Böcker i Memoirs of the American Mathematical Society-serien

Indecomposable symmetric Lorentzian manifolds of non-constant curvature are called Cahen-Wallach spaces. Their isometry classes are described by continuous families of real parameters. The authors derive necessary and sufficient conditions for the existence of compact quotients of Cahen-Wallach spaces in terms of these parameters.

Provides new characterizations of the curvature dimension condition in the context of metric measure spaces $(X,\mathsf d,\mathfrak m)$. The authors' approach takes into account suitable weighted action functionals, and uses the nonlinear diffusion semigroup induced by the $N$-dimensional entropy, in place of the heat flow

Uses methods from birational geometry to study the Hodge filtration on the localization along a hypersurface. This filtration leads to a sequence of ideal sheaves, called Hodge ideals, the first of which is a multiplier ideal.

For a finite group $G$ of Lie type and a prime $p$, the authors compare the automorphism groups of the fusion and linking systems of $G$ at $p$ with the automorphism group of $G$ itself. When $p$ is the defining characteristic of $G$, they are all isomorphic, with a very short list of exceptions.

The author studies continuous processes indexed by a special family of graphs. Processes indexed by vertices of graphs are known as probabilistic graphical models. In 2011, Burdzy and Pal proposed a continuous version of graphical models indexed by graphs with an embedded time structure - so-called time-like graphs.

Considers the nonlinear equation $-\frac 1m=z+Sm$ with a parameter $z$ in the complex upper half plane $\mathbb H $, where $S$ is a positivity preserving symmetric linear operator acting on bounded functions.

The authors consider the energy super critical semilinear heat equation $\partial _{t}u=\Delta u u^{p}, x\in \mathbb{R}^3, p>5.$. The authors draws a route map for the derivation of the existence and stability of self-similar blow up in nonradial energy super critical settings.

Develops various enhancements of the theory of spectral invariants of Hamiltonian Floer homology and of Entov-Polterovich theory of spectral symplectic quasi-states and quasi-morphisms by incorporating bulk deformations - i.e. deformations by ambient cycles of symplectic manifolds, of the Floer homology and quantum cohomology.

Causal fermion systems and Riemannian fermion systems are proposed as a framework for describing non-smooth geometries. In particular, this framework provides a setting for spinors on singular spaces. The underlying topological structures are introduced and analysed. The connection to the spin condition in differential topology is worked out.

The automorphisms of a two-generator free group $\mathsf F_2$ acting on the space of orientation-preserving isometric actions of $\mathsf F_2$ on hyperbolic 3-space defines a dynamical system.

Studies high energy resonances for the operators $-\Delta_{\partial\Omega,\delta}:=-\Delta \delta_{\partial\Omega}\otimes V\quad \textrm{and}\quad -\Delta_{\partial\Omega,\delta'}:=-\Delta \delta_{\partial\Omega}'\otimes V\partial_\nu$ where $\Omega\subset{\mathbb{R}}^{d}$ is strictly convex with smooth boundary.

This paper is an interval dynamics counterpart of three theories founded earlier by the authors in the setting of the iteration of rational maps on the Riemann sphere: the equivalence of several notions of non-uniform hyperbolicity, Geometric Pressure, and Nice Inducing Schemes methods leading to results in thermodynamical formalism.

Examines the moduli space of trace-free irreducible rank 2 connections over a curve of genus 2 and the forgetful map towards the moduli space of underlying vector bundles (including unstable bundles), for which they compute a natural Lagrangian rational section.

A Moufang set is essentially a doubly transitive permutation group such that each point stabilizer contains a normal subgroup which is regular on the remaining vertices; these regular normal subgroups are called the root groups, and they are assumed to be conjugate and to generate the whole group.

Presents a constant rank theorem for the second fundamental form of the space-time level sets of a space-time quasiconcave solution of the heat equation. Utilizing this constant rank theorem, the authors obtain some results of the spatial and space-time level sets of the space-time quasiconcave solution of the heat equation in a convex ring.

Examines constructions of reproducing kernel Banach spaces (RKBSs) which may be viewed as a generalization of reproducing kernel Hilbert spaces (RKHSs). A key point is to endow Banach spaces with reproducing kernels such that machine learning in RKBSs can be well-posed and of easy implementation.

These notes explore Galois-theoretic, automorphic, and motivic analogues and refinements of Tate's basic result that continuous projective representations $\mathrm{Gal}(\overline{F}/F) \to \mathrm{PGL}_n(\mathbb{C})$ lift to $\mathrm{GL}_n(\mathbb{C})$.

Provides a contribution to the "quantitative Hamiltonian perturbation theory" initiated in previous works on the optimality of long term stability estimates and diffusion times. The emphasis here is on discrete systems because this is the natural setting to study wandering domains.

Introduces the concept of finitely coloured equivalence for unital $^*$-homomorphisms between $\mathrm C^*$-algebras, for which unitary equivalence is the $1$-coloured case.

Given $n$ general points $p_1, p_2, \ldots, p_n \in \mathbb P^r$, it is natural to ask when there exists a curve $C \subset \mathbb P^r$, of degree $d$ and genus $g$, passing through $p_1, p_2, \ldots, p_n$. In this paper, the authors give a complete answer to this question for curves $C$ with nonspecial hyperplane section.

This memoir begins a program to classify a large subclass of the class of simple saturated 2-fusion systems of component type. Such a classification would be of great interest in its own right, but in addition it should lead to a significant simplification of the proof of the theorem classifying the finite simple groups.

The authors study algebras of singular integral operators on $\mathbb R^n$ and nilpotent Lie groups that arise when considering the composition of Calderon-Zygmund operators with different homogeneities, such as operators occuring in sub-elliptic problems and those arising in elliptic problems.

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.