Publications related to Hyperkähler manifold

A b-symplectic slice theorem

In this article, motivated by the study of symplectic structures on manifolds with boundary and the systematic study of b-symplectic manifolds started in Guillemin, Miranda, and Pires Adv. Math. 264 (2014), 864-896, we prove a slice theorem for Lie group a ...

WILEY2022

Shrinking Scale Equidistribution for Monochromatic Random Waves on Compact Manifolds

Matthew De Courcy-Ireland

We prove equidistribution at shrinking scales for the monochromatic ensemble on a compact Riemannian manifold of any dimension. This ensemble on an arbitrary manifold takes a slowly growing spectral window in order to synthesize a random function. With hig ...

OXFORD UNIV PRESS2021

Slow-fast Dynamics of Strongly Coupled Adaptive Frequency Oscillators*

Auke Ijspeert, Jonas Buchli, Ludovic Righetti

Oscillators have two main limitations: their synchronization properties are limited (i.e., they have a finite synchronization region) and they have no memory of past interactions (i.e., they return to their intrinsic frequency whenever the entraining signa ...

SIAM PUBLICATIONS2021

Gaussians on Riemannian Manifolds for Robot Learning and Adaptive Control

Sylvain Calinon

This article presents an overview of robot learning and adaptive control applications that can benefit from a joint use of Riemannian geometry and probabilistic representations. The roles of Riemannian manifolds, geodesics and parallel transport in robotic ...

2020

Robot skills learning with Riemannian manifolds: Leveraging geometry-awareness in robot learning, optimization and control

Noémie Laure Gwendoline Jaquier

Humans exhibit outstanding learning and adaptation capabilities while performing various types of manipulation tasks. When learning new skills, humans are able to extract important information by observing examples of a task and efficiently refine a priori ...

EPFL2020

Escaping from saddle points on Riemannian manifolds

Nicolas Henri Bernard Flammarion, Yue Sun

We consider minimizing a nonconvex, smooth function f on a Riemannian manifold M. We show that a perturbed version of Riemannian gradient descent algorithm converges to a second-order stationary point (and hence is able to escape saddle points on the manif ...

2019

Renormalization of quantum field theory on Riemannian manifolds

In this paper, we provide a simple pedagogical proof of the existence of covariant renormalizations in Euclidean perturbative quantum field theory on closed Riemannian manifolds, following the Epstein–Glaser philosophy. We rely on a local method that allow ...

2019

A Gauss-Bonnet Theorem for Asymptotically Conical Manifolds and Manifolds with Conical Singularities

Adrien Giuliano Marcone

The purpose of this thesis is to provide an intrinsic proof of a Gauss-Bonnet-Chern formula for complete Riemannian manifolds with finitely many conical singularities and asymptotically conical ends. A geometric invariant is associated to the link of both ...

EPFL2019

Improved Bounds for Discretization of Langevin Diffusions: Near-Optimal Rates without Convexity

Nicolas Henri Bernard Flammarion

We consider minimizing a nonconvex, smooth function

f

on a Riemannian manifold

\mathcal{M}

. We show that a perturbed version of Riemannian gradient descent algorithm converges to a second-order stationary point (and hence is able to escape saddle point ...

2019

A central limit theorem for integrals of random waves

Marius Christopher Lemm, Matthew De Courcy-Ireland

We derive a central limit theorem for the mean-square of random waves in the high-frequency limit over shrinking sets. Our proof applies to any compact Riemannian manifold of arbitrary dimension, thanks to the universality of the local Weyl law. The key te ...

2019

Hyperkähler manifold

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A b-symplectic slice theorem

Shrinking Scale Equidistribution for Monochromatic Random Waves on Compact Manifolds

Slow-fast Dynamics of Strongly Coupled Adaptive Frequency Oscillators*

Gaussians on Riemannian Manifolds for Robot Learning and Adaptive Control

Robot skills learning with Riemannian manifolds: Leveraging geometry-awareness in robot learning, optimization and control

Escaping from saddle points on Riemannian manifolds

Renormalization of quantum field theory on Riemannian manifolds

A Gauss-Bonnet Theorem for Asymptotically Conical Manifolds and Manifolds with Conical Singularities

Improved Bounds for Discretization of Langevin Diffusions: Near-Optimal Rates without Convexity

A central limit theorem for integrals of random waves

A b-symplectic slice theorem

Robot skills learning with Riemannian manifolds: Leveraging geometry-awareness in robot learning, optimization and control

Gaussians on Riemannian Manifolds for Robot Learning and Adaptive Control

Shrinking Scale Equidistribution for Monochromatic Random Waves on Compact Manifolds

Escaping from saddle points on Riemannian manifolds

Renormalization of quantum field theory on Riemannian manifolds

A Gauss-Bonnet Theorem for Asymptotically Conical Manifolds and Manifolds with Conical Singularities

Improved Bounds for Discretization of Langevin Diffusions: Near-Optimal Rates without Convexity

A central limit theorem for integrals of random waves

Slow-fast Dynamics of Strongly Coupled Adaptive Frequency Oscillators*