Bøger i Memoirs of the American Mathematical Society serien

Introduces time-continuous numerical schemes to simulate stochastic differential equations (SDEs) arising in mathematical finance, population dynamics, chemical kinetics, epidemiology, biophysics, and polymeric fluids.

Proves the existence of an almost full measure set of $(3n-2)$-dimensional quasi-periodic motions in the planetary problem with $(1+n)$ masses, with eccentricities arbitrarily close to the Levi-Civita limiting value and relatively high inclinations. This extends previous results, where smallness of eccentricities and inclinations was assumed.

Studies the non-semisimple terms in the geometric side of the Arthur trace formula for the split symplectic similitude group and the split symplectic group of rank $2$ over any algebraic number field.

Let $X$ be an abstract not necessarily compact orientable CR manifold of dimension $2n-1$, $n\geqslant 2$, and let $L^k$ be the $k$-th tensor power of a CR complex line bundle $L$ over $X$. Given $q\in \{0,1,\ldots,n-1\}$, let $\Box ^{(q)}_{b,k}$ be the Gaffney extension of Kohn Laplacian for $(0,q)$ forms with values in $L^k$.

Develops a theory of crossed products by actions of Hecke pairs $(G, \Gamma )$, motivated by applications in non-abelian $C^*$-duality. The author's approach gives back the usual crossed product construction whenever $G / \Gamma $ is a group and retains many of the aspects of crossed products by groups.

Examines the maximal accretive realizations of geometric Kramers-Fokker-Planck operators on manifolds with boundaries. A general class of boundary conditions is introduced which ensures the maximal accretivity and some global subelliptic estimates. Those estimates imply nice spectral properties as well as exponential decay properties for the associated semigroup.

The Cuntz semigroup of a $C^*$-algebra is an important invariant in the structure and classification theory of $C^*$-algebras. It captures more information than $K$-theory but is often more delicate to handle. The authors systematically study the lattice and category theoretic aspects of Cuntz semigroups.

Develops the theory of operads and analytic functors. In particular, the authors introduce the bicategory $\operatorname{OpdBim}_{\mathcal{V}}$ of operad bimodules, that has operads as $0$-cells, operad bimodules as $1$-cells and operad bimodule maps as 2-cells, and prove that it is cartesian closed.

The authors consider a generic configuration of regions, consisting of a collection of distinct compact regions $\{ \Omega_i\}$ in $\mathbb{R}^{n+1}$ which may be either regions with smooth boundaries disjoint from the others or regions which meet on their piecewise smooth boundaries $\mathcal{B}_i$ in a generic way.

"Volume 250, Number 1190 (third of 6 numbers), November 2017."

Considers scalar lattice differential equations posed on square lattices in two space dimensions. Under certain natural conditions they show that wave-like solutions exist when obstacles (characterized by "holes") are present in the lattice.

Examines the stability of certain liquid drops in a gravity field satisfying a mixed boundary condition. The author also considers as special cases portions of cylinders that model either the zero gravity case or soap films with the same kind of boundary behavior.

Develops a general theory based on rare events for studying integrability properties such as moment bounds for discrete-time stochastic processes. Using this approach, the authors establish moment bounds for fully and partially drift-implicit Euler methods and for a class of new explicit approximation methods which require only a few more arithmetical operations than the Euler-Maruyama method.

Shows that the finite time type II blow up solutions for the energy critical nonlinear wave equation $ \Box u = -u^5 $ on $\mathbb R^3+1$ constructed in Krieger, Schlag, and Tataru (2009) and Krieger and Schlag (2014) are stable along a co-dimension three manifold of radial data perturbations in a suitable topology.

Proves a twisted version of the local trace formula of Arthur over a local field. This formula is an equality between two expressions, one involving weighted orbital integrals, the other one involving weighted characters; and provides a symmetric form of the local trace formula as in Arthur's paper on Fourier Transform of Orbital integral and describes any twisted orbital integral.

The authors study the Jacobian $J$ of the smooth projective curve $C$ of genus $r-1$ with affine model $y^r = x^r-1(x + 1)(x + t)$ over the function field $\mathbb F_p(t)$, when $p$ is prime and $r\ge 2$ is an integer prime to $p$.

The authors study small disturbances to the periodic, plane Couette flow in the 3D incompressible Navier-Stokes equations at high Reynolds number Re. They prove that for sufficiently regular initial data of size $\epsilon \leq c_0\mathbf {Re}^-1$ for some universal $c_0 > 0$, the solution is global.

The normal matrix model with algebraic potential has gained a lot of attention recently, partially in virtue of its connection to several other topics as quadrature domains, inverse potential problems and the Laplacian growth. In this volume the authors consider the normal matrix model with cubic plus linear potential.

The authors develop a theory of $THH$ and $TC$ of Waldhausen categories and prove the analogues of Waldhausen's theorems for $K$-theory. They resolve the longstanding confusion about localization sequences in $THH$ and $TC$, and establish a specialized devissage theorem.

Two of the central concepts for the study of degree structures in computability theory are computably enumerable degrees and minimal degrees. This book considers how minimal weak truth table degrees interact with computably enumerable Turing degrees and obtain three main results.

The aim of this work is to adapt the complex analytic methods originating in modern Oka theory to the study of non-orientable conformal minimal surfaces in $\mathbb{R}^n$ for any $n\ge 3$.

Introduces and studies the bounded word problem and the precise word problem for groups given by means of generators and defining relations. The main technical result of the paper states that, for certain finite presentations of groups the bounded word problem and the precise word problem can be solved in polylogarithmic space.

Develops a decomposition theory for subgroups of $\mathsf{Out}(F_n)$ which generalizes the decomposition theory for individual elements of $\mathsf{Out}(F_n)$ found in the work of Bestvina, Feighn, and Handel, and which is analogous to the decomposition theory for subgroups of mapping class groups found in the work of Ivanov.

The author considers semilinear parabolic equations of the form $u_t=u_xx f(u),\quad x\in \mathbb R,t>0,$ where $f$ a $C^1$ function. Assuming that $0$ and $\gamma >0$ are constant steady states, the author investigates the large-time behavior of the front-like solutions.

In this paper, the authors prove global well-posedness of the massless Maxwell-Dirac equation in the Coulomb gauge on $\mathbb{R}^{1+d} (d\geq 4)$ for data with small scale-critical Sobolev norm, as well as modified scattering of the solutions.

Sets up a language to deal with Dirac operators on manifolds with corners of arbitrary co-dimension. This book develops a theory of boundary reductions, introducing the notion of a taming of a Dirac operator as an invertible perturbation by a smoothing operator.

Presents generalization of Szemeredi's Regularity Lemma to a certain hypergraph setting.

The main idea of this article is to carry out a Lubin-Tate generalization of the theory of cyclotomic $(\varphi,\Gamma )$-modules in a different fashion. Instead of the $p$-adic open unit disk, the authors work over a character variety that parameterizes the locally $L$-analytic characters on $o_L$.

Presents a detailed analysis of 2-complete stable homotopy groups, both in the classical context and in the motivic context over $\mathbb C$. The author uses the motivic May spectral sequence to compute the cohomology of the motivic Steenrod algebra over $\mathbb C$ through the 70-stem.

The authors construct cornered Floer homology invariants of 3-manifolds with codimension-2 corners and prove that the bordered Floer homology of a 3-manifold with boundary, split into two pieces with corners, can be recovered as a tensor product of the cornered invariants of the pieces.