Related papers: Quantization of the Serre spectral sequence
After an introductory chapter on the quantum supersymmetric string, in which particular attention will be devoted to the techniques via which phenomenologically viable models can be obtained from the ultraviolet microscopic degrees of…
The phenomenom of emerging regular spectral features from random interactions is addressed in the context of the vibron model. A mean-field analysis links different regions of the parameter space with definite geometric shapes. The results…
We build a spectral sequence converging to the cohomology of a fusion system with a strongly closed subgroup. This spectral sequence is related to the Lyndon-Hochschild-Serre spectral sequence and coincides with it for the case of an…
We give criteria for the existence of bifurcations of symmetric periodic orbits in reversible Hamiltonian systems in terms of local equivariant Lagrangian Rabinowitz Floer homology. As an example, we consider the family of the direct…
The variation operator in singularity theory maps relative homology cycles to compact cycles in the Milnor fiber using the monodromy. We construct its symplectic analogue for an isolated singularity. We define the monodromy Lagrangian Floer…
Generalisations of the bent property of a boolean function are presented, by proposing spectral analysis with respect to a well-chosen set of local unitary transforms. Quadratic boolean functions are related to simple graphs and it is shown…
We consider the harmonic map heat flow for maps from the plane taking values in the sphere, under equivariant symmetry. It is known that solutions to the initial value problem can exhibit bubbling along a sequence of times -- the solution…
The spectra of parallel flows (that is, flows governed by first-order differential operators parallel to one direction) are investigated, on both $L^2$ spaces and weighted-$L^2$ spaces. As a consequence, an example of a flow admitting a…
For any finite group G, we construct a spectral sequence for computing the Bredon cohomology of a G-CW complex X, starting with the cohomology of X^H/\cup_{K>H}X^K with suitable local coefficients, for various H \leq G.
Schwarz showed that when a closed symplectic manifold (M,\om) is symplectically aspherical (i.e. the symplectic form and the first Chern class vanish on \pi_2(M)) then the spectral invariants, which are initially defined on the universal…
In this paper, we develop a structure theory for generalized spectral sequences, which are derived from chain complexes that are filtered over arbitrary partially ordered sets. Also, a more general construction method reminiscent of exact…
This work reports an experimental characterisation of the flow properties in a homogeneous bubble swarm rising at high-Reynolds-numbers within a homogeneous and isotropic turbulent flow. Both the gas volume fraction {\alpha} and the…
Using Morse-Bott-Floer spectral sequences, we describe a filtration by ideals on quantum cohomology for symplectic manifolds with a Hamiltonian $S^1$-action that extends to a pseudoholomorphic $\mathbb{C}^*$-action. These spaces include all…
We introduce a formalism to produce several families of spectral sequences involving the derived functors of the limit and colimit functors over a finite partially ordered set. The first type of spectral sequences involves the left derived…
This paper describes the structure of the moduli space of holomorphic curves and constructs Gromov Witten invariants in the category of exploded manifolds. This includes defining Gromov Witten invariants relative to normal crossing divisors…
An ensemble model of turbulence is proposed. The ensemble consists of flow fields in which the flux of an inviscid conserved quantity, such as energy (or enstrophy in two-dimensional flow fields), across the wavenumber $k$ is a constant…
We consider the harmonic map heat flow for maps from the plane to the two-sphere. It is known that solutions to the initial value problem exhibit bubbling along a well-chosen sequence of times. We prove that every sequence of times admits a…
The goal of this paper is to discuss some of the results in [31] and [32] and expand upon the work there by proving a global weak existence result as well as a first bubbling analysis in finite time. In addition, an alternative local…
New monodromy relations of loop amplitudes are derived in open string theory. We particularly study N-point one-loop amplitudes described by a world-sheet cylinder (planar and non-planar) and derive a set of relations between subamplitudes…
We compute spectra of symmetric random matrices defined on graphs exhibiting a modular structure. Modules are initially introduced as fully connected sub-units of a graph. By contrast, inter-module connectivity is taken to be incomplete.…