Concept
4-manifold
Publications associées (53)
From low-rank retractions to dynamical low-rank approximation and back
Daniel Kressner, Axel Elie Joseph Séguin, Gianluca Ceruti
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 ...
Springer2024Bounded and unbounded cohomology of homeomorphism and diffeomorphism groups
We determine the bounded cohomology of the group of homeomorphisms of certain low-dimensional manifolds. In particular, for the group of orientation-preserving homeomorphisms of the circle and of the closed 2-disc, it is isomorphic to the polynomial ring g ...
SPRINGER HEIDELBERG2023Retraction-based numerical methods for continuation, interpolation and time integration on manifolds
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 ...
EPFL2023A 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 ...
WILEY2022How Lagrangian States Evolve Into Random Waves
In this paper, we consider a compact connected manifold (X, g) of negative curvature, and a family of semi-classical Lagrangian states f(h)(x) = a(x)e(i phi(x)/h) on X. For a wide family of phases phi, we show that f(h), when evolved by the semi-classical ...
ECOLE POLYTECHNIQUE2022Realizing doubles: a conjugation zoo
Conjugation spaces are topological spaces equipped with an involution such that their fixed points have the same mod 2 cohomology (as a graded vector space, a ring and even an unstable algebra) but with all degrees divided by two, generalizing the classica ...
CAMBRIDGE UNIV PRESS2021Slow-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 PUBLICATIONS2021On Topological Equivalence in Linear Quadratic Optimal Control
Dynamical systems are topologically equivalent when their orbits can be mapped onto each other via a homeomorphic change of coordinates. We will show that in general, closed-loop systems resulting from Linear Quadratic Optimal Control problems are all topo ...
2021