Automorphisms Oftwo Generator Free Groups And Spaces Of Isometric Actions On The Hyperbolic Plane

Author : William Goldman,Greg McShane,George Stantchev,Ser Peow Tan
Publisher : American Mathematical Soc.
Page : 78 pages
File Size : 48,8 Mb
Release : 2019-06-10
Category : Automorphisms
ISBN : 9781470436148

Get Book

Automorphisms ofTwo-Generator Free Groups and Spaces of Isometric Actions on the Hyperbolic Plane by William Goldman,Greg McShane,George Stantchev,Ser Peow Tan Pdf

The automorphisms of a two-generator free group F acting on the space of orientation-preserving isometric actions of F on hyperbolic 3-space defines a dynamical system. Those actions which preserve a hyperbolic plane but not an orientation on that plane is an invariant subsystem, which reduces to an action of a group on by polynomial automorphisms preserving the cubic polynomial and an area form on the level surfaces .

Author : Jørgen Ellegaard Andersen,Andrew Dancer,Oscar García-Prada
Publisher : Oxford University Press
Page : 400 pages
File Size : 50,7 Mb
Release : 2018-10-18
Category : Mathematics
ISBN : 9780192522375

Get Book

Geometry and Physics: Volume 2 by Jørgen Ellegaard Andersen,Andrew Dancer,Oscar García-Prada Pdf

Nigel Hitchin is one of the world's foremost figures in the fields of differential and algebraic geometry and their relations with mathematical physics, and he has been Savilian Professor of Geometry at Oxford since 1997. Geometry and Physics: A Festschrift in honour of Nigel Hitchin contain the proceedings of the conferences held in September 2016 in Aarhus, Oxford, and Madrid to mark Nigel Hitchin's 70th birthday, and to honour his far-reaching contributions to geometry and mathematical physics. These texts contain 29 articles by contributors to the conference and other distinguished mathematicians working in related areas, including three Fields Medallists. The articles cover a broad range of topics in differential, algebraic and symplectic geometry, and also in mathematical physics. These volumes will be of interest to researchers and graduate students in geometry and mathematical physics.

Author : Jørgen Ellegaard Andersen,Andrew Dancer,Oscar García-Prada
Publisher : Oxford University Press, USA
Page : 347 pages
File Size : 45,6 Mb
Release : 2018
Category : Mathematics
ISBN : 9780198802020

Get Book

Geometry and Physics by Jørgen Ellegaard Andersen,Andrew Dancer,Oscar García-Prada Pdf

Nigel Hitchin is one of the world's foremost figures in the fields of differential and algebraic geometry and their relations with mathematical physics, and he has been Savilian Professor of Geometry at Oxford since 1997. Geometry and Physics: A Festschrift in honour of Nigel Hitchin contain the proceedings of the conferences held in September 2016 in Aarhus, Oxford, and Madrid to mark Nigel Hitchin's 70th birthday, and to honour his far-reaching contributions to geometry and mathematical physics. These texts contain 29 articles by contributors to the conference and other distinguished mathematicians working in related areas, including three Fields Medallists. The articles cover a broad range of topics in differential, algebraic and symplectic geometry, and also in mathematical physics. These volumes will be of interest to researchers and graduate students in geometry and mathematical physics.

Author : Gonzalo Fiz Pontiveros,Simon Griffiths,Robert Morris
Publisher : American Mathematical Soc.
Page : 125 pages
File Size : 40,5 Mb
Release : 2020-04-03
Category : Education
ISBN : 9781470440718

Get Book

The Triangle-Free Process and the Ramsey Number R(3,k) by Gonzalo Fiz Pontiveros,Simon Griffiths,Robert Morris Pdf

The areas of Ramsey theory and random graphs have been closely linked ever since Erdős's famous proof in 1947 that the “diagonal” Ramsey numbers R(k) grow exponentially in k. In the early 1990s, the triangle-free process was introduced as a model which might potentially provide good lower bounds for the “off-diagonal” Ramsey numbers R(3,k). In this model, edges of Kn are introduced one-by-one at random and added to the graph if they do not create a triangle; the resulting final (random) graph is denoted Gn,△. In 2009, Bohman succeeded in following this process for a positive fraction of its duration, and thus obtained a second proof of Kim's celebrated result that R(3,k)=Θ(k2/logk). In this paper the authors improve the results of both Bohman and Kim and follow the triangle-free process all the way to its asymptotic end.

Author : S. V. Ivanov
Publisher : American Mathematical Soc.
Page : 106 pages
File Size : 51,9 Mb
Release : 2020-05-13
Category : Education
ISBN : 9781470441432

Get Book

The Bounded and Precise Word Problems for Presentations of Groups by S. V. Ivanov Pdf

The author introduces and studies the bounded word problem and the precise word problem for groups given by means of generators and defining relations. For example, for every finitely presented group, the bounded word problem is in NP, i.e., it can be solved in nondeterministic polynomial time, and the precise word problem is in PSPACE, i.e., it can be solved in polynomial space. The main technical result of the paper states that, for certain finite presentations of groups, which include the Baumslag-Solitar one-relator groups and free products of cyclic groups, the bounded word problem and the precise word problem can be solved in polylogarithmic space. As consequences of developed techniques that can be described as calculus of brackets, the author obtains polylogarithmic space bounds for the computational complexity of the diagram problem for free groups, for the width problem for elements of free groups, and for computation of the area defined by polygonal singular closed curves in the plane. The author also obtains polynomial time bounds for these problems.

Author : Laurent Berger,Peter Schneider,Bingyong Xie
Publisher : American Mathematical Soc.
Page : 75 pages
File Size : 55,8 Mb
Release : 2020-04-03
Category : Education
ISBN : 9781470440732

Get Book

Rigid Character Groups, Lubin-Tate Theory, and (φ,Γ)-Modules by Laurent Berger,Peter Schneider,Bingyong Xie Pdf

The construction of the p-adic local Langlands correspondence for GL2(Qp) uses in an essential way Fontaine's theory of cyclotomic (φ,Γ)-modules. Here cyclotomic means that Γ=Gal(Qp(μp∞)/Qp) is the Galois group of the cyclotomic extension of Qp. In order to generalize the p-adic local Langlands correspondence to GL2(L), where L is a finite extension of Qp, it seems necessary to have at our disposal a theory of Lubin-Tate (φ,Γ)-modules. Such a generalization has been carried out, to some extent, by working over the p-adic open unit disk, endowed with the action of the endomorphisms of a Lubin-Tate group. The main idea of this article is to carry out a Lubin-Tate generalization of the theory of cyclotomic (φ,Γ)-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 oL. They study (φ,Γ)-modules in this setting and relate some of them to what was known previously.

Author : Michael Handel,Lee Mosher
Publisher : American Mathematical Soc.
Page : 276 pages
File Size : 45,8 Mb
Release : 2020-05-13
Category : Education
ISBN : 9781470441135

Get Book

Subgroup Decomposition in Out(Fn) by Michael Handel,Lee Mosher Pdf

In this work the authors develop a decomposition theory for subgroups of Out(Fn) which generalizes the decomposition theory for individual elements of Out(Fn) 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.

Author : Cristian Gavrus,Sung-Jin Oh
Publisher : American Mathematical Soc.
Page : 94 pages
File Size : 51,5 Mb
Release : 2020-05-13
Category : Education
ISBN : 9781470441111

Get Book

Global Well-Posedness of High Dimensional Maxwell–Dirac for Small Critical Data by Cristian Gavrus,Sung-Jin Oh Pdf

In this paper, the authors prove global well-posedness of the massless Maxwell–Dirac equation in the Coulomb gauge on R1+d(d≥4) for data with small scale-critical Sobolev norm, as well as modified scattering of the solutions. Main components of the authors' proof are A) uncovering null structure of Maxwell–Dirac in the Coulomb gauge, and B) proving solvability of the underlying covariant Dirac equation. A key step for achieving both is to exploit (and justify) a deep analogy between Maxwell–Dirac and Maxwell-Klein-Gordon (for which an analogous result was proved earlier by Krieger-Sterbenz-Tataru, which says that the most difficult part of Maxwell–Dirac takes essentially the same form as Maxwell-Klein-Gordon.

Author : Jaroslav Nešetřil,Patrice Ossona de Mendez
Publisher : American Mathematical Soc.
Page : 108 pages
File Size : 52,5 Mb
Release : 2020-04-03
Category : Education
ISBN : 9781470440657

Get Book

A Unified Approach to Structural Limits and Limits of Graphs with Bounded Tree-Depth by Jaroslav Nešetřil,Patrice Ossona de Mendez Pdf

In this paper the authors introduce a general framework for the study of limits of relational structures and graphs in particular, which is based on a combination of model theory and (functional) analysis. The authors show how the various approaches to graph limits fit to this framework and that the authors naturally appear as “tractable cases” of a general theory. As an outcome of this, the authors provide extensions of known results. The authors believe that this puts these into a broader context. The second part of the paper is devoted to the study of sparse structures. First, the authors consider limits of structures with bounded diameter connected components and prove that in this case the convergence can be “almost” studied component-wise. They also propose the structure of limit objects for convergent sequences of sparse structures. Eventually, they consider the specific case of limits of colored rooted trees with bounded height and of graphs with bounded tree-depth, motivated by their role as “elementary bricks” these graphs play in decompositions of sparse graphs, and give an explicit construction of a limit object in this case. This limit object is a graph built on a standard probability space with the property that every first-order definable set of tuples is measurable. This is an example of the general concept of modeling the authors introduce here. Their example is also the first “intermediate class” with explicitly defined limit structures where the inverse problem has been solved.

Author : Victor Beresnevich,Alan Haynes,Sanju Velani
Publisher : American Mathematical Soc.
Page : 77 pages
File Size : 51,6 Mb
Release : 2020-04-03
Category : Education
ISBN : 9781470440954

Get Book

Sums of Reciprocals of Fractional Parts and Multiplicative Diophantine Approximation by Victor Beresnevich,Alan Haynes,Sanju Velani Pdf

Author : Antonio Alarcón,Franc Forstnerič,Francisco J. López
Publisher : American Mathematical Soc.
Page : 77 pages
File Size : 54,7 Mb
Release : 2020-05-13
Category : Education
ISBN : 9781470441616

Get Book

New Complex Analytic Methods in the Study of Non-Orientable Minimal Surfaces in Rn by Antonio Alarcón,Franc Forstnerič,Francisco J. López Pdf

All the new tools mentioned above apply to non-orientable minimal surfaces endowed with a fixed choice of a conformal structure. This enables the authors to obtain significant new applications to the global theory of non-orientable minimal surfaces. In particular, they construct proper non-orientable conformal minimal surfaces in Rn with any given conformal structure, complete non-orientable minimal surfaces in Rn with arbitrary conformal type whose generalized Gauss map is nondegenerate and omits n hyperplanes of CPn−1 in general position, complete non-orientable minimal surfaces bounded by Jordan curves, and complete proper non-orientable minimal surfaces normalized by bordered surfaces in p-convex domains of Rn.

Author : Jean-François Coulombel,Mark Williams
Publisher : American Mathematical Soc.
Page : 143 pages
File Size : 53,6 Mb
Release : 2020-04-03
Category : Education
ISBN : 9781470440374

Get Book

Geometric Optics for Surface Waves in Nonlinear Elasticity by Jean-François Coulombel,Mark Williams Pdf

This work is devoted to the analysis of high frequency solutions to the equations of nonlinear elasticity in a half-space. The authors consider surface waves (or more precisely, Rayleigh waves) arising in the general class of isotropic hyperelastic models, which includes in particular the Saint Venant-Kirchhoff system. Work has been done by a number of authors since the 1980s on the formulation and well-posedness of a nonlinear evolution equation whose (exact) solution gives the leading term of an approximate Rayleigh wave solution to the underlying elasticity equations. This evolution equation, which is referred to as “the amplitude equation”, is an integrodifferential equation of nonlocal Burgers type. The authors begin by reviewing and providing some extensions of the theory of the amplitude equation. The remainder of the paper is devoted to a rigorous proof in 2D that exact, highly oscillatory, Rayleigh wave solutions uε to the nonlinear elasticity equations exist on a fixed time interval independent of the wavelength ε, and that the approximate Rayleigh wave solution provided by the analysis of the amplitude equation is indeed close in a precise sense to uε on a time interval independent of ε. This paper focuses mainly on the case of Rayleigh waves that are pulses, which have profiles with continuous Fourier spectrum, but the authors' method applies equally well to the case of wavetrains, whose Fourier spectrum is discrete.

Author : Peter Poláčik
Publisher : American Mathematical Soc.
Page : 87 pages
File Size : 52,5 Mb
Release : 2020-05-13
Category : Education
ISBN : 9781470441128

Get Book

Propagating Terraces and the Dynamics of Front-Like Solutions of Reaction-Diffusion Equations on R by Peter Poláčik Pdf

The author considers semilinear parabolic equations of the form ut=uxx+f(u),x∈R,t>0, where f a C1 function. Assuming that 0 and γ>0 are constant steady states, the author investigates the large-time behavior of the front-like solutions, that is, solutions u whose initial values u(x,0) are near γ for x≈−∞ and near 0 for x≈∞. If the steady states 0 and γ are both stable, the main theorem shows that at large times, the graph of u(⋅,t) is arbitrarily close to a propagating terrace (a system of stacked traveling fonts). The author proves this result without requiring monotonicity of u(⋅,0) or the nondegeneracy of zeros of f. The case when one or both of the steady states 0, γ is unstable is considered as well. As a corollary to the author's theorems, he shows that all front-like solutions are quasiconvergent: their ω-limit sets with respect to the locally uniform convergence consist of steady states. In the author's proofs he employs phase plane analysis, intersection comparison (or, zero number) arguments, and a geometric method involving the spatial trajectories {(u(x,t),ux(x,t)):x∈R}, t>0, of the solutions in question.

Author : David Carchedi
Publisher : American Mathematical Soc.
Page : 120 pages
File Size : 47,5 Mb
Release : 2020
Category : Education
ISBN : 9781470441449

Get Book

Higher Orbifolds and Deligne-Mumford Stacks as Structured Infinity-Topoi by David Carchedi Pdf

The author develops a universal framework to study smooth higher orbifolds on the one hand and higher Deligne-Mumford stacks (as well as their derived and spectral variants) on the other, and use this framework to obtain a completely categorical description of which stacks arise as the functor of points of such objects. He chooses to model higher orbifolds and Deligne-Mumford stacks as infinity-topoi equipped with a structure sheaf, thus naturally generalizing the work of Lurie, but his approach applies not only to different settings of algebraic geometry such as classical algebraic geometry, derived algebraic geometry, and the algebraic geometry of commutative ring spectra but also to differential topology, complex geometry, the theory of supermanifolds, derived manifolds etc., where it produces a theory of higher generalized orbifolds appropriate for these settings. This universal framework yields new insights into the general theory of Deligne-Mumford stacks and orbifolds, including a representability criterion which gives a categorical characterization of such generalized Deligne-Mumford stacks. This specializes to a new categorical description of classical Deligne-Mumford stacks, which extends to derived and spectral Deligne-Mumford stacks as well.

Author : Henri Lombardi,Daniel Perrucci,Marie-Françoise Roy
Publisher : American Mathematical Soc.
Page : 113 pages
File Size : 41,7 Mb
Release : 2020-04-03
Category : Education
ISBN : 9781470441081

Get Book

An Elementary Recursive Bound for Effective Positivstellensatz and Hilbert’s 17th Problem by Henri Lombardi,Daniel Perrucci,Marie-Françoise Roy Pdf

The authors prove an elementary recursive bound on the degrees for Hilbert's 17th problem. More precisely they express a nonnegative polynomial as a sum of squares of rational functions and obtain as degree estimates for the numerators and denominators the following tower of five exponentials 222d4k where d is the number of variables of the input polynomial. The authors' method is based on the proof of an elementary recursive bound on the degrees for Stengle's Positivstellensatz. More precisely the authors give an algebraic certificate of the emptyness of the realization of a system of sign conditions and obtain as degree bounds for this certificate a tower of five exponentials, namely 22(2max{2,d}4k+s2kmax{2,d}16kbit(d)) where d is a bound on the degrees, s is the number of polynomials and k is the number of variables of the input polynomials.