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Towards new invariants for principal bundles

Related publications (28)

Cochains are all you need

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

FIBERED TORIC VARIETIES

Leonid Monin

A toric variety is called fibered if it can be represented as a total space of fibre bundle over toric base and with toric fiber. Fibered toric varieties form a special case of toric variety bundles. In this note we first give an introduction to the class ...

Independent Univ Moscow-Ium2023

Conditional Flatness, Fiberwise Localizations, And Admissible Reflections

Jérôme Scherer

We extend the group-theoretic notion of conditional flatness for a localization functor to any pointed category, and investigate it in the context of homological categories and of semi-abelian categories. In the presence of functorial fiberwise localizatio ...

CAMBRIDGE UNIV PRESS2023

Bounded and unbounded cohomology of homeomorphism and diffeomorphism groups

Nicolas Monod

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 HEIDELBERG2023

Correspondence functors and duality

Jacques Thévenaz, Serge Bouc

A correspondence functor is a functor from the category of finite sets and correspondences to the category of k-modules, where k is a commutative ring. By means of a suitably defined duality, new correspondence functors are constructed, having remarkable p ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2023

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

Nonlocally-resonant metamaterials

Aleksi Antoine Bossart

In this thesis, we unveil a third design path to manipulate elastic waves within architected media, distinct from the traditional phononic crystal and locally-resonant metamaterial concepts. The core innovation lies in the concept of nonlocal resonances, d ...

EPFL2023

Scattering from Time-Modulated Transmission-Line Loads: Theory and Experiments in Acoustics

Romain Christophe Rémy Fleury, Matthieu Francis Malléjac

Scattering wave systems that are periodically modulated in time offer many new degrees of freedom to control waves in both the spatial and frequency domains. Such systems, albeit linear, do not conserve frequency and require the adaptation of the usual the ...

American Physical Society (APS)2023

A Shadow Perspective on Equivariant Hochschild Homologies

Kathryn Hess Bellwald, Inbar Klang

Shadows for bicategories, defined by Ponto, provide a useful framework that generalizes classical and topological Hochschild homology. In this paper, we define Hochschild-type invariants for monoids in a symmetric monoidal, simplicial model category V, as ...

OXFORD UNIV PRESS2022

The cohomology of semi-simple Lie groups, viewed from infinity

Nicolas Monod

We prove that the real cohomology of semi-simple Lie groups admits boundary values, which are measurable cocycles on the Furstenberg boundary. This generalises known invariants such as the Maslov index on Shilov boundaries, the Euler class on projective sp ...

2022

Axonal and Dendritic Morphology of Excitatory Neurons in Layer 2/3 Mouse Barrel Cortex Imaged Through Whole-Brain Two-Photon Tomography and Registered to a Digital Brain Atlas

Carl Petersen, Sylvain Crochet, Georgios Foustoukos, Yanqi Liu

Communication between cortical areas contributes importantly to sensory perception and cognition. On the millisecond time scale, information is signaled from one brain area to another by action potentials propagating across long-range axonal arborizations. ...

FRONTIERS MEDIA SA2022

Landau levels of the Euler class topology

Oleg Yazyev, Yifei Guan

Two-dimensional systems with C2T (PT) symmetry exhibit the Euler class topology E is an element of Z in each two-band subspace realizing a fragile topology beyond the symmetry indicators. By systematically studying the energy levels of Euler insulating pha ...

AMER PHYSICAL SOC2022

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

Unramified F-divided objects and the etale fundamental pro-groupoid in positive characteristic

Giulio Orecchia

Let X /S be a flat algebraic stack of finite presentation. We define a new & eacute;tale fundamental pro-groupoid pi(1)(X /S), generalizing Grothendieck's enlarged & eacute;tale fundamental group from SGA 3 to the relative situation. When S is of equal pos ...

GEOMETRY & TOPOLOGY PUBLICATIONS2022

Computational tools for twisted topological Hochschild homology of equivariant spectra

Kathryn Hess Bellwald, Inbar Klang

Twisted topological Hochschild homology of Cn-equivariant spectra was introduced by Angeltveit, Blumberg, Gerhardt, Hill, Lawson, and Mandell, building on the work of Hill, Hopkins, and Ravenel on norms in equivariant homotopy theory. In this paper we intr ...

ELSEVIER2022

A Hopf algebra model for Dwyer's tame spaces

Haoqing Wu

In this thesis, we give a modern treatment of Dwyer's tame homotopy theory using the language of

\infty

-categories. We introduce the notion of tame spectra and show it has a concrete algebraic description. We then carry out a study of

\infty

-operads an ...

EPFL2022

Bundle-Specific Axon Diameter Index as a New Contrast to Differentiate White Matter Tracts

Jean-Philippe Thiran, Giorgio Innocenti, David Paul Roger Romascano, Cristina Granziera, Alessandro Daducci, Muhamed Barakovic, Gabriel Girard, Maxime Descoteaux

In the central nervous system of primates, several pathways are characterized by different spectra of axon diameters. In vivo methods, based on diffusion-weighted magnetic resonance imaging, can provide axon diameter index estimates non-invasively. However ...

2021

Three-dimensional fabrication of sub-micron optical waveguides in PDMS and other polymer materials

Giulia Panusa

Optical waveguides are one of the most important photonic components. They are indispensable tools in many of todayâ s technologies because of their capacity of guiding light. In particular, compact, low loss, flexible polymer optical waveguides are cruci ...

EPFL2021

Serre-Tate theory for Calabi-Yau varieties

Maciej Emilian Zdanowicz

Classical Serre-Tate theory describes deformations of ordinary abelian varieties. It implies that every such variety has a canonical lift to characteristic zero and equips the base of its universal deformation with a Frobenius lifting and canonical multipl ...

WALTER DE GRUYTER GMBH2021

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

Related publications (28)

Axonal and Dendritic Morphology of Excitatory Neurons in Layer 2/3 Mouse Barrel Cortex Imaged Through Whole-Brain Two-Photon Tomography and Registered to a Digital Brain Atlas

Carl Petersen, Sylvain Crochet, Georgios Foustoukos, Yanqi Liu

FRONTIERS MEDIA SA2022

\infty

-categories. We introduce the notion of tame spectra and show it has a concrete algebraic description. We then carry out a study of

\infty

-operads an ...

EPFL2022