Carlos Simpson - Böcker
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3 produkter
3 produkter
Del 19 - New Mathematical Monographs
Homotopy Theory of Higher Categories
From Segal Categories to n-Categories and Beyond
Inbunden, Engelska, 2011
1 060 kr
Skickas inom 7-10 vardagar
The study of higher categories is attracting growing interest for its many applications in topology, algebraic geometry, mathematical physics and category theory. In this highly readable book, Carlos Simpson develops a full set of homotopical algebra techniques and proposes a working theory of higher categories. Starting with a cohesive overview of the many different approaches currently used by researchers, the author proceeds with a detailed exposition of one of the most widely used techniques: the construction of a Cartesian Quillen model structure for higher categories. The fully iterative construction applies to enrichment over any Cartesian model category, and yields model categories for weakly associative n-categories and Segal n-categories. A corollary is the construction of higher functor categories which fit together to form the (n+1)-category of n-categories. The approach uses Tamsamani's definition based on Segal's ideas, iterated as in Pelissier's thesis using modern techniques due to Barwick, Bergner, Lurie and others.
2 416 kr
Skickas inom 7-10 vardagar
This book brings together contributions by top-level experts from a wide range of topics in modern Hodge theory, originating in the authors’ participation in the special years on Hodge theory at the Institute of Mathematical Sciences of the Americas (IMSA) in Miami.One of the main themes is the study of moduli spaces and their compactifications. Several articles speak of the singularities occuring in the boundaries of geometrical or Hodge-theoretic compactifications, semistable reduction, the implications of canonical models for model theory in the sense of logic, and fundamental groups of moduli spaces and their associated Torelli groups. Other topics include Mukai lattices, derived moduli spaces, foliations, Higgs bundles and hyperbolicity, the study of pseudoconvexity properties of neighborhoods of infinity, contributions to the theory of degenerations and limiting mixed Hodge structures.This text will provide an indispensable reference for research mathematicians and specialist graduate students, where the modern approaches to moduli spaces are illustrated by their realizations and applications in examples of interest for the interplay between Hodge theory and moduli spaces.
Del 1502 - Lecture Notes in Mathematics
Asymptotic Behavior of Monodromy
Singularly Perturbed Differential Equations on a Riemann Surface
Häftad, Engelska, 1991
271 kr
Skickas inom 10-15 vardagar
This monograph concerns the question of how the solution of a system of ODE's varies when the differential equation varies. The goal is to give non-zero asymptotic expansions for the solution in terms of a parameter expressing how some coefficients go to infinity. A particular class of families of equations is considered, where the answer exhibits a new kind of behaviour not seen in most work known until now. The techniques include Laplace transform and the method of stationary phase, and combinatorial techniques for estimating the contributions of terms in an infinite series expansion for the solution. Addressed primarily to researchers in algebraic geometry, ordinary differential equations and complex analysis, the book will also be of interest to applied mathematicians working on asymptotics of singular perturbations and the numerical solution of ODE's.