CRM Proceedings & Lecture Notes, Volume: 54
2011; 334 pp; softcover
ISBN-13: 978-0-8218-7283-3
Expected publication date is November 16, 2011.
This volume grew out of an international conference which was held in June 2009 at McGill University, in honour of Professor Peter Russell, on the occasion of his 70th birthday and his retirement from McGill. It contains 19 refereed articles, essentially all in the area of affine algebraic geometry and, more specifically, in the following subjects: automorphisms and group actions, surfaces, embeddings of certain rational curves in the affine plane, and problems in positive characteristic geometry. These are also some of the themes running through the very substantial body of work done by Professor Russell in this relatively young branch of algebraic geometry. The volume also includes a foreword, in which Professor Russell shares some personal reminiscences on the development of affine algebraic geometry, a field he describes as "loosely speaking, the study of affine spaces and algebraic varieties closely resembling them."
Graduate students and research mathematicians interested in affine algebraic geometry.
P. Cassou-Nogues -- Newton trees at infinity of algebraic curves
D. Daigle -- Polynomials f(X,Y,Z) of low LND-degree
H. Flenner, S. Kaliman, and M. Zaidenberg -- Corrigendum to our paper "Birational transformations of weighted graphs"
G. Freudenburg -- Bivariate analogues of Chebyshev polynomials with application to embeddings of affine spaces
R. Ganong -- The pencil of translates of a line in the plane
R. V. Gurjar -- A geometric proof of Boutot's result on singularities of quotients
S. Kaliman and F. Kutzschebauch -- On the present state of the Andersen-Lempert theory
T. Kishimoto, Y. Prokhorov, and M. Zaidenberg -- Group actions on affine cones
M. Koras -- mathbb{C}^* in mathbb{C}^2 is birationally equivalent to a
line
S. Kuroda -- Initial algebras and the Jung-van der Kulk theorem
S. S.-Y. Lu -- Holomorphic curves on irregular varieties of general type starting from surfaces
L. Makar-Limanov -- Locally nilpotent derivations of affine domains
K. Masuda -- Equivariant derivations and additive group actions
M. Miyanishi -- Frobenius sandwiches of affine algebraic surfaces
L. Moser-Jauslin -- Automorphism groups of Koras-Russell threefolds of the first kind
K. Palka -- Recent progress in the geometry of mathbb{Q}-acyclic surfaces
V. L. Popov -- On the Makar-Limanov, Derksen invariants, and finite automorphism groups of algebraic varieties
A. Sathaye -- Embeddings of hyperbolas
Y. Takeda -- Groups of Russell type and tango structures
Fields Institute Communications, Volume: 61
2011; 163 pp; hardcover
ISBN-13: 978-0-8218-4849-4
Expected publication date is November 26, 2011.
This volume represents the proceedings of the Noncommutative Geometry Workshop that was held as part of the thematic program on operator algebras at the Fields Institute in May 2008.
Pioneered by Alain Connes starting in the late 1970s, noncommutative geometry was originally inspired by global analysis, topology, operator algebras, and quantum physics. Its main applications were to settle some long-standing conjectures, such as the Novikov conjecture and the Baum-Connes conjecture.
Next came the impact of spectral geometry and the way the spectrum of a geometric operator, like the Laplacian, holds information about the geometry and topology of a manifold, as in the celebrated Weyl law. This has now been vastly generalized through Connes' notion of spectral triples.
Finally, recent years have witnessed the impact of number theory, algebraic geometry and the theory of motives, and quantum field theory on noncommutative geometry. Almost all of these aspects are touched upon with new results in the papers of this volume.
Graduate students and research mathematicians interested in noncommutative geometry.
M.-T. Benameur and A. Gorokhovsky -- Local index theorem for projective families
A. L. Carey, J. Phillips, I. F. Putnam, and A. Rennie -- Type III KMS states
on a class of C^*-algebras containing O_n and mathcal{Q}_N and their modular
index
H. Emerson -- Duality, correspondences and the Lefschetz map in equivariant KK-theory: A survey
F. Fathizadeh and M. Khalkhali -- Twisted spectral triples and Connes' character formula
B. Nica -- Spectral morphisms, K-theory, and stable ranks
A. Pourkia -- A survey of braided Hopf cyclic cohomology
R. Rochberg, X. Tang, and Y.-J. Yao -- A survey of Rankin-Cohen deformations
O. Uuye -- Pseudo-differential operators and regularity of spectral triples
***
Proceedings of Symposia in Applied Mathematics, Volume: 69
2011; 171 pp; hardcover
ISBN-13: 978-0-8218-5326-9
Expected publication date is December 1, 2011.
This volume is based on lectures delivered at the 2011 AMS Short Course on Evolutionary Game Dynamics, held January 4-5, 2011 in New Orleans, Louisiana.
Evolutionary game theory studies basic types of social interactions in populations of players. It combines the strategic viewpoint of classical game theory (independent rational players trying to outguess each other) with population dynamics (successful strategies increase their frequencies). A substantial part of the appeal of evolutionary game theory comes from its highly diverse applications such as social dilemmas, the evolution of language, or mating behaviour in animals. Moreover, its methods are becoming increasingly popular in computer science, engineering, and control theory. They help to design and control multi-agent systems, often with a large number of agents (for instance, when routing drivers over highway networks or data packets over the Internet).
While these fields have traditionally used a top down approach by directly controlling the behaviour of each agent in the system, attention has recently turned to an indirect approach allowing the agents to function independently while providing incentives that lead them to behave in the desired way. Instead of the traditional assumption of equilibrium behaviour, researchers opt increasingly for the evolutionary paradigm and consider the dynamics of behaviour in populations of agents employing simple, myopic decision rules.
Graduate students and research mathematicians interested in game theory and dynamical systems.
K. Sigmund -- Introduction to evolutionary game theory
R. Cressman -- Beyond the symmetric normal form: Extensive form games, asymmetric games and games with continuous strategy spaces
J. Hofbauer -- Deterministic evolutionary game dynamics
S. Sorin -- On some global and unilateral adaptive dynamics
W. H. Sandholm -- Stochastic evolutionary game dynamics: Foundations, deterministic approximation, and equilibrium selection
S. Lessard -- Evolution of cooperation in finite populations
Index
Mathematical Surveys and Monographs,Volume: 178
2011; 363 pp; hardcover
ISBN-13: 978-0-8218-5361-0
Expected publication date is November 10, 2011.
Every book on numerical analysis covers methods for the approximate calculation of definite integrals. The authors of this book provide a complementary treatment of the topic by presenting a coherent theory of quadrature methods that encompasses many deep and elegant results as well as a large number of interesting (solved and open) problems.
The inclusion of the word "theory" in the title highlights the authors' emphasis on analytical questions, such as the existence and structure of quadrature methods and selection criteria based on strict error bounds for quadrature rules. Systematic analyses of this kind rely on certain properties of the integrand, called "co-observations," which form the central organizing principle for the authors' theory, and distinguish their book from other texts on numerical integration. A wide variety of co-observations are examined, as a detailed understanding of these is useful for solving problems in practical contexts.
While quadrature theory is often viewed as a branch of numerical analysis, its influence extends much further. It has been the starting point of many far-reaching generalizations in various directions, as well as a testing ground for new ideas and concepts. The material in this book should be accessible to anyone who has taken the standard undergraduate courses in linear algebra, advanced calculus, and real analysis.
Graduate students and research mathematicians interested in quadrature theory, numerical integration, and approximation theory.
Introduction
The abstract framework
Norm and kernel of the remainder functional
Co-observations
Quadrature rules of interpolatory type
Gaussian quadrature
Quadrature rules with equidistant nodes
Periodic integrands
Variance and Chebyshev-type rules
Problems
Orthogonal polynomials
Bernoulli polynomials
Validation of co-observations
Bibliography
Symbols
Index
Contemporary Mathematics, Volume: 555
2011; 215 pp; softcover
ISBN-13: 978-0-8218-4959-0
Expected publication date is November 19, 2011.
This volume contains papers based on presentations given at the Pan-American Advanced Studies Institute (PASI) on commutative algebra and its connections to geometry, which was held August 3-14, 2009, at the Universidade Federal de Pernambuco in Olinda, Brazil.
The main goal of the program was to detail recent developments in commutative algebra and interactions with such areas as algebraic geometry, combinatorics and computer algebra. The articles in this volume concentrate on topics central to modern commutative algebra: the homological conjectures, problems in positive and mixed characteristic, tight closure and its interaction with birational geometry, integral dependence and blowup algebras, equisingularity theory, Hilbert functions and multiplicities, combinatorial commutative algebra, Grobner bases and computational algebra.
Graduate students and research mathematicians interested in commutative algebra and algebraic geometry.
J. Martinez-Bernal, C. Renteria-Marquez, and R. H. Villarreal -- Combinatorics of symbolic Rees algebras of edge ideals of clutters
W. Bruns, C. Krattenthaler, and J. Uliczka -- Hilbert depth of powers of the maximal ideal
C-Y.J. Chan and J.-C. Liu -- A note on reductions of monomial ideals in
k[x,y]_{(x,y)}
C. Ciliberto and V. Di Gennaro -- Plucker-Clebsch formula in higher dimension
E. De Negri and E. Gorla -- Invariants of ideals generated by pfaffians
J. Elias and J. Martinez-Borruel -- Hilbert polynomial and the intersection of ideals
V. Ferrer and I. Vainsencher -- Polynomial vector fields with algebraic trajectories
P. Gimenez, I. Sengupta, and H. Srinivasan -- Minimal free resolutions for certain affine monomial curves
S. Goto and K. Ozeki -- Uniform bounds for Hilbert coefficients of parameters
C. Huneke -- Absolute integral closure
G. Lyubeznik, W. Zhang, and Y. Zhang -- A property of the Frobenius map of a polynomial ring
M. Majidi-Zolbanin and B. Snapp -- A note on the variety of pairs of matrices whose product is symmetric
P. Roberts and A. K. Singh -- Reconciling Riemann-Roch results
M. E. Rossi -- Hilbert functions of Cohen-Macaulay local rings
J. Striuli and A. Vraciu -- Some homological properties of almost Gorenstein rings