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Some properties of non-positively curved lattices

Related publications (25)

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

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

Transition to chaos in extended systems and their quantum impurity models

Camille Didier Georges Aron

Chaos sets a fundamental limit to quantum-information processing schemes. We study the onset of chaos in spatially extended quantum many-body systems that are relevant to quantum optical devices. We consider an extended version of the Tavis-Cummings model ...

Iop Publishing Ltd2024

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

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

Disagreement and fragmentation in growing groups

Jiyong Zhang, Yubo Xie

The arise of disagreement is an emergent phenomenon that can be observed within a growing social group and, beyond a certain threshold, can lead to group fragmentation. To better understand how disagreement emerges, we introduce an analytically tractable m ...

PERGAMON-ELSEVIER SCIENCE LTD2023

Digital Doubles: The Major Agency of Minor Bits

Lucia-Nieves Garcia de Jalon Oyarzun

In a world that seeks to describe, codify and quantify everything, and particularly our viscerality and its interactions with our actual and digital environments, can we find interstitial spaces, currently unseen, unobserved and unlegislated, where we migh ...

2022

A Functional Perspective on Information Measures

Amedeo Roberto Esposito

Since the birth of Information Theory, researchers have defined and exploited various information measures, as well as endowed them with operational meanings. Some were born as a "solution to a problem", like Shannon's Entropy and Mutual Information. Other ...

EPFL2022

Invariant integrals on topological groups

Vasco Schiavo

We generalize the fixed-point property for discrete groups acting on convex cones given by Monod in [23] to topological groups. At first, we focus on describing this fixed-point property from a functional point of view, and then we look at the class of gro ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2022

Collapse-invariant properties of spaces equipped with signals or directions

Stefania Ebli

Collapsing cell complexes was first introduced in the 1930's as a way to deform a space into a topological-equivalent subspace with a sequence of elementary moves. Recently, discrete Morse theory techniques provided an efficient way to construct deformatio ...

EPFL2022

Generalised Implicit Neural Representations

Pierre Vandergheynst

We consider the problem of learning implicit neural representations (INRs) for signals on non-Euclidean domains. In the Euclidean case, INRs are trained on a discrete sampling of a signal over a regular lattice. Here, we assume that the continuous signal e ...

2022