Covering extended affine Lie algebras and their root systems, this work is intended for graduate students, research mathematicians, and mathematical physicists interested in Lie theory.

Concerned with the calculation of the cohomology of the mapping class group of a closed oriented surface of genus two, this book uses methods involving braid groups, modular representations of symmetric groups and configuration spaces.

Subdivision methods in computer graphics constitute a large class of recursive schemes for computing curves and surfaces. They seem to have their origin in the geometric problem of smoothing the corners of a given polyhedral surface - in fact, these methods are sometimes called wood carver algorithms because the repeated smoothing operations are analogous to sculpting wood. This book presents a systematic development of the basic mathematical principles and concepts associated with stationary subdivision algorithms. The authors pay special attention to the structure of such algorithms in a...

This volume studies the behaviour of a random heat kernel associated with a stochastic partial differential equation, and gives short-time expansion of this heat kernel. The author finds that the dominant exponential term is classical and depends only on the Riemannian distance function. The second exponential term is a work term and also has classical meaning. There is also a third non-negligible exponential term which blows up. The author finds an expression for this third exponential term which involves a random translation of the index form and the equations of Jacobi fields. In the...

In part 1 of this title the authors construct a diffeomorphism invariant (Colombeau-type) differential algebra canonically containing the space of distributions in the sense of L. Schwartz. Employing differential calculus in infinite dimensional (convenient) vector spaces, previous attempts in this direction are unified and completed. Several classification results are achieved and applications to nonlinear differential equations involving singularities are given.

This memoir considers the Dirichlet problem for parabolic operators in a half space with singular drift terms. Chapter I begins the study of a parabolic PDE modelled on the pullback of the heat equation in certain time varying domains considered by Lewis-Murray and Hofmann-Lewis. Chapter II obtains mutual absolute continuity of parabolic measure and Lebesgue measure on the boundary of this halfspace and also that the $L DEGREESq(R DEGREESn)$ Dirichlet problem for these PDEs has a solution when $q$ is large enough. Chapter III proves an analogue of a theorem of Fefferman, Kenig, and Pipher for...

The general aim of the present monograph is to study boundary-value problems for second-order elliptic operators in Lipschitz subdomains of Riemannian manifolds. In the first part it develops a theory for Cauchy type operators on Lipschitz submanifolds of codimension one (focused on boundedness properties and jump relations). The solution is represented in the form of layer potentials and optimal nontangential maximal function estimates are established. This analysis is carried out under smoothness assumptions (for the coefficients of the operator, metric tensor and the underlying domain)...

This book is intended for researchers and graduate students in commutative algebra, algebraic topology and invariant theory.

This book is intended for graduate students and research mathematicians interested in calculus of variations and optimal control; optimization.

This book is intended for graduate students and research mathematicians interested in algebraic topology.