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A Shadow Perspective on Equivariant Hochschild Homologies

Related publications (29)

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

Multiplicity-free Representations of Algebraic Groups

Donna Testerman, Martin W. Liebeck

Let K be an algebraically closed field of characteristic zero, and let G be a connected reductive algebraic group over K. We address the problem of classifying triples (G, H, V ), where H is a proper connected subgroup of G, and V is a finitedimensional ir ...

Amer Mathematical Soc2024

Topological photonic transport in disordered scattering networks

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

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

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

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

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

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

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

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

Johann Michler, Ashish Sharma, 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

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

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

Distributed Lossy Computation with Structured Codes: From Discrete to Continuous Sources

Michael Christoph Gastpar, Adriano Pastore, Sung Hoon Lim, Chen Feng

This paper considers the problem of distributed lossy compression where the goal is to recover one or more linear combinations of the sources at the decoder, subject to distortion constraints. For certain configurations, it is known that codes with algebra ...

2023

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

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

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

Generic direct summands of tensor products for simple algebraic groups and quantum groups at roots of unity

Jonathan Gruber

Let G be either a simple linear algebraic group over an algebraically closed field of characteristic l>0 or a quantum group at an l-th root of unity. The category Rep(G) of finite-dimensional G-modules is non-semisimple. In this thesis, we develop new tech ...

EPFL2022

Hopf algebras and Hopf-Galois extensions in infinity-categories

Aras Ergus

In this thesis, we study interactions between algebraic and coalgebraic structures in infinity-categories (more precisely, in the quasicategorical model of (infinity, 1)-categories). We define a notion of a Hopf algebra H in an E-2-monoidal infinity-catego ...

EPFL2022

Connecting Hodge and Sakaguchi-Kuramoto through a mathematical framework for coupled oscillators on simplicial complexes

Alexis Arnaudon

Phase synchronizations in models of coupled oscillators such as the Kuramoto model have been widely studied with pairwise couplings on arbitrary topologies, showing many unexpected dynamical behaviors. Here, based on a recent formulation the Kuramoto model ...

NATURE PORTFOLIO2022

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