Grothendieck's theory of Dessins d'Enfants involves combinatorially determined affine, reflective and conformal structures on compact surfaces. This work presents a general method for uniformizing these dessin surfaces and for approximating their as…
Let G be a simple algebraic group defined over an algebraically closed field k whose characteristic is either 0 or a good prime for G, and let uEG be unipotent. The authors study the centralizer CG(u), especially its centre Z(CG(u)). They calculate…
Concerned with the nonnegative solutions of $\Delta u = u^2$ in a bounded and smooth domain in $\mathbb{R}^d$, this title intends to prove that they are uniquely determined by their fine trace on the boundary as defined in [DK98a], answering a major…
The main purpose of this paper is to prove the existence, and in some cases the uniqueness, of unitarily invariant measures on formal completions of groups associated to affine Kac-Moody algebras, and associated homogeneous spaces. The basic invaria…
Considers linear bounded operators on a Hilbert space $H$ having $\overline \Omega$ as spectral set, and no normal summand with spectrum in $\gamma$. For each operator satisfying these properties, this work defines a weak$^*$-continuous functional c…
The author studies the group of rational concordance classes of codimension two knots in rational homology spheres. He gives a full calculation of its algebraic theory by developing a complete set of new invariants. For computation, he relates these…
This book is intended for graduate students and research mathematicians interested in operator theory, functional analysis, and vector lattices.
On the assumption that the $\Gamma$-orbits all have dimension equal to that of $\Gamma$, this title shows that there is a naturally defined $F$- and $\Gamma$-invariant measure $\nu$ of maximal entropy on $\Lambda$ (it is not assumed that the action…
Defines the class of cycle-free partial orders (CFPOs), and analyzes the CFPOs fulfilling a natural transitivity assumption, called $k$-connected set transitivity ($k$-$CS$-transitivity). This work generalizes Droste's classification of the countabl…
The author investigates the anticanonical height zeta function of a (not necessarily split) toric variety defined over a global field of positive characteristic, drawing inspiration from the method used by Batyrev and Tschinkel to deal with the anal…
This text is intended for graduate students and research mathematicians interested in partial differential equations. It covers quasilinear elliptic equations and quasilinear parabolic equations.
The author shows that for any $\epsilon>0$ all eigenvalues aside from $\lambda 1=d$ are bounded by $2\sqrt{d-1}\;+\epsilon$ with probability $1-O(n{-\tau})$, where $\tau=\lceil \bigl(\sqrt{d-1}\;+1\bigr)/2 \rceil-1$.
The main objective of this paper is to prove the monodromy conjecture for the local Igusa zeta function of a quasi-ordinary polynomial of arbitrary dimension defined over a number field. In order to do it, we compute the local Denef-Loeser motivic z…
Contributes to the liaison and obstruction theory of subschemes in $\mathbb{P}^n$ having codimension at least three. This title establishes several basic results on Gorenstein liaison. It also studies groups which are invariant under complete inters…
The authors prove that if $F$ is a finitely generated free group and $\phi$ is an automorphism of $F$ then $F\rtimes_\phi\mathbb Z$ satisfies a quadratic isoperimetric inequality. The authors' proof of this theorem rests on a direct study of the geo…
Let $G$ be a compact, simply connected, simple Lie group. By applying the notion of a twisted tensor product in the senses of Brown as well as of Hess, we construct an economical injective resolution to compute, as an algebra, the cotorsion product…
This book develops a new topological invariant called the m-structure, which incorporates all information contained in the canonical coproduct and the Steenrod operations. Given a chain complex equipped with an m-structure, Smith shows that its coba…
This text looks at topics that include: preliminaries on category theory; non-commutative geometry; pseudo-compact rings; Cohen-Macaulay curves embedded in quasi-schemes; derived categories; quantum plane geometry; and non-commutative cubic surfaces.
Dedicated to extensive research on basic almost-poised hypergeometric series, this title establishes approximately 200 formulas. It also provides their applications to bilateral series, $q$-Clausen formulae, and Rogers-Ramanujan identities.
Containing two papers, this title first uses the classical Adams spectral sequence to study the symplectic cobordism ring $\Omega ^*_{Sp}$. It then uses the results of the first paper to analyze the symplectic Adams-Novikov spectral sequence converg…
Generalizing the Bieri-Neumann-Strebel-Renz Invariants, this Memoir presents the foundations of a theory of (not necessarily discrete) actions $\rho$ of a (suitable) group $G$ by isometries on a proper CAT(0) space $M$. The passage from groups $G$ t…
In this paper the author classifies symplectic actions of $2$-tori on compact connected symplectic $4$-manifolds, up to equivariant symplectomorphisms. This extends results of Atiyah, Guillemin-Sternberg, Delzant and Benoist. The classification is i…
The G-spectrum or generative complexity of a class $\mathcal{C}$ of algebraic structures is the function $\mathrm{G}_\mathcal{C}(k)$ that counts the number of non-isomorphic models in $\mathcal{C}$ that are generated by at most $k$ elements. We cons…
When a domain in the plane is specified by the requirement that there exists a harmonic function which is zero on its boundary and additionally satisfies a prescribed Neumann condition there, the boundary is called a Bernoulli free boundary. (The bo…
Features an article that intends to present a uniform algebraic structure for Moufang quadrangles, and to classify these structures without referring back to the original Moufang quadrangles from which they arise, thereby also giving a new proof for…
Presents a study of semi linear parabolic systems on the full space that admit a family of exponentially decaying pulse-like steady states obtained via translations. This book considers multi-pulse solutions which are the sum of infinitely many such…
Introduces a notion of boundary values for functions along real analytic boundaries, without any restriction on the growth of the functions. This titleoffers a definition that does not depend on having the functions satisfy a differential equation,…
