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New Publications Offered by The New Publications Offered by the AMS To subscribe to email notification of new AMS publications, please go to www.ams.org/bookstore-email. Algebra and Algebraic Geometry Analysis Noncommutative Analysis, Complex Motives Geometry, and Gonçalo Tabuada, Massachusetts Mathematical Physics Institute of Technology, Cambridge, In Honor of Duong H. Phong MA Paul M. N. Feehan and Jian Song, The theory of motives began in the early Rutgers University, Piscataway, 1960s when Grothendieck envisioned NJ, Ben Weinkove, Northwestern the existence of a “universal cohomology theory of algebraic varieties”. The theory University, Evanston, IL, and of noncommutative motives is more recent. Richard A. Wentworth, University It began in the 1980s when the Moscow school (Beilinson, Bondal, of Maryland, College Park, MD, Kapranov, Manin, and others) began the study of algebraic varieties Editors via their derived categories of coherent sheaves, and continued in the 2000s when Kontsevich conjectured the existence of a “universal This volume contains the proceedings of the Conference on Analysis, invariant of noncommutative algebraic varieties”. Complex Geometry and Mathematical Physics: In Honor of Duong H. This book, prefaced by Yuri I. Manin, gives a rigorous overview of some Phong, which was held from May 7–11, 2013, at Columbia University, of the main advances in the theory of noncommutative motives. It is New York. The conference featured thirty speakers who spoke on divided into three main parts. The first part, which is of independent a range of topics reflecting the breadth and depth of the research interest, is devoted to the study of DG categories from a homotopical interests of Duong H. Phong on the occasion of his sixtieth birthday. A viewpoint. The second part, written with an emphasis on examples common thread, familiar from Phong’s own work, was the focus and applications, covers the theory of noncommutative pure motives, on the interplay between the deep tools of analysis and the rich noncommutative standard conjectures, noncommutative motivic structures of geometry and physics. Galois groups, and also the relations between these notions and their Papers included in this volume cover topics such as the complex commutative counterparts. The last part is devoted to the theory of Monge-Ampère equation, pluripotential theory, geometric partial noncommutative mixed motives. The rigorous formalization of this differential equations, theories of integral operators, integrable latter theory requires the language of Grothendieck derivators, which, systems and perturbative superstring theory. for the reader’s convenience, is revised in a brief appendix. This item will also be of interest to those working in mathematical Contents: Introduction; Differential graded categories; Additive physics. invariants; Background on pure motives; Noncommutative pure Contents: Z. Błocki, Bergman kernel and pluripotential theory; T. C. motives; Noncommutative (standard) conjugates; Noncommutative Collins and A. Jacob, On the convergence of the Sasaki-Ricci flow; motivic Galois groups; Jacobians of noncommutative Chow Q. Dai, X.-J. Wang, and B. Zhou, The signed mean curvature measure; motives; Localizing invariants; Noncommutative mixed motives; E. D’Hoker, Topics in two-loop superstring perturbation theory; Noncommutative motivic Hopf dg algebras; Appendix; Bibliography; P. Guan and X. S. Shen, A rigidity theorem for hypersurfaces in higher Index. dimensional space forms; P. Eyssidieux, V. Guedj, and A. Zeriahi, University Lecture Series, Volume 63 Continuous approximation of quasiplurisubharmonic functions; C. Hongler, K. Kytölä, and A. Zahabi, Discrete holomorphicity and October 2015, 114 pages, Softcover, ISBN: 978-1-4704-2397-1, LC Ising model operator formalism; A. Jacob, Stable Higgs bundles and 2015018204, 2010 Mathematics Subject Classification: 14A22, 14C15, Hermitian-Einstein metrics on non-Kähler manifolds; S. Kołodziej 18D20; 18E30, 18G55, 19D55, AMS members US$35.20, List US$44, and N. N. Cuong, Weak solutions to the complex Monge-Ampère Order code ULECT/63 equation on Hermitian manifolds; C.-J. Liu and Z. Lu, Uniform 998 Notices of the AMS Volume 62, Number 8 New Publications Offered by the AMS asymptotic expansion on Riemann surfaces; X. Ma, G. Marinescu, space of vector-valued functions on the unit ball; S. K. Srivastava and S. Zelditch, Scaling asymptotics of heat kernels of line and U. Singh, Trigonometric approximation of periodic functions p bundles; L. Ni, Parabolic frequency monotonicity and a theorem of belonging to weighted Lipschitz class W (L ; Ψ(t), β); J. Wermer, Hardy-Pólya-Szegö; M.-C. Shaw, Topology of Dolbeault cohomology Analytic structure of polynomial hulls. groups; B. Shiffman, Uniformly bounded orthonormal sections of Contemporary Mathematics, Volume 645 positive line bundles on complex manifolds; M. Taylor, Poisson equations, uniformization, and geometrical optics; V.‘Tosatti, August 2015, 301 pages, Softcover, ISBN: 978-1-4704-1694-2, LC Non-Kähler Calabi-Yau manifolds; Rakesh and G. Uhlmann, The 2015000884, 2010 Mathematics Subject Classification: 46B04, 46E10, point source inverse back-scattering problem; Y. Wang, Local 46E15, 46E25, 46E30, 46H05, 46J10, 46J15, AMS members US$84, regularity of the complex Monge-Ampère equation; E. Witten, Notes List US$105, Order code CONM/645 on holomorphic string and superstring theory measures of low genus. Contemporary Mathematics, Volume 644 Mathematics++ August 2015, 359 pages, Softcover, ISBN: 978-1-4704-1464-1, LC 2014050310, 2010 Mathematics Subject Classification: 31C10, 32J25, Selected Topics Beyond the 53C07, 35R01, 53C44, 53C55, 53C80, AMS members US$84, List Basic Courses US$105, Order code CONM/644 Ida Kantor, Charles University, Prague, Czech Republic, Jiˇrí Function Spaces in Matoušek, Charles University, Analysis Prague, Czech Republic, and ETH, Zurich, Switzerland, and Robert Krzysztof Jarosz, Southern Illinois Šámal, Charles University, Prague, University at Edwardsville, IL, Czech Republic Editor Mathematics++ is a concise introduction to six selected areas This volume contains the proceedings of of 20th century mathematics providing numerous modern the Seventh Conference on Function Spaces, mathematical tools used in contemporary research in computer which was held from May 20–24, 2014 at science, engineering, and other fields. The areas are: measure theory, Southern Illinois University at Edwardsville. high-dimensional geometry, Fourier analysis, representations of groups, multivariate polynomials, and topology. For each of the areas, The papers cover a broad range of topics, including spaces and the authors introduce basic notions, examples, and results. The algebras of analytic functions of one and of many variables (and presentation is clear and accessible, stressing intuitive understanding, operators on such spaces), spaces of integrable functions, spaces of and it includes carefully selected exercises as an integral part. Banach-valued functions, isometries of function spaces, geometry of Theory is complemented by applications—some quite surprising—in Banach spaces, and other related subjects. theoretical computer science and discrete mathematics. The chapters Contents: M. Abel, On algebraic properties of the spectrum are independent of one another and can be studied in any order. and spectral radius of elements in a unital algebra; M. Abel, It is assumed that the reader has gone through the basic mathematics Automatic continuity of surjective homomorphisms between courses. Although the book was conceived while the authors were topological algebras; J. T. Anderson, Characterization of teaching Ph.D. students in theoretical computer science and discrete holomorphic and meromorphic functions via maximum principles; p mathematics, it will be useful for a much wider audience, such as F. Botelho and J. Jamison, Hermitian operators on H (4n); J. A. H mathematicians specializing in other areas, mathematics students Chávez-Domínguez and T. Oikhberg, Some notions of transitivity deciding what specialization to pursue, or experts in engineering or for operator spaces; J. Craig, J. F. Feinstein, and P. Patrick, other fields. Removability of exceptional sets for differentiable and Lipschitz functions; D. E. Edmunds and J. Lang, Generalizing trigonometric This item will also be of interest to those working in algebra and functions from different points of view; G. O. S. Ekhaguere, algebraic geometry, number theory, and geometry and topology. ∗ Partial W -dynamical systems and their dilations; J. F. Feinstein, Contents: Measaure and integral; High-dimensional geometry and S. Morley, and H. Yang, Swiss cheeses and their applications; measure concentration; Fourier analysis; Representations of finite O. Hatori, Isometries on the special unitary group; T. Hõim and D. A. groups; Polynomials; Topology; Index. Robbins, Amenability as a hereditary property in some algebras of vector-valued functions; P. Jain, M. Singh, and A. P. Singh, Student Mathematical Library, Volume 75 Weighted norm inequalities for Hardy type operators on monotone September 2015, 353 pages, Softcover, ISBN: 978-1-4704-2261-5, LC functions; K. Jarosz, Norms on normal function algebras; A. Yu. 2015016136, 2010 Mathematics Subject Classification: 14-01, 20Cxx, Karlovich, Maximally modulated singular integral operators and their 28-01, 43-01, 52Axx, 54-01, 55-01, AMS members US$39.20, All applications to pseudodifferential operators on Banach function Individuals US$39.20, List US$49, Order code STML/75 spaces; S. G. Krantz,
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