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Concept

Hodge structure

Publications associées (21)

Cochains are all you need

Kelly Spry Maggs

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

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

Reduced representations of complexes, signals, and multifiltrations

Celia Camille Hacker

The field of computational topology has developed many powerful tools to describe the shape of data, offering an alternative point of view from classical statistics. This results in a variety of complex structures that are not always directly amenable for ...

EPFL2022

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

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

Birational boundedness of low-dimensional elliptic Calabi-Yau varieties with a section

Roberto Svaldi

We prove that there are finitely many families, up to isomorphism in codimension one, of elliptic Calabi-Yau manifolds Y -> X with a rational section, provided that dim(Y)

2021

Algebraic Homotopy Interleaving Distance

Nicolas Michel Berkouk

The theory of persistence, which arises from topological data analysis, has been intensively studied in the one-parameter case both theoretically and in its applications. However, its extension to the multi-parameter case raises numerous difficulties, wher ...

SPRINGER INTERNATIONAL PUBLISHING AG2021

The Tonal Diffusion Model

Martin Alois Rohrmeier, Fabian Claude Moss, Robert Lieck

Pitch-class distributions are of central relevance in music information retrieval, computational musicology and various other fields, such as music perception and cognition. However, despite their structure being closely related to the cognitively and musi ...

2020

Representations and descriptors unifying the study of molecular and bulk systems

Kevin Rossi

Establishing a unified framework for describing the structures of molecular and periodic systems is a long-standing challenge in physics, chemistry, and material science. With the rise of machine learning methods in these fields, there is a growing need fo ...

WILEY2019

Approximate Cloaking via Transformation Optics for Electromagnetic Waves

Xuan Loc Tran

Cloaking via transformation optics was introduced by Pendry, Schurig, and Smith for the Maxwell system and Leonhardt in the geometric optics setting. They used a singular change of variables which blows up a point into a cloaked region. The same transforma ...

EPFL2018

Riemannian Optimization for Solving High-Dimensional Problems with Low-Rank Tensor Structure

Michael Maximilian Steinlechner

In this thesis, we present a Riemannian framework for the solution of high-dimensional optimization problems with an underlying low-rank tensor structure. Here, the high-dimensionality refers to the size of the search space, while the cost function is scal ...

EPFL2016

Moments And Growth Indices For The Nonlinear Stochastic Heat Equation With Rough Initial Conditions

Robert Dalang, Le Chen

We study the nonlinear stochastic heat equation in the spatial domain R, driven by space-time white noise. A central special case is the parabolic Anderson model. The initial condition is taken to be a measure on R, such as the Dirac delta function, but th ...

Inst Mathematical Statistics2015

Deformation of complex structures and the coupled Kahler-Yang-Mills equations

Mario Garcia Fernandez

In this work, we define a deformation theory for the coupled Kahler-Yang-Mills equations, generalizing work of Sz,kelyhidi on constant scalar curvature Kahler metrics. We use the theory to find new solutions of the equations via deformation of the complex ...

Oxford University Press2014

On Certain Kahler Quotients of Quaternionic Kahler Manifolds

Paul Smyth

We prove that, given a certain isometric action of a two-dimensional Abelian group A on a quaternionic Kahler manifold M which preserves a submanifold N aS, M, the quotient M' = N/A has a natural Kahler structure. We verify that the assumptions on the grou ...

Springer-Verlag2013

Balanced metrics on vector bundles and polarized manifolds

Mario Garcia Fernandez

We consider a notion of balanced metrics for triples (X, L, E) which depend on a parameter alpha, where X is a smooth complex manifold with an ample line bundle L and E is a holomorphic vector bundle over X. For generic choice of alpha, we prove that the l ...

Oxford University Press2013

Some remarks on orbit sets of unimodular rows

Jean Fasel

Let A be a d-dimensional smooth algebra over a perfect field of characteristic not 2. Let Um(n+1)(A)/En+1 (A) be the set of unimodular rows of length n + 1 up to elementary transformations. If n >= (d + 2)/2, it carries a natural structure of group as disc ...

2011

On the Hodge decomposition in $\mathbb{R}^n$

Marc Troyanov

We prove a version of the

L^p

hodge decomposition for differential forms in Euclidean space and a generalization to the class of Lizorkin currents. We also compute the

L_{qp}-

cohomology of

\mathbb{R}^n

. ...

2009

Foncteurs de Mackey projectifs

This work deals with the study of projective Mackey functors. Mackey functors are algebraic structures with operations which behave like induction, restriction and conjugation in group representation theory. These objects have properties which generalize m ...

EPFL2008

Generic representations of orthogonal groups: the mixed functors

In previous work, we defined the category of functors F-quad, associated to F-2-vector spaces equipped with a nondegenerate quadratic form. In this paper, we define a special family of objects in the category F-quad, named the mixed functors. We give the c ...

2007

Soft masses in superstring models with anomalous U(1) symmetries

Claudio Scrucca

We analyze the general structure of soft scalar masses emerging in superstring models involving anomalous U(1) symmetries, with the aim of characterizing more systematically the circumstances under which they can happen to be flavor universal. We consider ...

Springer Nature2007