Publications related to General linear group

Unlikely intersections on the p-adic formal ball

We investigate generalizations along the lines of the Mordell-Lang conjecture of the author's p-adic formal Manin-Mumford results for n-dimensional p-divisible formal groups F. In particular, given a finitely generated subgroup (sic) of F(Q(p)) and a close ...

SPRINGER INT PUBL AG2023

Gait Phase Estimation in Steady Walking: A Comparative Study of Methods Based on the Phase Portrait of the Hip Angle

Auke Ijspeert, Mohamed Bouri, Ali Reza Manzoori, Coline Lugaz, Tian Ye, Davide Malatesta

Accurate real-time estimation of the gait phase (GP) is crucial for many control methods in exoskeletons and prostheses. A class of approaches to GP estimation construct the phase portrait of a segment or joint angle, and use the normalized polar angle of ...

IEEE Xplore2023

Eigenvalue multiplicities of group elements in irreducible representations of simple linear algebraic groups

Ana-Maria Retegan

Let k be an algebraically closed field of arbitrary characteristic, let G be a simple simply connected linear algebraic group and let V be a rational irreducible tensor-indecomposable finite-dimensional kG-module. For an element g of G we denote by $V_{g}( ...

EPFL2022

Lie groups as permutation groups: Ulam's problem in the nilpotent case

Nicolas Monod

Ulam asked whether every connected Lie group can be represented on a countable structure. This is known in the linear case. We establish it for the first family of non-linear groups, namely in the nilpotent case. Further context is discussed to illustrate ...

WALTER DE GRUYTER GMBH2022

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

Spherical birational sheets in reductive groups

Filippo Ambrosio

We classify the spherical birational sheets in a complex simple simply-connected algebraic group. We use the classification to show that, when G is a connected reductive complex algebraic group with simply-connected derived subgroup, two conjugacy classes ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2021

Invariant Integrals on Topological Groups and Applications

Vasco Schiavo

We study a fixed point property for linear actions of discrete groups on weakly complete convex proper cones in locally convex topological vector spaces. We search to understand the class of discrete groups which enjoys this property and we try to generali ...

EPFL2021

Arithmetically rigid schemes via deformation theory of equivariant vector bundles

Maciej Emilian Zdanowicz

We analyze the deformation theory of equivariant vector bundles. In particular, we provide an effective criterion for verifying whether all infinitesimal deformations preserve the equivariant structure. As an application, using rigidity of the Frobenius ho ...

SPRINGER HEIDELBERG2021

Phase retrieval in high dimensions: Statistical and computational phase transitions

Florent Gérard Krzakala, Lenka Zdeborová, Bruno Loureiro, Bruno Loureiro

We consider the phase retrieval problem of reconstructing a n -dimensional real or complex signal X ⋆ from m (possibly noisy) observations Y μ = | ∑ n i = 1 Φ μ i X ⋆ i / √ n | , for a large class of correlated real and complex random sensing matrices Φ , ...

Curran Associates, Inc.2020

Weak teachers: assisted specification of discrete choice models using ensemble learning algorithms

Timothy Michael Hillel

Discrete Choice Models (DCMs) have a distinct advantage over Machine Learning (ML) classification algorithms, in that they employ a highly interpretable linear structure. However, a key drawback of DCMs compared to ML is the need to specify the utility fun ...

2019

Non-linear modelling of saturated internal and external MHD instabilities in tokamaks

Andreas Kleiner

Macroscopic instabilities and their unfavourable effects on plasma confinement pose a central challenge for the development of reactor relevant tokamak scenarios. Some promising operation scenarios feature extended regions of low magnetic shear. These are ...

EPFL2019

Cryptanalysis of Enhanced MORE

Serge Vaudenay, Damian Vizár

Fully homomorphic encryption (FHE) has been among the most popular research topics of the last decade. While the bootstrapping-based, public key cryptosystems that follow Gentry's original design are getting more and more efficient, their performance is st ...

2018

Reductive overgroups of distinguished unipotent elements in simple algebraic groups

Mikko Tapani Korhonen

Let

G

be a simple linear algebraic group over an algebraically closed field

K

of characteristic

p \geq 0

. In this thesis, we investigate closed connected reductive subgroups

X < G

that contain a given distinguished unipotent element

u

of

G

. Our ...

EPFL2018

Stable and Passive High-Power Dual Active Bridge Converters Interfacing MVDC Grids

Drazen Dujic, Francisco Daniel Freijedo Fernández, Enrique Rodriguez Diaz

Dual active bridge (DAB) is a topology that is receiving more and more attention as a potential solution to interface dc grids of different voltage levels. From a system level, the implications of DABs on the stability of complex power systems are addresse ...

2018

On the fundamental domain of affine Springer fibers

Zongbin Chen

Let G be a connected reductive algebraic group over an algebraically closed field k,gamma is an element of g( k(( epsilon ))) a semisimple regular element, we introduce a fundamental domain F gamma for the affine Springer fibers X gamma. We show that the p ...

Springer Heidelberg2017

Invariant forms on irreducible modules of simple algebraic groups

Mikko Tapani Korhonen

Let G be a simple linear algebraic group over an algebraically dosed field K of characteristic p >= 0 and let V be an irreducible rational G-module with highest weight A. When is self-dual, a basic question to ask is whether V has a non-degenerate G-invari ...

Elsevier2017

Bilinear forms with Kloosterman sums and applications

Philippe Michel

We prove nontrivial bounds for general bilinear forms in hyper-Kloosterman sums when the sizes of both variables may be below the range controlled by Fourier-analytic methods (Polya-Vinogradov range). We then derive applications to the second moment of cus ...

Annal Mathematics2017

Linear and non-linear studies of spurious backward-wave instabilities in a smooth-wall gyrotron beam duct

Stefano Alberti, Jérémy Genoud, Trach-Minh Tran

Recently developed self-consistent models for beam-wave interaction simulations of a gyrotron oscillator are used to study spurious backward-wave instabilities in smooth-wall metallic beam ducts. Starting from a simple case with a basic geometry, the influ ...

2017

Generalization of the Concept of Extents to Distributed Reaction Systems

Dominique Bonvin, Julien Léo Billeter, Diogo Filipe Mateus Rodrigues

In the chemical industry, a large class of processes involving reactions can be described by partial differential equations that depend on time and on one or more spatial coordinates. Examples of such distributed reaction systems are tubular reactors and r ...

Elsevier2017

Special Reductive Groups Over An Arbitrary Field

Mathieu Huruguen

A linear algebraic group G defined over a field k is called special if every G-torsor over every field extension of k is trivial. In 1958 Grothendieck classified special groups in the case where the base field is algebraically closed. In this paper we desc ...

Springer Birkhauser2016