Download or read book Spectral Invariants with Bulk Quasi Morphisms and Lagrangian Floer Theory written by Kenji Fukaya and published by American Mathematical Soc.. This book was released on 2019-09-05 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper the authors first develop 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. Essentially the same kind of construction is independently carried out by Usher in a slightly less general context. Then the authors explore various applications of these enhancements to the symplectic topology, especially new construction of symplectic quasi-states, quasi-morphisms and new Lagrangian intersection results on toric and non-toric manifolds. The most novel part of this paper is its use of open-closed Gromov-Witten-Floer theory and its variant involving closed orbits of periodic Hamiltonian system to connect spectral invariants (with bulk deformation), symplectic quasi-states, quasi-morphism to the Lagrangian Floer theory (with bulk deformation). The authors use this open-closed Gromov-Witten-Floer theory to produce new examples. Using the calculation of Lagrangian Floer cohomology with bulk, they produce examples of compact symplectic manifolds which admits uncountably many independent quasi-morphisms . They also obtain a new intersection result for the Lagrangian submanifold in .
Download or read book Lagrangian Floer Theory and Its Deformations written by Yong-Geun Oh and published by Springer Nature. This book was released on with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Cornered Heegaard Floer Homology written by Christopher L Douglas and published by American Mathematical Soc.. This book was released on 2020-02-13 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bordered Floer homology assigns invariants to 3-manifolds with boundary, such that the Heegaard Floer homology of a closed 3-manifold, split into two pieces, can be recovered as a tensor product of the bordered invariants of the pieces. 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.
Download or read book Quasi periodic Standing Wave Solutions of Gravity Capillary Water Waves written by Massimiliano Berti and published by American Mathematical Soc.. This book was released on 2020-04-03 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors prove the existence and the linear stability of small amplitude time quasi-periodic standing wave solutions (i.e. periodic and even in the space variable x) of a 2-dimensional ocean with infinite depth under the action of gravity and surface tension. Such an existence result is obtained for all the values of the surface tension belonging to a Borel set of asymptotically full Lebesgue measure.
Download or read book Degree Theory of Immersed Hypersurfaces written by Harold Rosenberg and published by American Mathematical Soc.. This book was released on 2020-09-28 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors develop a degree theory for compact immersed hypersurfaces of prescribed $K$-curvature immersed in a compact, orientable Riemannian manifold, where $K$ is any elliptic curvature function.
Download or read book The Mother Body Phase Transition in the Normal Matrix Model written by Pavel M. Bleher and published by American Mathematical Soc.. This book was released on 2020-09-28 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this present paper, the authors consider the normal matrix model with cubic plus linear potential.
Download or read book Affine Flag Varieties and Quantum Symmetric Pairs written by Zhaobing Fan and published by American Mathematical Soc.. This book was released on 2020-09-28 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: The quantum groups of finite and affine type $A$ admit geometric realizations in terms of partial flag varieties of finite and affine type $A$. Recently, the quantum group associated to partial flag varieties of finite type $B/C$ is shown to be a coideal subalgebra of the quantum group of finite type $A$.
Download or read book Minimal Weak Truth Table Degrees and Computably Enumerable Turing Degrees written by Rodney G. Downey and published by American Mathematical Soc.. This book was released on 2020-09-28 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: First, there are sets with minimal weak truth table degree which bound noncomputable computably enumerable sets under Turing reducibility. Second, no set with computable enumerable Turing degree can have minimal weak truth table degree. Third, no $Delta^0_2$ set which Turing bounds a promptly simple set can have minimal weak truth table degree.
Download or read book Localization for THH ku and the Topological Hochschild and Cyclic Homology of Waldhausen Categories written by Andrew J. Blumberg and published by American Mathematical Soc.. This book was released on 2020-09-28 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors resolve the longstanding confusion about localization sequences in $THH$ and $TC$ and establish a specialized devissage theorem.
Download or read book Rigid Character Groups Lubin Tate Theory and Modules written by Laurent Berger and published by American Mathematical Soc.. This book was released on 2020-04-03 with total page 75 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Compact Quotients of Cahen Wallach Spaces written by Ines Kath and published by American Mathematical Soc.. This book was released on 2020-02-13 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Local Relative Trace Formula for the Ginzburg Rallis Model The Geometric Side written by Chen Wan and published by American Mathematical Soc.. This book was released on 2019-12-02 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: Following the method developed by Waldspurger and Beuzart-Plessis in their proofs of the local Gan-Gross-Prasad conjecture, the author is able to prove the geometric side of a local relative trace formula for the Ginzburg-Rallis model. Then by applying such formula, the author proves a multiplicity formula of the Ginzburg-Rallis model for the supercuspidal representations. Using that multiplicity formula, the author proves the multiplicity one theorem for the Ginzburg-Rallis model over Vogan packets in the supercuspidal case.
Download or read book Time Like Graphical Models written by Tvrtko Tadić and published by American Mathematical Soc.. This book was released on 2019-12-02 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. The author extends the notion of time-like graphs and finds properties of processes indexed by them. In particular, the author solves the conjecture of uniqueness of the distribution for the process indexed by graphs with infinite number of vertices. The author provides a new result showing the stochastic heat equation as a limit of the sequence of natural Brownian motions on time-like graphs. In addition, the author's treatment of time-like graphical models reveals connections to Markov random fields, martingales indexed by directed sets and branching Markov processes.
Download or read book Quadratic Vector Equations on Complex Upper Half Plane written by Oskari Ajanki and published by American Mathematical Soc.. This book was released on 2019-12-02 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider the nonlinear equation −1m=z+Sm with a parameter z in the complex upper half plane H, where S is a positivity preserving symmetric linear operator acting on bounded functions. The solution with values in H is unique and its z-dependence is conveniently described as the Stieltjes transforms of a family of measures v on R. In a previous paper the authors qualitatively identified the possible singular behaviors of v: under suitable conditions on S we showed that in the density of v only algebraic singularities of degree two or three may occur. In this paper the authors give a comprehensive analysis of these singularities with uniform quantitative controls. They also find a universal shape describing the transition regime between the square root and cubic root singularities. Finally, motivated by random matrix applications in the authors' companion paper they present a complete stability analysis of the equation for any z∈H, including the vicinity of the singularities.
Download or read book Dimensions of Affine Deligne Lusztig Varieties A New Approach Via Labeled Folded Alcove Walks and Root Operators written by Elizabeth Milićević and published by American Mathematical Soc.. This book was released on 2019-12-02 with total page 101 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let G be a reductive group over the field F=k((t)), where k is an algebraic closure of a finite field, and let W be the (extended) affine Weyl group of G. The associated affine Deligne–Lusztig varieties Xx(b), which are indexed by elements b∈G(F) and x∈W, were introduced by Rapoport. Basic questions about the varieties Xx(b) which have remained largely open include when they are nonempty, and if nonempty, their dimension. The authors use techniques inspired by geometric group theory and combinatorial representation theory to address these questions in the case that b is a pure translation, and so prove much of a sharpened version of a conjecture of Görtz, Haines, Kottwitz, and Reuman. The authors' approach is constructive and type-free, sheds new light on the reasons for existing results in the case that b is basic, and reveals new patterns. Since they work only in the standard apartment of the building for G(F), their results also hold in the p-adic context, where they formulate a definition of the dimension of a p-adic Deligne–Lusztig set. The authors present two immediate applications of their main results, to class polynomials of affine Hecke algebras and to affine reflection length.
Download or read book Subgroup Decomposition in Out Fn written by Michael Handel and published by American Mathematical Soc.. This book was released on 2020-05-13 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Triangle Free Process and the Ramsey Number R 3 k written by Gonzalo Fiz Pontiveros and published by American Mathematical Soc.. This book was released on 2020-04-03 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
