Publications associées à On defect groups for generalized blocks of the symmetric group

Multiplicity-free Representations of Algebraic Groups

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

The multivariate Serre conjecture ring

Luc Guyot

It is well-known that for any integral domain R, the Serre conjecture ring R(X), i.e., the localization of the univariate polynomial ring R[X] at monic polynomials, is a Bezout domain of Krull dimension

Academic Press Inc Elsevier Science2023

From Trees to Barcodes and Back Again: A Combinatorial, Probabilistic and Geometric Study of a Topological Inverse Problem

Adélie Eliane Garin

In this thesis, we investigate the inverse problem of trees and barcodes from a combinatorial, geometric, probabilistic and statistical point of view. Computing the persistent homology of a merge tree yields a barcode B. Reconstructing a tree from B invol ...

EPFL2022

Optimal radial basis for density-based atomic representations

Félix Benedito Clément Musil, Michele Ceriotti, Alexander Jan Goscinski, Jigyasa Nigam, Sergey Pozdnyakov

The input of almost every machine learning algorithm targeting the properties of matter at the atomic scale involves a transformation of the list of Cartesian atomic coordinates into a more symmetric representation. Many of the most popular representations ...

2021

Local invertibility and sensitivity of atomic structure-feature mappings

Michele Ceriotti, Sergey Pozdnyakov

Background: The increasingly common applications of machine-learning schemes to atomic-scale simulations have triggered efforts to better understand the mathematical properties of the mapping between the Cartesian coordinates of the atoms and the variety o ...

2021

From Trees to Barcodes and Back Again: Theoretical and Statistical Perspectives

Kathryn Hess Bellwald, Lida Kanari, Adélie Eliane Garin

Methods of topological data analysis have been successfully applied in a wide range of fields to provide useful summaries of the structure of complex data sets in terms of topological descriptors, such as persistence diagrams. While there are many powerful ...

2020

On arithmetic progressions in symmetric sets in finite field model

Jan Hazla

We consider two problems regarding arithmetic progressions in symmetric sets in the finite field (product space) model. ...

ELECTRONIC JOURNAL OF COMBINATORICS2020

Generalization of the Haldane conjecture to SU(n) chains

Frédéric Mila, Miklos Lajko

Recently, SU(3) chains in the symmetric and self-conjugate representations have been studied using field theory techniques. For certain representations, namely rank-psymmetric ones with pnot a multiple of 3, it was argued that the ground state exhibits gap ...

2020

Coherent actions by homeomorphisms on the real line or an interval

Yash Lodha

We study actions of groups by orientation preserving homeomorphisms on R (or an interval) that are minimal, have solvable germs at +/-infinity and contain a pair of elements of a certain dynamical type. We call such actions coherent. We establish that such ...

HEBREW UNIV MAGNES PRESS2020

Approximating nonabelian free groups by groups of homeomorphisms of the real line

Yash Lodha

We show that for a large class C of finitely generated groups of orientation preserving homeomorphisms of the real line, the following holds: Given a group G of rank k in C, there is a sequence of k-markings (G,S-n), n is an element of N whose limit in the ...

2020

Haldane Gap of the Three-Box Symmetric SU(3) Chain

Frédéric Mila, Samuel Gozel, Pierre Marcel Nataf

Motivated by the recent generalization of the Haldane conjecture to SU(3) chains [Lajko et al., Nucl. Phys. B924, 508 (2017)] according to which a Haldane gap should be present for symmetric representations if the number of boxes in the Young diagram is a ...

2020

Large charge, semiclassics and superfluids : from broken symmetries to conformal field theories

Gabriel Francisco Cuomo

This thesis explores the application of semiclassical methods in the study of states with large quantum numbers for theories invariant under internal symmetries. In the first part of the thesis, we study zero-temperature superfluids. These provide a gener ...

EPFL2020

Aspects of Gauge Theories Vacua

Adrien Florio

This thesis is concerned with gauge theories, their complicated vacuum and resulting effects. After an introduction to the subject, it is divided into four parts. Firstly, we treat the problem of chiral charge dynamics at finite temperature. Quantum field ...

EPFL2020

Extensive amenability and a Tits alternative for topological full groups

Nóra Gabriella Szoke

This dissertation investigates the amenability of topological full groups using a property of group actions called extensive amenability. Extensive amenability is a core concept of several amenability results for groups of dynamical origin. We study its pr ...

EPFL2019

Hasse principles for multinorm equations

Eva Bayer Fluckiger, Ting-Yu Lee

A classical result of Hasse states that the norm principle holds for finite cyclic extensions of global fields, in other words local norms are global norms. We investigate the norm principle for finite dimensional commutative kale algebras over global fiel ...

2019

Characteristic classes as complete obstructions

Martina Rovelli

In the first part of this paper, we propose a uniform interpretation of characteristic classes as obstructions to the reduction of the structure group and to the existence of an equivariant extension of a certain homomorphism defined a priori only on a sin ...

SPRINGER HEIDELBERG2019

The Center of Small Quantum Groups I: The Principal Block in Type A

Anna Lachowska

We develop an elementary algebraic method to compute the center of the principal block of a small quantum group associated with a complex semisimple Lie algebra at a root of unity. The cases of sl(3) and sl(4) are computed explicitly. This allows us to for ...

OXFORD UNIV PRESS2018

Non-Abelian chiral spin liquid in a quantum antiferromagnet revealed by an iPEPS study

Abelian and non-Abelian topological phases exhibiting protected chiral edge modes are ubiquitous in the realm of the fractional quantum Hall (FQH) effect. Here, we investigate a spin-1 Hamiltonian on the square lattice which could, potentially, host the sp ...

2018

Arithmetic and geometric structures in cryptography

Benjamin Pierre Charles Wesolowski

We explore a few algebraic and geometric structures, through certain questions posed by modern cryptography. We focus on the cases of discrete logarithms in finite fields of small characteristic, the structure of isogeny graphs of ordinary abelian varietie ...

EPFL2018

On finitely generated modules over quasi-Euclidean rings

Luc Guyot

Let R be a unital commutative ring, and let M be an R-module that is generated by k elements but not less. Let be the subgroup of generated by the elementary matrices. In this paper we study the action of by matrix multiplication on the set of unimodular r ...

Springer Verlag2017