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Gorenstein Liaison, Complete Intersection Liaison Invariants and Unobstructedness
This paper contributes to the liaison and obstruction theory of subschemes in $\mathbb{P}^n$ having codimension at least three. The first part establishes several basic results on Gorenstein liaison. A classical result of Gaeta on liaison classes of projectively normal curves in $\mathbb{P}^3$ is generalized to the statement that every codimension $c$ ``standard determinantal scheme'' (i.e. a scheme defined by the maximal minors of a $t\times (t+c-1)$ homogeneous matrix), is in the Gorenstein liaison class of a complete intersection. Then Gorenstein liaison (G-liaison) theory is developed as a theory of generalized divisors on arithmetically Cohen-Macaulay schemes. In particular, a rather ge...
Strong Boundary Values, Analytic Functionals, and Nonlinear Paley-Wiener Theory
This work is intended for graduate students and research mathematicians interested in functional analysis, several complex variables, analytic spaces, and differential equations.
A Stability Index Analysis of 1-D Patterns of the Gray-Scott Model
This work is intended for graduate students and research mathematicians interested in partial differential equations.
Equivariant Analytic Localization of Group Representations
This book is intended for graduate students and research mathematicians interested in topological groups, Lie groups, category theory, and homological algebra.
The Dirichlet Problem for Parabolic Operators with Singular Drift Terms
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 certain parabolic PDEs with singular drift terms. Each of the chapters that comprise this memoir has its own numbering system and list
Desingularization of Nilpotent Singularities in Families of Planar Vector Fields
This work aims to prove a desingularization theorem for analytic families of two-dimensional vector fields, under the hypothesis that all its singularities have a non-vanishing first jet. Application to problems of singular perturbations and finite cyclicity are discussed in the last chapter.
The Submanifold Geometries Associated to Grassmannian Systems
This work is intended for graduate students and research mathematicians interested in differential geometry and partial differential equations.
Sub-Laplacians with Drift on Lie Groups of Polynomial Volume Growth
This work is intended for graduate students and research mathematicians interested in topological groups, Lie groups, and harmonic analysis.
Blowing Up of Non-Commutative Smooth Surfaces
This book is intended for graduate students and research mathematicians interested in associative rings and algebras, and noncommutative geometry.
The $AB$ Program in Geometric Analysis: Sharp Sobolev Inequalities and Related Problems
Function theory and Sobolev inequalities have been the target of investigation for many years. Sharp constants in these inequalities constitute a critical tool in geometric analysis. The $AB$ programme is concerned with sharp Sobolev inequalities on compact Riemannian manifolds. This text summarizes the results of contemporary research and gives an up-to-date report on the field.
