Geometry

Related publications (31)

HYPERBOLA METHOD ON TORIC VARIETIES

We develop a very general version of the hyperbola method which extends the known method by Blomer and Brudern for products of projective spaces to complete smooth split toric varieties. We use it to count Campana points of bounded log-anticanonical height ...

Ecole Polytechnique2024

Anomalous and Chern topological waves in hyperbolic networks

Romain Christophe Rémy Fleury, Aleksi Antoine Bossart, Haoye Qin, Zhechen Zhang

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 ...

Nature Research2024

A Note on Lenses in Arrangements of Pairwise Intersecting Circles in the Plane

Rom Pinchasi

Let F be a family of n pairwise intersecting circles in the plane. We show that the number of lenses, that is convex digons, in the arrangement induced by F is at most 2n - 2. This bound is tight. Furthermore, if no two circles in F touch, then the geometr ...

Electronic Journal Of Combinatorics2024

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 ...

Springer2024

BPS invariants from p-adic integrals

Dimitri Stelio Wyss, Francesca Carocci, Giulio Orecchia

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 ...

Cambridge Univ Press2024

On the boundedness of n-folds with κ(X) = n - 1

Stefano Filipazzi

In this note, we study certain sufficient conditions for a set of minimal klt pairs ( X, triangle) with kappa ( X, triangle) = dim( X ) - 1 to be bounded. ...

European Mathematical Soc-Ems2024

Some Mordell-Weil lattices and applications to sphere packings

Gauthier Leterrier

We provide new explicit examples of lattice sphere packings in dimensions 54, 55, 162, 163, 486 and 487 that are the densest known so far, using Kummer families of elliptic curves over global function fields. In some cases, these families of elliptic curve ...

EPFL2024

'Fraternal-twin' ferroelectricity: competing polar states in hydrogen-doped samarium nickelate from first principles

Michele Kotiuga

In ferroelectric switching, an applied electric field switches the system between two polar symmetry-equivalent states. In this work, we use first-principles calculations to explore the polar states of hydrogen-doped samarium nickelate (SNO) at a concentra ...

Iop Publishing Ltd2024

Cochains are all you need

Kelly Spry Maggs

In this thesis, we apply cochain complexes as an algebraic model of space in a diverse range of mathematical and scientific settings. We begin with an algebraic-discrete Morse theory model of auto-encoding cochain data, connecting the homotopy theory of d ...

EPFL2024

Stable cones in the thin one-phase problem

Xavier Fernandez-Real Girona

The aim of this work is to study homogeneous stable solutions to the thin (or fractional) one -phase free boundary problem. The problem of classifying stable (or minimal) homogeneous solutions in dimensions n >= 3 is completely open. In this context, axial ...

Johns Hopkins Univ Press2024

Band Gap Renormalization at Different Symmetry Points in Perovskites

Majed Chergui, Lijie Wang

Using ultrafast broad-band transient absorption (TA) spectroscopy of photoexcited MAPbBr3 thin films with probe continua in the visible and the mid- to deep-ultraviolet (UV) ranges, we capture the ultrafast renormalization at the fundamental gap at the R s ...

Amer Chemical Soc2024

Additive and geometric transversality of fractal sets in the integers

Florian Karl Richter

By juxtaposing ideas from fractal geometry and dynamical systems, Furstenberg proposed a series of conjectures in the late 1960's that explore the relationship between digit expansions with respect to multiplicatively independent bases. In this work, we in ...

2024

Geometric Learning: Leveraging differential geometry for learning and control

Bernardo Fichera

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 ...

EPFL2024

Reach For the Arcs: Reconstructing Surfaces from SDFs via Tangent Points

Yingying Ren

We introduce an algorithm to reconstruct a mesh from discrete samples of a shape's Signed Distance Function (SDF). A simple geometric reinterpretation of the SDF lets us formulate the problem through a point cloud, from which a surface can be extracted wit ...

Association for Computing Machinery2024

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

Silvestro Micera, Simone Romeni

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 ...

2024

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

Sylvain Alexandre Marie Sudan

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 ...

EPFL2024

Isogeny Problems with Level Structure

Tako Boris Fouotsa

Given two elliptic curves and the degree of an isogeny between them, finding the isogeny is believed to be a difficult problem—upon which rests the security of nearly any isogeny-based scheme. If, however, to the data above we add information about the beh ...

2024

The effect of smooth parametrizations on nonconvex optimization landscapes

Nicolas Boumal

We develop new tools to study landscapes in nonconvex optimization. Given one optimization problem, we pair it with another by smoothly parametrizing the domain. This is either for practical purposes (e.g., to use smooth optimization algorithms with good g ...

Springer Heidelberg2024

Incommensurate phases

Gervais Chapuis

Incommensurately modulated crystalline phases are part of a more general family called aperiodic crystals. Their symmetry is treated within the theoretical framework of superspace groups that is a generalization of the 3D space groups that are used for con ...

Academic Press2024

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

Jan Sickmann Hesthaven, Federico Pichi

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 ...

Academic Press Inc Elsevier Science2024