Some applications of symmetries in differential geometry and dynamical systems

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Fractionalization remains one of the most fascinating manifestations of strong interactions in quantum many-body systems. In quantum magnetism, the existence of spinons-collective magnetic excitations that behave as quasiparticles with fractional quantum n ...

In algorithms for solving optimization problems constrained to a smooth manifold, retractions are a well-established tool to ensure that the iterates stay on the manifold. More recently, it has been demonstrated that retractions are a useful concept for ot ...

Let K be an algebraically closed field of characteristic zero, and let G be a connected reductive algebraic group over K. We address the problem of classifying triples (G, H, V ), where H is a proper connected subgroup of G, and V is a finitedimensional ir ...

In this thesis we study stability from several viewpoints. After covering the practical importance, the rich history and the ever-growing list of manifestations of stability, we study the following. (i) (Statistical identification of stable dynamical syste ...

The combination of palladium salts and bipyridyl ligands can lead to the formation of a large variety of coordination complexes, with different shapes and sizes, displaying a very versatile host-guest chemistry. Increasing their structural complexity remai ...

Stabilizing liquid-liquid interfaces, whether between miscible or immiscible liquids, is crucial for a wide range of applications, including energy storage, microreactors, and biomimetic structures. In this study, a versatile approach for stabilizing the w ...

The occurrence of manufacturing defects in wind turbine blade (WTB) production can result in significant increases in operation and maintenance costs of WTBs, reduce capacity factors of wind farms, and occasionally lead to severe and disastrous consequence ...

In this thesis, we concentrate on advancing high-level behavioral control policies for robotic systems within the framework of Dynamical Systems (DS). Throughout the course of this research, a unifying thread weaving through diverse fields emerges, and tha ...

This paper presents the new 2D electrostatic particle -in -cell code FENNECS developed to study the formation of magnetized non -neutral plasmas in geometries with azimuthal symmetry. This code has been developed in the domain of gyrotron electron gun desi ...

The integration of the new plasma position reflectometer in the RFX-mod2 experiment (the upgraded version of the previous RFX-mod that operated until 2015) is presented in this contribution. Particular attention has been devoted to the high field side subs ...

Glacial moulins (cylindrical meltwater drainage shafts) provide valuable insights into glacier dynamics, but are inaccessible and hazardous environments for humans to study. Exploring them using passive sensor probes has revealed their complex geometry, wh ...

We propose a structured prediction approach for robot imitation learning from demonstrations. Among various tools for robot imitation learning, supervised learning has been observed to have a prominent role. Structured prediction is a form of supervised le ...

Ulam asked whether all Lie groups can be represented faithfully on a countable set. We establish a reduction of Ulam's problem to the case of simple Lie groups. In particular, we solve the problem for all solvable Lie groups and more generally Lie groups w ...

The goal of this thesis is the development and the analysis of numerical methods for problems where the unknown is a curve on a smooth manifold. In particular, the thesis is structured around the three following problems: homotopy continuation, curve inter ...

A toric variety is called fibered if it can be represented as a total space of fibre bundle over toric base and with toric fiber. Fibered toric varieties form a special case of toric variety bundles. In this note we first give an introduction to the class ...

We determine the dimensions of Ext -groups between simple modules and dual generalized Verma modules in singular blocks of parabolic versions of category O for complex semisimple Lie algebras and affine Kac-Moody algebras. ...

E. E. Floyd showed in 1973 that there exist only two nontrivial cobor-dism classes that contain manifolds with three cells, and that they lie in dimen-sions 10 and 5. We prove that there is an action of the cyclic group C2 on the 10-dimensional Floyd manif ...

Side-by-side hybrid textiles are an intermediate step for the production of fibre-reinforced thermoplastic composites. Press moulding these materials combining reinforcing fibre textiles and thermoplastic matrix textiles or flexible layers is a promising m ...

Simplicial Kuramoto models have emerged as a diverse and intriguing class of models describing oscillators on simplices rather than nodes. In this paper, we present a unified framework to describe different variants of these models, categorized into three ...

We show that mixed-characteristic and equicharacteristic small deformations of 3-dimensional canonical (resp., terminal) singularities with perfect residue field of characteristic p>5 are canonical (resp., terminal). We discuss applications to arithmetic a ...

Some applications of symmetries in differential geometry and dynamical systems

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Confined and Deconfined Spinon Excitations in the Rectangular-lattice Quantum Antiferromagnet

From low-rank retractions to dynamical low-rank approximation and back

Multiplicity-free Representations of Algebraic Groups

Stability: a search for structure

Palladium-based supramolecular assemblies: from complex structures to water-soluble anion-receptors

A Versatile Approach to Stabilize Liquid-Liquid Interfaces using Surfactant Self-Assembly

Non-contact sensing for anomaly detection in wind turbine blades: A focus-SVDD with complex-valued auto-encoder approach

Geometric Learning: Leveraging differential geometry for learning and control

FENNECS: a novel particle-in-cell code for simulating the formation of magnetized non-neutral plasmas trapped by electrodes of complex geometries

Technology challenges and integration of the plasma position reflectometer in RFX-mod2

Into the ice: Exploration and data capturing in glacial moulins by a tethered robot

A structured prediction approach for robot imitation learning

Lie groups in the symmetric group: Reducing Ulam's problem to the simple case

Retraction-based numerical methods for continuation, interpolation and time integration on manifolds

FIBERED TORIC VARIETIES

Cohomology in singular blocks of parabolic category O

Floyd's manifold is a conjugation space

A multi scale consolidation model for press moulding of hybrid textiles into complex geometries

A unified framework for Simplicial Kuramoto models

Arithmetic and geometric deformations of threefolds