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Concept

Unimodular lattice

Publications associées (25)

Mean value theorems for collections of lattices with a prescribed group of symmetries

Nihar Prakash Gargava

Euclidean lattices are mathematical objects of increasing interest in the fields of cryptography and error-correcting codes. This doctoral thesis is a study on high-dimensional lattices with the motivation to understand how efficient they are in terms of b ...

EPFL2024

High-Resolution Modeling Without Computation Slowdown for PETALE in CROCUS

Andreas Pautz, Vincent Pierre Lamirand, Axel Guy Marie Laureau, Thomas Jean-François Ligonnet

In a collaboration between Ecole Polytechnique Fédérale de Lausanne (EPFL) and CEA, in the fall of 2020, the experimental Programme d’Étude en Transmission de l’Acier Lourd et ses Eléments (PETALE) was successfully carried out in the CROCUS reactor of EPFL ...

2024

Computer-assisted proof of kernel inequalities

Maryna Viazovska

This data set provides a computer-assisted proof for the kernel inequalities needed to prove universal optimality in the paper "Universal optimality of the E_8 and Leech lattices and interpolation formulas" (by Cohn, Kumar, Miller, Radchenko, and Viazovska ...

EPFL Infoscience2023

Nonlinear dynamics and Kerr frequency comb formation in lattices of coupled microresonators

Tobias Kippenberg, Alexey Tikan, Aleksandr Tusnin

Recently, substantial progress has been made in the understanding of microresonators frequency combs based on dissipative Kerr solitons (DKSs). However, most of the studies have focused on the single-resonator level. Coupled resonator systems can open new ...

Nature Portfolio2023

Phase of Topological Lattice with Leaky Guided Mode Resonance

Kirsten Emilie Moselund, Kim Seonyeong

Topological nature in different areas of physics and electronics has often been characterized and controlled through topological invariants depending on the global properties of the material. The validity of bulk-edge correspondence and symmetry-related to ...

MDPI2023

Direct high-temperature growth of single-crystalline GaN on ScAlMgO4 substrates by metalorganic chemical vapor deposition

Elison de Nazareth Matioli, Alessandro Floriduz

In this note, we demonstrate direct high-temperature growth of single-crystalline GaN on c-plane ScAlMgO4 substrates by metalorganic chemical vapor deposition, without using low-temperature buffers. We found that a trimethylaluminium preflow was crucial to ...

IOP Publishing Ltd2022

Almost impossible E_8 and Leech lattices

Maryna Viazovska

We start this short note by introducing two remarkable mathematical objects: the E8E8 root lattice Lambda8Lambda8 in 8-dimensional Euclidean space and the Leech lattice Lambda24Lambda24 in 24-dimensional space. These two lattices stand out among their lat ...

2021

Automorphisms of even unimodular lattices and equivariant Witt groups

Eva Bayer Fluckiger

We characterize the irreducible polynomials that occur as the characteristic polynomial of an automorphism of an even unimodular lattice of a given signature, generalizing a theorem of Gross and McMullen. As part of the proof, we give a general criterion i ...

EUROPEAN MATHEMATICAL SOC2020

On compact representations of Voronoi cells of lattices

Matthias Schymura, Christoph Hunkenschröder

In a seminal work, Micciancio and Voulgaris (SIAM J Comput 42(3):1364-1391, 2013) described a deterministic single-exponential time algorithm for the closest vector problem (CVP) on lattices. It is based on the computation of the Voronoi cell of the given ...

SPRINGER HEIDELBERG2020

New Results in Integer and Lattice Programming

Christoph Hunkenschröder

An integer program (IP) is a problem of the form

\min \{f(x) : \, Ax = b, \ l \leq x \leq u, \ x \in \Z^n\}

, where

A \in \Z^{m \times n}

b \in \Z^m

l,u \in \Z^n

, and

f: \Z^n \rightarrow \Z

is a separable convex objective function. The problem o ...

EPFL2020

On compact representations of Voronoi cells of lattices

Matthias Schymura, Christoph Hunkenschröder

In a seminal work, Micciancio & Voulgaris (2010) described a deterministic single-exponential time algorithm for the Closest Vector Problem (CVP) on lattices. It is based on the computation of the Voronoi cell of the given lattice and thus may need exponen ...

SPRINGER INTERNATIONAL PUBLISHING AG2018

Patching And Weak Approximation In Isometry Groups

Eva Bayer Fluckiger

Let R be a semilocal principal ideal domain. Two algebraic objects over R in which scalar extension makes sense (e.g. quadratic spaces) are said to be of the same genus if they become isomorphic after extending scalars to all completions of R and its fract ...

Amer Mathematical Soc2017

Strongly bound excitons in anatase TiO2 single crystals and nanoparticles

Helmuth Berger, Majed Chergui, Marco Grioni, Arnaud Magrez, Simon Karl Moser, Edoardo Baldini, Gerald Auböck

Anatase TiO2 is among the most studied materials for light-energy conversion applications, but the nature of its fundamental charge excitations is still unknown. Yet it is crucial to establish whether light absorption creates uncorrelated electron-hole pai ...

Nature Publishing Group2017

A variational investigation of the SU(N) Heisenberg model in antisymmetric irreducible representations

Jérôme Dufour

Motivated by recent experimental progress in the context of ultra-cold multi-colour fermionic atoms in optical lattices, this thesis investigates the properties of the antiferromagnetic SU(N) Heisenberg models with fully antisymmetric irreducible represent ...

EPFL2016

Photocapacitance spectroscopy of InAlN nearly lattice-matched to GaN

Nicolas Grandjean, Jean-François Carlin, Marcel Py, Lorenzo Lugani

We study the deep levels in InAlN nearly lattice-matched to GaN by photocapacitance spectroscopy. This technique allows the study of very deep levels having too slow thermal emission rates to be detected by other deep level spectroscopy techniques. We will ...

Amer Inst Physics2016

Improved hardness results for unique shortest vector problem

Divesh Aggarwal

The unique shortest vector problem on a rational lattice is the problem of finding the shortest non-zero vector under the promise that it is unique (up to multiplication by -1). We give several incremental improvements on the known hardness of the unique s ...

Elsevier2016

L-2-Betti numbers and Plancherel measure

Henrik Densing Petersen

We compute L-2-Betti numbers of postliminal, locally compact, unimodular groups in terms of ordinary dimensions of reduced cohomology with coefficients in irreducible unitary representations and the Plancherel measure. This allows us to compute the L-2-Bet ...

Academic Press Inc Elsevier Science2014

A sieve algorithm based on overlattices

In this paper, we present a heuristic algorithm for solving exact, as well as approximate, shortest vector and closest vector problems on lattices. The algorithm can be seen as a modified sieving algorithm for which the vectors of the intermediate sets lie ...

Cambridge Univ Press2014

Hermitian Categories, Extension Of Scalars And Systems Of Sesquilinear Forms

Eva Bayer Fluckiger, Daniel Arnold Moldovan

We prove that the category of systems of sesquilinear forms over a given hermitian category is equivalent to the category of unimodular 1-hermitian forms over another hermitian category. The sesquilinear forms are not required to be unimodular or defined o ...

Pacific Journal Mathematics2014

On the number of lattice points in a small sphere and a recursive lattice decoding algorithm

Annika Meyer

Let L be a lattice in . This paper provides two methods to obtain upper bounds on the number of points of L contained in a small sphere centered anywhere in . The first method is based on the observation that if the sphere is sufficiently small then the la ...

Springer US2013