Download or read book Intersection Cohomology Simplicial Blow Up and Rational Homotopy written by David Chataur and published by American Mathematical Soc.. This book was released on 2018-08-09 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let X be a pseudomanifold. In this text, the authors use a simplicial blow-up to define a cochain complex whose cohomology with coefficients in a field, is isomorphic to the intersection cohomology of X, introduced by M. Goresky and R. MacPherson. The authors do it simplicially in the setting of a filtered version of face sets, also called simplicial sets without degeneracies, in the sense of C. P. Rourke and B. J. Sanderson. They define perverse local systems over filtered face sets and intersection cohomology with coefficients in a perverse local system. In particular, as announced above when X is a pseudomanifold, the authors get a perverse local system of cochains quasi-isomorphic to the intersection cochains of Goresky and MacPherson, over a field. We show also that these two complexes of cochains are quasi-isomorphic to a filtered version of Sullivan's differential forms over the field Q. In a second step, they use these forms to extend Sullivan's presentation of rational homotopy type to intersection cohomology.

Download or read book Singular Intersection Homology written by Greg Friedman and published by Cambridge University Press. This book was released on 2020-09-24 with total page 824 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intersection homology is a version of homology theory that extends Poincaré duality and its applications to stratified spaces, such as singular varieties. This is the first comprehensive expository book-length introduction to intersection homology from the viewpoint of singular and piecewise-linear chains. Recent breakthroughs have made this approach viable by providing intersection homology and cohomology versions of all the standard tools in the homology tool box, making the subject readily accessible to graduate students and researchers in topology as well as researchers from other fields. This text includes both new research material and new proofs of previously-known results in intersection homology, as well as treatments of many classical topics in algebraic and manifold topology. Written in a detailed but expository style, this book is suitable as an introduction to intersection homology or as a thorough reference.

Download or read book Handbook of Geometry and Topology of Singularities II written by José Luis Cisneros-Molina and published by Springer Nature. This book was released on 2021-11-01 with total page 581 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second volume of the Handbook of the Geometry and Topology of Singularities, a series which aims to provide an accessible account of the state-of-the-art of the subject, its frontiers, and its interactions with other areas of research. This volume consists of ten chapters which provide an in-depth and reader-friendly survey of some of the foundational aspects of singularity theory and related topics. Singularities are ubiquitous in mathematics and science in general. Singularity theory interacts energetically with the rest of mathematics, acting as a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject, and in other subjects. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.

Download or read book An Alpine Bouquet of Algebraic Topology written by Jérôme Scherer and published by American Mathematical Soc.. This book was released on 2018-05-30 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Alpine Algebraic and Applied Topology Conference, held from August 15–21, 2016, in Saas-Almagell, Switzerland. The papers cover a broad range of topics in modern algebraic topology, including the theory of highly structured ring spectra, infinity-categories and Segal spaces, equivariant homotopy theory, algebraic -theory and topological cyclic, periodic, or Hochschild homology, intersection cohomology, and symplectic topology.

Download or read book Bellman Function for Extremal Problems in BMO II Evolution written by Paata Ivanisvili and published by American Mathematical Soc.. This book was released on 2018-10-03 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a previous study, the authors built the Bellman function for integral functionals on the space. The present paper provides a development of the subject. They abandon the majority of unwanted restrictions on the function that generates the functional. It is the new evolutional approach that allows the authors to treat the problem in its natural setting. What is more, these new considerations lighten dynamical aspects of the Bellman function, in particular, the evolution of its picture.

Download or read book On Mesoscopic Equilibrium for Linear Statistics in Dyson s Brownian Motion written by Maurice Duits and published by American Mathematical Soc.. This book was released on 2018-10-03 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper the authors study mesoscopic fluctuations for Dyson's Brownian motion with β=2 . Dyson showed that the Gaussian Unitary Ensemble (GUE) is the invariant measure for this stochastic evolution and conjectured that, when starting from a generic configuration of initial points, the time that is needed for the GUE statistics to become dominant depends on the scale we look at: The microscopic correlations arrive at the equilibrium regime sooner than the macrosopic correlations. The authors investigate the transition on the intermediate, i.e. mesoscopic, scales. The time scales that they consider are such that the system is already in microscopic equilibrium (sine-universality for the local correlations), but have not yet reached equilibrium at the macrosopic scale. The authors describe the transition to equilibrium on all mesoscopic scales by means of Central Limit Theorems for linear statistics with sufficiently smooth test functions. They consider two situations: deterministic initial points and randomly chosen initial points. In the random situation, they obtain a transition from the classical Central Limit Theorem for independent random variables to the one for the GUE.

Download or read book Strichartz Estimates and the Cauchy Problem for the Gravity Water Waves Equations written by T. Alazard and published by American Mathematical Soc.. This book was released on 2019-01-08 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: This memoir is devoted to the proof of a well-posedness result for the gravity water waves equations, in arbitrary dimension and in fluid domains with general bottoms, when the initial velocity field is not necessarily Lipschitz. Moreover, for two-dimensional waves, the authors consider solutions such that the curvature of the initial free surface does not belong to L2. The proof is entirely based on the Eulerian formulation of the water waves equations, using microlocal analysis to obtain sharp Sobolev and Hölder estimates. The authors first prove tame estimates in Sobolev spaces depending linearly on Hölder norms and then use the dispersive properties of the water-waves system, namely Strichartz estimates, to control these Hölder norms.

Download or read book Cluster Algebras and Triangulated Surfaces Part II Lambda Lengths written by Sergey Fomin and published by American Mathematical Soc.. This book was released on 2018-10-03 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: For any cluster algebra whose underlying combinatorial data can be encoded by a bordered surface with marked points, the authors construct a geometric realization in terms of suitable decorated Teichmüller space of the surface. On the geometric side, this requires opening the surface at each interior marked point into an additional geodesic boundary component. On the algebraic side, it relies on the notion of a non-normalized cluster algebra and the machinery of tropical lambda lengths. The authors' model allows for an arbitrary choice of coefficients which translates into a choice of a family of integral laminations on the surface. It provides an intrinsic interpretation of cluster variables as renormalized lambda lengths of arcs on the surface. Exchange relations are written in terms of the shear coordinates of the laminations and are interpreted as generalized Ptolemy relations for lambda lengths. This approach gives alternative proofs for the main structural results from the authors' previous paper, removing unnecessary assumptions on the surface.

Download or read book On the Geometric Side of the Arthur Trace Formula for the Symplectic Group of Rank 2 written by Werner Hoffmann and published by American Mathematical Soc.. This book was released on 2018-10-03 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors study 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 over any algebraic number field. In particular, they express the global coefficients of unipotent orbital integrals in terms of Dedekind zeta functions, Hecke -functions, and the Shintani zeta function for the space of binary quadratic forms.

Download or read book Global Regularity for 2D Water Waves with Surface Tension written by Alexandru D. Ionescu and published by American Mathematical Soc.. This book was released on 2019-01-08 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider the full irrotational water waves system with surface tension and no gravity in dimension two (the capillary waves system), and prove global regularity and modified scattering for suitably small and localized perturbations of a flat interface. An important point of the authors' analysis is to develop a sufficiently robust method (the “quasilinear I-method”) which allows the authors to deal with strong singularities arising from time resonances in the applications of the normal form method (the so-called “division problem”). As a result, they are able to consider a suitable class of perturbations with finite energy, but no other momentum conditions. Part of the authors' analysis relies on a new treatment of the Dirichlet-Neumann operator in dimension two which is of independent interest. As a consequence, the results in this paper are self-contained.

Download or read book Interpolation for Normal Bundles of General Curves written by Atanas Atanasov and published by American Mathematical Soc.. This book was released on 2019-02-21 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: Given n general points p1,p2,…,pn∈Pr, it is natural to ask when there exists a curve C⊂Pr, of degree d and genus g, passing through p1,p2,…,pn. In this paper, the authors give a complete answer to this question for curves C with nonspecial hyperplane section. This result is a consequence of our main theorem, which states that the normal bundle NC of a general nonspecial curve of degree d and genus g in Pr (with d≥g+r) has the property of interpolation (i.e. that for a general effective divisor D of any degree on C, either H0(NC(−D))=0 or H1(NC(−D))=0), with exactly three exceptions.

Download or read book Quiver Grassmannians of Extended Dynkin Type D Part I Schubert Systems and Decompositions into Affine Spaces written by Oliver Lorscheid and published by American Mathematical Soc.. This book was released on 2019-12-02 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let Q be a quiver of extended Dynkin type D˜n. In this first of two papers, the authors show that the quiver Grassmannian Gre–(M) has a decomposition into affine spaces for every dimension vector e– and every indecomposable representation M of defect −1 and defect 0, with the exception of the non-Schurian representations in homogeneous tubes. The authors characterize the affine spaces in terms of the combinatorics of a fixed coefficient quiver for M. The method of proof is to exhibit explicit equations for the Schubert cells of Gre–(M) and to solve this system of equations successively in linear terms. This leads to an intricate combinatorial problem, for whose solution the authors develop the theory of Schubert systems. In Part 2 of this pair of papers, they extend the result of this paper to all indecomposable representations M of Q and determine explicit formulae for the F-polynomial of M.

Download or read book Multilinear Singular Integral Forms of Christ Journ Type written by Andreas Seeger and published by American Mathematical Soc.. This book was released on 2019-02-21 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book An SO 3 Monopole Cobordism Formula Relating Donaldson and Seiberg Witten Invariants written by Paul Feehan and published by American Mathematical Soc.. This book was released on 2019-01-08 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors prove an analogue of the Kotschick–Morgan Conjecture in the context of monopoles, obtaining a formula relating the Donaldson and Seiberg–Witten invariants of smooth four-manifolds using the -monopole cobordism. The main technical difficulty in the -monopole program relating the Seiberg–Witten and Donaldson invariants has been to compute intersection pairings on links of strata of reducible monopoles, namely the moduli spaces of Seiberg–Witten monopoles lying in lower-level strata of the Uhlenbeck compactification of the moduli space of monopoles. In this monograph, the authors prove—modulo a gluing theorem which is an extension of their earlier work—that these intersection pairings can be expressed in terms of topological data and Seiberg–Witten invariants of the four-manifold. Their proofs that the -monopole cobordism yields both the Superconformal Simple Type Conjecture of Moore, Mariño, and Peradze and Witten's Conjecture in full generality for all closed, oriented, smooth four-manifolds with and odd appear in earlier works.

Download or read book Algebras of Singular Integral Operators with Kernels Controlled by Multiple Norms written by Alexander Nagel and published by American Mathematical Soc.. This book was released on 2019-01-08 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors study algebras of singular integral operators on R and nilpotent Lie groups that arise when considering the composition of Calderón-Zygmund operators with different homogeneities, such as operators occuring in sub-elliptic problems and those arising in elliptic problems. These algebras are characterized in a number of different but equivalent ways: in terms of kernel estimates and cancellation conditions, in terms of estimates of the symbol, and in terms of decompositions into dyadic sums of dilates of bump functions. The resulting operators are pseudo-local and bounded on for . . While the usual class of Calderón-Zygmund operators is invariant under a one-parameter family of dilations, the operators studied here fall outside this class, and reflect a multi-parameter structure.

Download or read book One Dimensional Empirical Measures Order Statistics and Kantorovich Transport Distances written by Sergey Bobkov and published by American Mathematical Soc.. This book was released on 2019-12-02 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is devoted to the study of rates of convergence of the empirical measures μn=1n∑nk=1δXk, n≥1, over a sample (Xk)k≥1 of independent identically distributed real-valued random variables towards the common distribution μ in Kantorovich transport distances Wp. The focus is on finite range bounds on the expected Kantorovich distances E(Wp(μn,μ)) or [E(Wpp(μn,μ))]1/p in terms of moments and analytic conditions on the measure μ and its distribution function. The study describes a variety of rates, from the standard one 1n√ to slower rates, and both lower and upper-bounds on E(Wp(μn,μ)) for fixed n in various instances. Order statistics, reduction to uniform samples and analysis of beta distributions, inverse distribution functions, log-concavity are main tools in the investigation. Two detailed appendices collect classical and some new facts on inverse distribution functions and beta distributions and their densities necessary to the investigation.

Download or read book Continuous Time Random Walks for the Numerical Solution of Stochastic Differential Equations written by Nawaf Bou-Rabee and published by American Mathematical Soc.. This book was released on 2019-01-08 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper introduces time-continuous numerical schemes to simulate stochastic differential equations (SDEs) arising in mathematical finance, population dynamics, chemical kinetics, epidemiology, biophysics, and polymeric fluids. These schemes are obtained by spatially discretizing the Kolmogorov equation associated with the SDE in such a way that the resulting semi-discrete equation generates a Markov jump process that can be realized exactly using a Monte Carlo method. In this construction the jump size of the approximation can be bounded uniformly in space, which often guarantees that the schemes are numerically stable for both finite and long time simulation of SDEs.