some main ideas Thompson factorizationand its failure: FFmethods Recognition theorms for simple groups Representation theory of simple groups Maximal subgroups and primitive representations Geometries for simple groups Some fusion techniques for classification problems Some applications close to finite group theory Some applications farther afield from finite groups Appendix A: Some supplementary notes to the text Appendix B: Further remarks on certain exercises Bibliography Index.
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QA3 .A4 V.230  Unknown 
 Kaniuth, Eberhard, author.
 Providence, Rhode Island : American Mathematical Society, [2018] ©2018.
 Description
 Book — xi, 306 pages ; 26 cm.
 Summary

 Preliminaries Basic theory of Fourier and FourierStieltjes algebras Miscellaneous further topics Amenability properties of $A(G)$ and $B(G)$ Multiplier algebras of Fourier algebras Spectral synthesis and ideal theory Extension and separation properties of positive definite functions Appendix Bibliography Index.
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QA3 .A4 V.231  Unknown 
 Qin, Zhenbo, author.
 Providence, Rhode Island : American Mathematical Society, [2018]
 Description
 Book — xi, 336 pages ; 26 cm.
 Summary

 Hilbert schemes of points on surfaces: Basic results on Hilbert schemes of points The nef cone and flip structure of $(\mathbb{P}^2)^{[n]}$ Hilbert schemes and infinite dimensional Lie algebras: Hilbert schemes and infinite dimensional Lie algebras Chern character operators Multiple $q$zeta values and Hilbert schemes Lie algebras and incidence Hilbert schemes Cohomology rings of Hilbert schemes of points: The cohomology rings of Hilbert schemes of points on surfaces Ideals of the cohomology rings of Hilbert schemes Integral cohomology of Hilbert schemes The ring structure of $H^*_{\textrm{orb}}(X^{(n)})$ Equivariant cohomology of the Hilbert schemes of points: Equivariant cohomology of Hilbert schemes Hilbert/GromovWitten correspondence GromovWitten theory of the Hilbert schemes of points: Cosection localization for the Hilbert schemes of points Equivariant quantum operator of OkounkovPandharipande The genus0 extremal GromovWitten invariants Ruan's Cohomological Crepant Resolution Conjecture Bibliography Index.
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QA3 .A4 V.228  Unknown 
 Khavinson, Dmitry, 1956 author.
 Providence, Rhode Island : American Mathematical Society, [2018]
 Description
 Book — x, 214 pages : illustrations (chiefly color) ; 27 cm.
 Summary

 Introduction: Some motivating questions The CauchyKovalevskaya theorem with estimates Remarks on the CauchyKovalevskaya theorem Zerner's theorem The method of globalizing families Holmgren's uniqueness theorem The continuity method of F. John The BonySchapira theorem Applications of the BonySchapira theorem: Part I  Vekua hulls Applications of the BonySchapira theorem: Part II  Szego's theorem revisited The reflection principle The reflection principle (continued) Cauchy problems and the Schwarz potential conjecture The Schwarz potential conjecture for spheres Potential theory on ellipsoids: Part I  The mean value property Potential theory on ellipsoids: Part II  There is no gravity in the cavity Potential theory on ellipsoids: Part III  The Dirichlet problem Singularities encountered by the analytic continuation of solutions to the Dirichlet problem An introduction to J. Leray's principle on propagation of singularities through $\mathbb{C}^n$ Global propagation of singularities in $\mathbb{C}^n$ Quadrature domains and Laplacian growth Other varieties of quadrature domains Bibliography Index.
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QA3 .A4 V.232  Unknown 
 Ammari, Habib, author.
 Providence, Rhode Island : American Mathematical Society, [2018]
 Description
 Book — viii, 509 pages : illustrations ; 27 cm.
 Summary

 Introduction
 Part 1. Mathematical and computation tools: Generalized argument principle and Rouche's theorem Layer potentials Perturbations of cavities and resonators
 Part 2. Diffraction gratings and bandgap materials: Diffraction gratings Photonic band gaps Phononic band gaps
 Part 3. Subwavelength resonant structures and superresolution: Plasmonic resonances for nanoparticles Imaging of small particles Superresolution imaging
 Part 4. Metamaterials: Nearcloaking Anomalous resonance cloaking and shielding Plasmonic metasurfaces
 Part 5. Subwavelength phonics: Helmholtz resonator Minnaert resonances for bubbles Appendix A. Spectrum of selfadjoint operators Appendix B. Optimal control and level set representation Bibliography Index.
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QA3 .A4 V.235  Unknown 
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