Quiver Grassmannians Of Extended Dynkin Type D Part I Schubert Systems And Decompositions Into Affine Spaces

Author : Oliver Lorscheid,Thorsten Weist
Publisher : American Mathematical Soc.
Page : 78 pages
File Size : 42,8 Mb
Release : 2019-12-02
Category : Education
ISBN : 9781470436476

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Quiver Grassmannians of Extended Dynkin Type D Part I: Schubert Systems and Decompositions into Affine Spaces by Oliver Lorscheid,Thorsten Weist Pdf

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.

Author : Oliver Lorscheid,Thorsten Weist
Publisher : Unknown
Page : 78 pages
File Size : 45,8 Mb
Release : 2019
Category : Electronic books
ISBN : 1470453991

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Quiver Grassmannians of Extended Dynkin Type D. by Oliver Lorscheid,Thorsten Weist Pdf

Let Q be a quiver of extended Dynkin type \widetildeD}_n. In this first of two papers, the authors show that the quiver Grassmannian \mathrmGr}_{underline{e}}(M) has a decomposition into affine spaces for every dimension vector underlinee} 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 \mathrmGr}_{underline{e}}(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.

Author : Jan Šťovíček,Jan Trlifaj
Publisher : American Mathematical Soc.
Page : 298 pages
File Size : 51,8 Mb
Release : 2020-11-13
Category : Education
ISBN : 9781470451318

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Representation Theory and Beyond by Jan Šťovíček,Jan Trlifaj Pdf

This volume contains the proceedings of the Workshop and 18th International Conference on Representations of Algebras (ICRA 2018) held from August 8–17, 2018, in Prague, Czech Republic. It presents several themes of contemporary representation theory together with some new tools, such as stable ∞ ∞-categories, stable derivators, and contramodules. In the first part, expanded lecture notes of four courses delivered at the workshop are presented, covering the representation theory of finite sets with correspondences, geometric theory of quiver Grassmannians, recent applications of contramodules to tilting theory, as well as symmetries in the representation theory over an abstract stable homotopy theory. The second part consists of six more-advanced papers based on plenary talks of the conference, presenting selected topics from contemporary representation theory: recollements and purity, maximal green sequences, cohomological Hall algebras, Hochschild cohomology of associative algebras, cohomology of local selfinjective algebras, and the higher Auslander–Reiten theory studied via homotopy theory.

Author : Michael Handel,Lee Mosher
Publisher : American Mathematical Soc.
Page : 276 pages
File Size : 50,6 Mb
Release : 2020-05-13
Category : Education
ISBN : 9781470441135

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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 : Oliver Lorscheid,Thorsten Weist
Publisher : Unknown
Page : 128 pages
File Size : 45,7 Mb
Release : 2019
Category : Electronic
ISBN : OCLC:1140664493

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Quiver Grassmannians of Extended Dynkin Type D by Oliver Lorscheid,Thorsten Weist Pdf

Author : Vasileios Chousionis,Jeremy T. Tyson,Mariusz Urbanski
Publisher : American Mathematical Soc.
Page : 153 pages
File Size : 45,8 Mb
Release : 2020-09-28
Category : Mathematics
ISBN : 9781470442156

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Conformal Graph Directed Markov Systems on Carnot Groups by Vasileios Chousionis,Jeremy T. Tyson,Mariusz Urbanski Pdf

The authors develop a comprehensive theory of conformal graph directed Markov systems in the non-Riemannian setting of Carnot groups equipped with a sub-Riemannian metric. In particular, they develop the thermodynamic formalism and show that, under natural hypotheses, the limit set of an Carnot conformal GDMS has Hausdorff dimension given by Bowen's parameter. They illustrate their results for a variety of examples of both linear and nonlinear iterated function systems and graph directed Markov systems in such sub-Riemannian spaces. These include the Heisenberg continued fractions introduced by Lukyanenko and Vandehey as well as Kleinian and Schottky groups associated to the non-real classical rank one hyperbolic spaces.

Author : Zhaobing Fan,Chun-Ju Lai,Yiqiang Li,Li Luo,Weiqiang Wang
Publisher : American Mathematical Soc.
Page : 123 pages
File Size : 46,9 Mb
Release : 2020-09-28
Category : Mathematics
ISBN : 9781470441753

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Affine Flag Varieties and Quantum Symmetric Pairs by Zhaobing Fan,Chun-Ju Lai,Yiqiang Li,Li Luo,Weiqiang Wang Pdf

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 $A$.

Author : Luigi Ambrosio,Andrea Mondino,Giuseppe Savaré
Publisher : American Mathematical Soc.
Page : 121 pages
File Size : 50,6 Mb
Release : 2020-02-13
Category : Education
ISBN : 9781470439132

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Nonlinear Diffusion Equations and Curvature Conditions in Metric Measure Spaces by Luigi Ambrosio,Andrea Mondino,Giuseppe Savaré Pdf

The aim of this paper is to provide new characterizations of the curvature dimension condition in the context of metric measure spaces (X,d,m). On the geometric side, the authors' new approach takes into account suitable weighted action functionals which provide the natural modulus of K-convexity when one investigates the convexity properties of N-dimensional entropies. On the side of diffusion semigroups and evolution variational inequalities, the authors' new approach uses the nonlinear diffusion semigroup induced by the N-dimensional entropy, in place of the heat flow. Under suitable assumptions (most notably the quadraticity of Cheeger's energy relative to the metric measure structure) both approaches are shown to be equivalent to the strong CD∗(K,N) condition of Bacher-Sturm.

Author : Antonio Alarcón,Franc Forstnerič,Francisco J. López
Publisher : American Mathematical Soc.
Page : 77 pages
File Size : 54,5 Mb
Release : 2020-05-13
Category : Education
ISBN : 9781470441616

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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 : 54,9 Mb
Release : 2020-04-03
Category : Education
ISBN : 9781470440374

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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 : Angel Castro,Diego Cordoba,Javier Gomez-Serrano
Publisher : American Mathematical Soc.
Page : 89 pages
File Size : 44,5 Mb
Release : 2020-09-28
Category : Mathematics
ISBN : 9781470442149

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Global Smooth Solutions for the Inviscid SQG Equation by Angel Castro,Diego Cordoba,Javier Gomez-Serrano Pdf

In this paper, the authors show the existence of the first non trivial family of classical global solutions of the inviscid surface quasi-geostrophic equation.

Author : Jacob Bedrossian,Pierre Germain,Nader Masmoudi
Publisher : American Mathematical Soc.
Page : 154 pages
File Size : 40,7 Mb
Release : 2020-09-28
Category : Mathematics
ISBN : 9781470442170

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Dynamics Near the Subcritical Transition of the 3D Couette Flow I: Below Threshold Case by Jacob Bedrossian,Pierre Germain,Nader Masmoudi Pdf

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 $epsilon leq c_0mathbf {Re}^-1$ for some universal $c_0 > 0$, the solution is global, remains within $O(c_0)$ of the Couette flow in $L^2$, and returns to the Couette flow as $t rightarrow infty $. For times $t gtrsim mathbf {Re}^1/3$, the streamwise dependence is damped by a mixing-enhanced dissipation effect and the solution is rapidly attracted to the class of ``2.5 dimensional'' streamwise-independent solutions referred to as streaks.

Author : Benjamin Jaye,Fedor Nazarov,Maria Carmen Reguera,Xavier Tolsa
Publisher : American Mathematical Soc.
Page : 97 pages
File Size : 46,8 Mb
Release : 2020-09-28
Category : Mathematics
ISBN : 9781470442132

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The Riesz Transform of Codimension Smaller Than One and the Wolff Energy by Benjamin Jaye,Fedor Nazarov,Maria Carmen Reguera,Xavier Tolsa Pdf

Fix $dgeq 2$, and $sin (d-1,d)$. The authors characterize the non-negative locally finite non-atomic Borel measures $mu $ in $mathbb R^d$ for which the associated $s$-Riesz transform is bounded in $L^2(mu )$ in terms of the Wolff energy. This extends the range of $s$ in which the Mateu-Prat-Verdera characterization of measures with bounded $s$-Riesz transform is known. As an application, the authors give a metric characterization of the removable sets for locally Lipschitz continuous solutions of the fractional Laplacian operator $(-Delta )^alpha /2$, $alpha in (1,2)$, in terms of a well-known capacity from non-linear potential theory. This result contrasts sharply with removability results for Lipschitz harmonic functions.

Author : Lisa Berger,Chris Hall,Rene Pannekoek,Rachel Pries,Shahed Sharif
Publisher : American Mathematical Soc.
Page : 131 pages
File Size : 53,9 Mb
Release : 2020-09-28
Category : Mathematics
ISBN : 9781470442194

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Explicit Arithmetic of Jacobians of Generalized Legendre Curves Over Global Function Fields by Lisa Berger,Chris Hall,Rene Pannekoek,Rachel Pries,Shahed Sharif Pdf

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 $rge 2$ is an integer prime to $p$. When $q$ is a power of $p$ and $d$ is a positive integer, the authors compute the $L$-function of $J$ over $mathbb F_q(t^1/d)$ and show that the Birch and Swinnerton-Dyer conjecture holds for $J$ over $mathbb F_q(t^1/d)$.

Author : Christophe Cornut
Publisher : American Mathematical Soc.
Page : 150 pages
File Size : 43,9 Mb
Release : 2020-09-28
Category : Mathematics
ISBN : 9781470442217

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Filtrations and Buildings by Christophe Cornut Pdf

The author constructs and studies a scheme theoretical version of the Tits vectorial building, relates it to filtrations on fiber functors, and uses them to clarify various constructions pertaining to affine Bruhat-Tits buildings, for which he also provides a Tannakian description.