Capacities, Systoles and Jacobians of Riemann Surfaces

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

We elaborate on a recently proposed geometric framework for scalar effective field theories. Starting from the action, a metric can be identified that enables the construction of geometric quantities on the associated functional manifold. These objects tra ...

Hyperbolic lattices are a new type of synthetic materials based on regular tessellations in non-Euclidean spaces with constant negative curvature. While so far, there has been several theoretical investigations of hyperbolic topological media, experimental ...

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 ...

We define p-adic BPS or pBPS invariants for moduli spaces M-beta,M-chi of one-dimensional sheaves on del Pezzo and K3 surfaces by means of integration over a non-archimedean local field F. Our definition relies on a canonical measure mu can on the F-analyt ...

A method for optimizing at least one of a geometry, an implantation procedure, and/or stimulation protocol of one or more electrodes for an electrical stimulation of a target structure in a nervous system of a living being by a computer device, the method ...

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 ...

In this thesis we explore the applications of projective geometry, a mathematical theory of the relation between 3D scenes and their 2D images, in modern learning-based computer vision systems. This is an interesting research question which contradicts the ...

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 local undercut defects at the weld toe provide a potential initiation site for fatigue cracks and significantly impact the structure's fatigue strength. The influence of continuous undercut depth on fatigue performance is widely studied, but the resear ...

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 ...

Modern optimization is tasked with handling applications of increasingly large scale, chiefly due to the massive amounts of widely available data and the ever-growing reach of Machine Learning. Consequently, this area of research is under steady pressure t ...

The present work proposes a framework for nonlinear model order reduction based on a Graph Convolutional Autoencoder (GCA-ROM). In the reduced order modeling (ROM) context, one is interested in obtaining real -time and many-query evaluations of parametric ...

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 ...

In this thesis, we propose to formally derive amplitude equations governing the weakly nonlinear evolution of non-normal dynamical systems, when they respond to harmonic or stochastic forcing, or to an initial condition. This approach reconciles the non-mo ...

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 ...

Soft robot are celebrated for their propensity to enable compliant and complex robot-environment interactions. Soft robotic manipulators, or slender continuum structure robots have the potential to exploit these interactions to enable new exploration and m ...

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 ...

Discrete domes are doubly curved structures comprising a network of beam-like elements. We study the mechanics of discrete domes made of ribbons woven in a pentagonal triaxial pattern. Experiments and finite element simulations are performed to characteriz ...

Strain is inevitable in two-dimensional (2D) materials, regardless of whether the film is suspended or supported. However, the direct measurement of strain response at the atomic scale is challenging due to the difficulties of maintaining both flexibility ...

In this paper, we study the rank-one convex hull of a differential inclusion associated to entropy solutions of a hyperbolic system of conservation laws. This was introduced in [B. Kirchheim, S. Muller and V. S(sic)ver & aacute;k, Studying Nonlinear PDE by ...

Capacities, Systoles and Jacobians of Riemann Surfaces

Chat with Graph Search

What is the geometry of effective field theories?

Anomalous and Chern topological waves in hyperbolic networks

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

BPS invariants from p-adic integrals

A method and system for optimizing design, implantation, and stimulation protocols of electrodes stimulating the nervous system

Geometric Learning: Leveraging differential geometry for learning and control

Incorporating Projective Geometry into Deep Learning

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

Strain-based analysis on the influence of local undercut geometry on fatigue crack initiation life

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

Scalable constrained optimization

A graph convolutional autoencoder approach to model order reduction for parametrized PDEs

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

Non-normal forms

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

Piecewise Affine Curvature model: a reduced-order model for soft robot-environment interaction beyond PCC

A structured prediction approach for robot imitation learning

Indentation and stability of woven domes

In-situ atomic level observation of the strain response of graphene lattice

T-5 configurations and hyperbolic systems