American Mathematical Society
Probability and number theory — Kanazawa 2005.
These proceedings of the International Conference on Probability and Number Theory held in June 2005 include 25 papers focusing on the interplay between these two disciplines. Topics include the Littlewood conjecture in fields of power series, series and polynomials representations for weighted Rogers-Ramanujan partitions and products modulo 6, limiting processes with dependent increments for measures on symmetric groups of permutations, the ramification of a shift by two, the dynamics associated with certain digital sequences, a new approach to probabalistic number theory through compactification and integration, low discrepancy sequences generated by dynamical systems, renormalized Rauzy functions, approximations for the Goldbach and twin prime problem and gaps between consecutive primes, eigenfunctions for substitution tiling systems, and a review of the highlights of the "marriage" of probability and number theory. Distributed in the US by the American Mathematical Society. (Annotation ©2008 Book News Inc. Portland, OR)
The q, t-Catalan numbers and the space of diagonal harmonics; with an appendix on the combinatorics of Macdonald polynomials.
The field of algebraic combinatorics is dynamic, and one of the most lively studies within the field is the combinatorics of the space of diagonal harmonics. Haglund (mathematics, U. of Pennsylvania) works from his successful lectures here with discussions of topics in the theory of symmetric functions, including work at the practical level such as plethystic substitutions. He includes a substantial number of examples and exercises as he introduces q-analogues and symmetric functions and then moves to MacDonald polynomials and the space of diagonal harmonics, the q, t-Catalan numbers, the q, t-Schröder polynomial, parking functions and the Hilbert series, the shuffle conjecture, and the proof of the q, t-Schröder theorem. In appendices he provides information on the combinatorics of Macdonald polynomials and the Loehr-Warrington conjecture along with solutions to the exercises. (Annotation ©2008 Book News Inc. Portland, OR)
Selected papers of Alberto P. Calderon with commentary.
Alberto P. Calderón (1920-1998) was an important Argentine mathematician known for his work on the theory of partial differential equations and singular integral operators. This volume collects 32 of his more significant papers, including "Uniqueness in the Cauchy problem for partial differential equations," seen by some as his most important. The papers were originally published between 1950 and 2000 and are here presented in chronological order. Also included are eight commentaries by other mathematicians on certain of Calderón's papers in addition to a pair of biographical essays, Calderón's curriculum vitae, and a full list of his publications. (Annotation ©2008 Book News Inc. Portland, OR)
Simple groups of finite Morley rank.
This book provides a detailed presentation of the classification of the simple groups of finite Morley rank which contain a nontrivial unipotent 2-subgroup (linear algebraic groups over algebraically closed fields of characteristic two). Much of the approach outlined in the book is modeled closely on the methods of finite group theory. Chapters are arranged in sections on methods, mixed-type groups, and even-type groups. The final chapter offers a detailed summary of applications of the main theorem presented. The audience for the book includes finite group theorists, model theorists, and algebraic geometers interested in group theoretic problems. (Annotation ©2008 Book News Inc. Portland, OR)
Singularities in PDE and the calculus of variations.
The formation of geometrical singularities in partial differential equation problems with a variational formulation was the topic of a workshop held in Montreal in July 2006. Two themes surfaced: the Cahn-Hillard model for phase transitions, and the family of Ginzburg-Landau models for superconductors, superfluids, and Bose-Einstein condensates. Not all of the 16 papers presented here, however, color within those lines. No index is provided. (Annotation ©2008 Book News Inc. Portland, OR)
St. Petersburg Mathematical Society; v.13.
This collection of papers covers a diverse range of mathematical subjects from analysis to partial differential equations and wavelets. Topics include Lp estimates for solutions to second order parabolic equations, decomposition of wavelets on non-uniform grids, Newton polyhedra and estimates for differential operators, nodal lines and uniqueness in solutions to linear water wave problems, integral models of algebraic tori and affine toric variables, a geometrical approach to computations of the optimal solution to the rectangle packing problem, a nonstationary Maxwell system with non-homogeneous boundary conditions in domains and conical points, exceptional sets for derivatives of Blaschke products, and asymptotics of solutions and artificial boundary conditions in the transmission problem with a layer-like inhomogeneity. Intended for graduate students and researchers. (Annotation ©2008 Book News Inc. Portland, OR)
Surveys on discrete and computational geometry; twenty years later; proceedings.
Three of the 20 papers delivered at the June 2006 conference survey algorithms for computing topological invariants of semi-algebraic sets, problems and methods concerning k-facets and k-sets, and several points of view on pseudo-triangulations. Other topics include metric graph theory and geometry, extremal problems for convex lattice polytopes, expansive motions, unfolding orthogonal polyhedra, the discharging method in combinatorial geometry, and line transversals to families of translated ovals. No index is provided. (Annotation ©2008 Book News Inc. Portland, OR)
