Publications related to Fundamental group

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

Relative plus constructions

Jérôme Scherer

Let h be a connective homology theory. We construct a functorial relative plus construction as a Bousfield localization functor in the category of maps of spaces. It allows us to associate to a pair (X,H), consisting of a connected space X and an hperfect ...

2023

Density-wave ordering in a unitary Fermi gas with photon-mediated interactions

Jean-Philippe Brantut, Victor Youri Helson, Kevin Etienne Robert Roux, Hideki Konishi, Timo Zwettler, Elvia Colella

A density wave (DW) is a fundamental type of long-range order in quantum matter tied to self-organization into a crystalline structure. The interplay of DW order with superfluidity can lead to complex scenarios that pose a great challenge to theoretical an ...

NATURE PORTFOLIO2023

Continuation Methods For Riemannian Optimization

Daniel Kressner, Axel Elie Joseph Séguin

Numerical continuation in the context of optimization can be used to mitigate convergence issues due to a poor initial guess. In this work, we extend this idea to Riemannian optimization problems, that is, the minimization of a target function on a Riemann ...

SIAM PUBLICATIONS2022

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

The Jordan property for local fundamental groups

Stefano Filipazzi, Roberto Svaldi

We show the Jordan property for regional fundamental groups of klt singularities of fixed dimension. Furthermore, we prove the existence of effective simultaneous index 1 covers for n-dimensional klt singularities. We give an application to the study of lo ...

2022

An Equivalence Between Data Poisoning and Byzantine Gradient Attacks

Rachid Guerraoui, Sadegh Farhadkhani, Le Nguyen Hoang, Oscar Jean Olivier Villemaud

To study the resilience of distributed learning, the “Byzantine" literature considers a strong threat model where workers can report arbitrary gradients to the parameter server. Whereas this model helped obtain several fundamental results, it has sometimes ...

PMLR2022

Algebra and geometry of link homology Lecture notes from the IHES 2021 Summer School

Oscar Salomon Kivinen

These notes cover the lectures of the first named author at 2021 IHES Summer School on "Enumerative Geometry, Physics and Representation Theory" with additional details and references. They cover the definition of Khovanov-Rozansky triply graded homology, ...

WILEY2022

Homotopical relations between 2-dimensional categories and their infinity-analogues

Lyne Moser

In this thesis, we study the homotopical relations of 2-categories, double categories, and their infinity-analogues. For this, we construct homotopy theories for the objects of interest, and show that there are homotopically full embeddings of 2-categories ...

EPFL2021

Control and Characterization of the Compactness of Single-Chain Nanoparticles

Francesco Stellacci, Luciano Andres Abriata, Lixia Wei, Suiyang Liao

Polymers when self-cross-linked into single-chain nanoparticles bear some resemblance to folded proteins; yet proteins have clear energy landscapes that determine precisely folded structures, while single-chain polymer nanoparticles (SCNPs) have more undef ...

American Chemical Society2021

Recent progress in silk fibroin-based flexible electronics

Jürgen Brugger, Xiao Sheng Zhang, Ya Wang, Peng Huang

With the rapid development of the Internet of Things (IoT) and the emergence of 5G, traditional silicon-based electronics no longer fully meet market demands such as nonplanar application scenarios due to mechanical mismatch. This provides unprecedented op ...

2021

Towards the K(2)-local homotopy groups of Z

Philip Egger

Previously (Adv. Math. 360 (2020) art. id. 106895), we introduced a class (Z) over tilde of 2-local finite spectra and showed that all spectra Z is an element of (Z) over tilde admit a v(2)-self-map of periodicity 1. The aim here is to compute the K(2)-loc ...

GEOMETRY & TOPOLOGY PUBLICATIONS2020

Structural transitions and mechanochemical coupling in the nucleoprotein filament explain homology selectivity and Rad51 protein cooperativity in cellular DNA repair

Daniel Migliozzi

The nucleoprotein filament (NPF) is the fundamental element of homologous recombination (HR), a major mechanism for the repair of double-strand DNA breaks in the cell. The NPF is made of the damaged DNA strand surrounded by recombinase proteins, and its se ...

AMER PHYSICAL SOC2020

Electrosorption at metal surfaces from first principles

Nicola Marzari

Electrosorption of solvated species at metal electrodes is a most fundamental class of processes in interfacial electrochemistry. Here, we use its sensitive dependence on the electric double layer to assess the performance of ab initio thermodynamics appro ...

NATURE PUBLISHING GROUP2020

Effect of tool-use observation on metric body representation and peripersonal space

Michela Bassolino, Matteo Franza

In everyday life, we constantly act and interact with objects and with others' people through our body. To properly perform actions, the representations of the dimension of body-parts (metric body representation, BR) and of the space surrounding the body ( ...

2020

Abitare oltre la pandemia: verso un nuovo habitat domestico

Boris Hamzeian

The search for ways of living adapted to the changes of society is gaining in importance in the context of the current Coronavirus pandemic. The domestic confinement, in fact, is revealing as never before the inadequacy of our homes to contemporary life. T ...

2020

A Homotopy Method with Adaptive Basis Selection for Computing Multiple Solutions of Differential Equations

Jan Sickmann Hesthaven

The homotopy continuation method has been widely used to compute multiple solutions of nonlinear differential equations, but the computational cost grows exponentially based on the traditional finite difference and finite element discretizations. In this w ...

SPRINGER/PLENUM PUBLISHERS2020

Oxygen Evolution Reaction in Ba0.5Sr0.5Co0.8Fe0.2O3-delta Aided by Intrinsic Co/Fe Spinel-Like Surface

Vasiliki Tileli, Thi Ha My Pham, Tzu-Hsien Shen, Jan Vávra

Among the perovskites used to catalyze the oxygen evolution reaction (OER), Ba0.5Sr0.5Co0.8Fe0.2O3-delta (BSCF) exhibits excellent activity which is thought to be related to dynamic reconstruction at the flexible perovskite surface due to accommodation of ...

AMER CHEMICAL SOC2020

Kaleidoscopic groups: permutation groups constructed from dendrite homeomorphisms

Nicolas Monod

Given a transitive permutation group, a fundamental object for studying its higher transitivity properties is the permutation action of its isotropy subgroup. We reverse this relationship and introduce a universal construction of infinite permutation group ...

POLISH ACAD SCIENCES INST MATHEMATICS-IMPAN2019

Twisting structures and morphisms up to strong homotopy

Kathryn Hess Bellwald

We define twisted composition products of symmetric sequences via classifying morphisms rather than twisting cochains. Our approach allows us to establish an adjunction that simultaneously generalizes a classic one for algebras and coalgebras, and the bar- ...

2020