scholarly journals Quiver Yangian from crystal melting

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Wei Li ◽  
Masahito Yamazaki
Keyword(s):  
Fixed Points ◽  
Moduli Spaces ◽  
Infinite Class ◽  
Infinite Dimensional ◽  
Crystal Melting ◽  
Bps States

Abstract We find a new infinite class of infinite-dimensional algebras acting on BPS states for non-compact toric Calabi-Yau threefolds. In Type IIA superstring compactification on a toric Calabi-Yau threefold, the D-branes wrapping holomorphic cycles represent the BPS states, and the fixed points of the moduli spaces of BPS states are described by statistical configurations of crystal melting. Our algebras are “bootstrapped” from the molten crystal configurations, hence they act on the BPS states. We discuss the truncation of the algebra and its relation with D4-branes. We illustrate our results in many examples, with and without compact 4-cycles.

A modified Krasnosellkii-Mann algorithms for computing fixed points of multivalued quasi-nonexpansive mappings in Banach spaces

2019 ◽  
Vol 28 (2) ◽  
pp. 191-198
Author(s):  
T. M. M. SOW
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Mann Iteration ◽  
Infinite Dimensional ◽  
Mann Algorithm

It is well known that Krasnoselskii-Mann iteration of nonexpansive mappings find application in many areas of mathematics and know to be weakly convergent in the infinite dimensional setting. In this paper, we introduce and study an explicit iterative scheme by a modified Krasnoselskii-Mann algorithm for approximating fixed points of multivalued quasi-nonexpansive mappings in Banach spaces. Strong convergence of the sequence generated by this algorithm is established. There is no compactness assumption. The results obtained in this paper are significant improvement on important recent results.

scholarly journals On groups whose actions on finite-dimensional CAT(0) spaces have global fixed points

2019 ◽  
Vol 22 (6) ◽  
pp. 1089-1099
Author(s):  
Motoko Kato
Keyword(s):  
Fixed Points ◽  
Topological Dimension ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Thompson’S Group ◽  
Simple Action ◽  
Cube Complexes

Abstract We give a criterion for group elements to have fixed points with respect to a semi-simple action on a complete CAT(0) space of finite topological dimension. As an application, we show that Thompson’s group T and various generalizations of Thompson’s group V have global fixed points when they act semi-simply on finite-dimensional complete CAT(0) spaces, while it is known that T and V act properly on infinite-dimensional CAT(0) cube complexes.

INFINITE DIMENSIONAL KRAWCZYK OPERATOR FOR FINDING PERIODIC ORBITS OF DISCRETE DYNAMICAL SYSTEMS

2007 ◽  
Vol 17 (12) ◽  
pp. 4261-4272 ◽  
Author(s):  
ZBIGNIEW GALIAS ◽  
PIOTR ZGLICZYŃSKI
Keyword(s):  
Dynamical Systems ◽  
Fixed Points ◽  
Periodic Orbits ◽  
Discrete Dynamical Systems ◽  
Krawczyk Operator ◽  
Infinite Dimensional ◽  
Dispersal Model ◽  
Period 2 ◽  
Existence Of Zeros

In this work, we introduce the Krawczyk operator for infinite dimensional maps. We prove two properties of this operator related to the existence of zeros of the map. We also show how the Krawczyk operator can be used to prove the existence of periodic orbits of infinite dimensional discrete dynamical systems and for finding all periodic orbits with a given period enclosed in a specified region. As an example, we consider the Kot–Schaffer growth-dispersal model, for which we find all fixed points and period-2 orbits enclosed in the region containing the attractor observed numerically.

Moduli of wild Higgs bundles on with -actions

2021 ◽  
pp. 1-34
Author(s):  
LAURA FREDRICKSON ◽  
ANDREW NEITZKE
Keyword(s):  
Fixed Points ◽  
Moduli Spaces ◽  
Vector Bundles ◽  
Central Charge ◽  
Higgs Field ◽  
Vertex Algebra ◽  
Higgs Bundles ◽  
Irregular Singularity ◽  
Isomorphism Classes ◽  
Type Decomposition

Abstract We study a set $\mathcal{M}_{K,N}$ parameterising filtered SL(K)-Higgs bundles over $\mathbb{C}P^1$ with an irregular singularity at $z = \infty$ , such that the eigenvalues of the Higgs field grow like $\vert \lambda \vert \sim \vert z^{N/K} \mathrm{d}z \vert$ , where K and N are coprime. $\mathcal{M}_{K,N}$ carries a $\mathbb{C}^\times$ -action analogous to the famous $\mathbb{C}^\times$ -action introduced by Hitchin on the moduli spaces of Higgs bundles over compact curves. The construction of this $\mathbb{C}^\times$ -action on $\mathcal{M}_{K,N}$ involves the rotation automorphism of the base $\mathbb{C}P^1$ . We classify the fixed points of this $\mathbb{C}^\times$ -action, and exhibit a curious 1-1 correspondence between these fixed points and certain representations of the vertex algebra $\mathcal{W}_K$ ; in particular we have the relation $\mu = {k-1-c_{\mathrm{eff}}}/{12}$ , where $\mu$ is a regulated version of the L 2 norm of the Higgs field, and $c_{\mathrm{eff}}$ is the effective Virasoro central charge of the corresponding W-algebra representation. We also discuss a Białynicki–Birula-type decomposition of $\mathcal{M}_{K,N}$ , where the strata are labeled by isomorphism classes of the underlying filtered vector bundles.

scholarly journals Convergence Theorems for Accretive Operators with Nonlinear Mappings in Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Yan-Lai Song ◽  
Lu-Chuan Ceng
Keyword(s):  
Fixed Points ◽  
Banach Spaces ◽  
Equilibrium Problems ◽  
Recent Literature ◽  
Common Element ◽  
Inclusion Problem ◽  
Accretive Operators ◽  
Convergence Theorems ◽  
Infinite Dimensional ◽  
Variational Inclusion Problem

The purpose of this paper is to present two new forward-backward splitting schemes with relaxations and errors for finding a common element of the set of solutions to the variational inclusion problem with two accretive operators and the set of fixed points of strict pseudocontractions in infinite-dimensional Banach spaces. Under mild conditions, some weak and strong convergence theorems for approximating these common elements are proved. The methods in the paper are novel and different from those in the early and recent literature. Further, we consider the problem of finding a common element of the set of solutions of a mathematical model related to equilibrium problems and the set of fixed points of a strict pseudocontractions.

Solitary Waves as Fixed Points of Infinite-Dimensional Maps in an Optical Bistable Ring Cavity

1983 ◽  
Vol 51 (2) ◽  
pp. 75-78 ◽  
Author(s):  
D. W. Mc Laughlin ◽  
J. V. Moloney ◽  
A. C. Newell
Keyword(s):  
Fixed Points ◽  
Solitary Waves ◽  
Ring Cavity ◽  
Infinite Dimensional

scholarly journals Gluing an Infinite Number of Instantons

2007 ◽  
Vol 188 ◽  
pp. 107-131 ◽  
Author(s):  
Masaki Tsukamoto
Keyword(s):  
Gauge Theory ◽  
Parameter Space ◽  
Infinite Number ◽  
Moduli Spaces ◽  
Dimensional Parameter ◽  
Yang Mills ◽  
Infinite Dimensional ◽  
Alternating Method ◽  
One Step ◽  
Infinite Energy

AbstractThis paper is one step toward infinite energy gauge theory and the geometry of infinite dimensional moduli spaces. We generalize a gluing construction in the usual Yang-Mills gauge theory to an “infinite energy” situation. We show that we can glue an infinite number of instantons, and that the resulting ASD connections have infinite energy in general. Moreover they have an infinite dimensional parameter space. Our construction is a generalization of Donaldson’s “alternating method”.

scholarly journals Refined large N duality for knots

2020 ◽  
pp. 2041001
Author(s):  
Masaya Kameyama ◽  
Satoshi Nawata
Keyword(s):  
Moduli Spaces ◽  
Bound States ◽  
Simons Theory ◽  
Global Symmetry ◽  
Torus Knots ◽  
Torus Knot ◽  
Large N ◽  
Bps Invariants ◽  
Bps States ◽  
Chern Simons

We formulate large [Formula: see text] duality of [Formula: see text] refined Chern–Simons theory with a torus knot/link in [Formula: see text]. By studying refined BPS states in M-theory, we provide the explicit form of low-energy effective actions of Type IIA string theory with D4-branes on the [Formula: see text]-background. This form enables us to relate refined Chern–Simons invariants of a torus knot/link in [Formula: see text] to refined BPS invariants in the resolved conifold. Assuming that the extra [Formula: see text] global symmetry acts on BPS states trivially, the duality predicts graded dimensions of cohomology groups of moduli spaces of M2–M5 bound states associated to a torus knot/link in the resolved conifold. Thus, this formulation can be also interpreted as a positivity conjecture of refined Chern–Simons invariants of torus knots/links. We also discuss about an extension to non-torus knots.

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