Publications related to Invariant Integrals on Topological Groups and Applications

Related publications (32)

Sobolev spaces via chains in metric measure spaces

We define the chain Sobolev space on a possibly non-complete metric measure space in terms of chain upper gradients. In this context, E-chains are finite collections of points with distance at most E between consecutive points. They play the role of discre ...

2025

High-throughput screening of Weyl semimetals

Nicola Marzari, Davide Campi, Davide Grassano

Topological Weyl semimetals represent a novel class of nontrivial materials, where band crossings with linear dispersions take place at generic momenta across reciprocal space. These crossings give rise to low -energy properties akin to those of Weyl fermi ...

Amer Physical Soc2024

Stability: a search for structure

Wouter Jongeneel

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 ...

EPFL2024

Topological photonic transport in disordered scattering networks

Zhe Zhang, Zhechen Zhang

This Ph.D. thesis unveils the unique topological phenomena occurring in such networks, focusing on the intricate interplay between their Floquet topology, the presence of disorder, and their unitary scattering at microscopic and macroscopic scales. Using t ...

EPFL2024

Anomalous and Chern topological waves in hyperbolic networks

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

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

The ABCD of topological recursion

Nicolas Gerson Orantin

Kontsevich and Soibelman reformulated and slightly generalised the topological recursion of [43], seeing it as a quantisation of certain quadratic Lagrangians in T*V for some vector space V. KS topological recursion is a procedure which takes as initial da ...

Academic Press Inc Elsevier Science2024

Mean value theorems for collections of lattices with a prescribed group of symmetries

Nihar Prakash Gargava

Euclidean lattices are mathematical objects of increasing interest in the fields of cryptography and error-correcting codes. This doctoral thesis is a study on high-dimensional lattices with the motivation to understand how efficient they are in terms of b ...

EPFL2024

Seeding and Emergence of Composite Skyrmions in a van der Waals Magnet

Klaus Kern, Marko Burghard, Lukas Powalla

Topological charge plays a significant role in a range of physical systems. In particular, observations of real-space topological objects in magnetic materials have been largely limited to skyrmions - states with a unitary topological charge. Recently, mor ...

Wiley-V C H Verlag Gmbh2023

Ultrafast control of emergent quantum matter probed by electron microscopy

Benoît Guilhem Michel Binh Truc

In the quest for controlling materials' properties, light as an external stimulus has a special place as it can create new states of matter and enable their ultrafast manipulation. In particular, spintronics, an exciting emergent field relying on the elect ...

EPFL2023

Anomalous topological waves in strongly amorphous scattering networks

Romain Christophe Rémy Fleury, Zhechen Zhang, Zhe Zhang, Pierre Delplace

Topological insulators are crystalline materials that have revolutionized our ability to control wave transport. They provide us with unidirectional channels that are immune to obstacles, defects, or local disorder and can even survive some random deformat ...

2023

Unlikely intersections on the p-adic formal ball

Vlad Serban

We investigate generalizations along the lines of the Mordell-Lang conjecture of the author's p-adic formal Manin-Mumford results for n-dimensional p-divisible formal groups F. In particular, given a finitely generated subgroup (sic) of F(Q(p)) and a close ...

SPRINGER INT PUBL AG2023

Crossing of the Branch Cut: The Topological Origin of a Universal 2 pi-Phase Retardation in Non-Hermitian Metasurfaces

Olivier Martin, Karim Achouri

Full wavefront control by photonic components requires that the spatial phase modulation on an incoming optical beam ranges from 0 to 2 pi. Because of their radiative coupling to the environment, all optical components are intrinsically non-Hermitian syste ...

WILEY-V C H VERLAG GMBH2023

Crystalline or amorphous? A critical evaluation of phenomenological phase selection rules

Johann Michler, Caroline Hain

In this work, we reviewed the available phase selection rules comprising atomic size and topological aspects, entropies, enthalpies, melting points, valence and itinerant electron concentrations, as well as electronegativity, and validated them using a car ...

ELSEVIER SCI LTD2023

Complementary screening for quantum spin Hall insulators in two-dimensional exfoliable materials

Nicola Marzari, Davide Campi, Antimo Marrazzo, Davide Grassano

Quantum spin Hall insulators are a class of topological materials that has been extensively studied during the past decade. One of their distinctive features is the presence of a finite band gap in the bulk and gapless, topologically protected edge states ...

Amer Physical Soc2023

Data-Driven Discovery of Organic Electronic Materials Enabled by Hybrid Top-Down/Bottom-Up Design

Anne-Clémence Corminboeuf, Rubén Laplaza Solanas, Sergio Vela Llausi, Jacob Terence Blaskovits

The high-throughput exploration and screening of molecules for organic electronics involves either a 'top-down' curation and mining of existing repositories, or a 'bottom-up' assembly of user-defined fragments based on known synthetic templates. Both are t ...

Wiley-V C H Verlag Gmbh2023

Persistence and the Sheaf-Function Correspondence

Nicolas Michel Berkouk

The sheaf-function correspondence identifies the group of constructible functions on a real analytic manifold M with the Grothendieck group of constructible sheaves on M. When M is a finite dimensional real vector space, Kashiwara-Schapira have recently in ...

Cambridge Univ Press2023

A full characterization of invariant embeddability of unimodular planar graphs

Laszlo Marton Toth

When can a unimodular random planar graph be drawn in the Euclidean or the hyperbolic plane in a way that the distribution of the random drawing is isometry-invariant? This question was answered for one-ended unimodular graphs in Benjamini and Timar, using ...

WILEY2023

Phase of Topological Lattice with Leaky Guided Mode Resonance

Kim Seonyeong, Kirsten Emilie Moselund

Topological nature in different areas of physics and electronics has often been characterized and controlled through topological invariants depending on the global properties of the material. The validity of bulk-edge correspondence and symmetry-related to ...

MDPI2023

Floyd's manifold is a conjugation space

Jérôme Scherer

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 ...

Scuola Normale Superiore2023