Publications related to Unimodular lattice

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

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

Single-Mode Laser in the Telecom Range by Deterministic Amplification of the Topological Interface Mode

Kirsten Emilie Moselund, Chang Won Lee

Photonic integrated circuits are paving the way for novel on-chip functionalities with diverse applications in communication, computing, and beyond. The integration of on-chip light sources, especially single-mode lasers, is crucial for advancing those pho ...

Washington2024

Computer-assisted proof of kernel inequalities

Maryna Viazovska, Abhinav Kumar

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, Aleksandr Tusnin, Kenichi Komagata, Alexey Tikan

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 ...

Berlin2023

Moments of the number of points in a bounded set for number field lattices

Maryna Viazovska, Nihar Prakash Gargava, Vlad Serban

We examine the moments of the number of lattice points in a fixed ball of volume

V

for lattices in Euclidean space which are modules over the ring of integers of a number field

K

. In particular, denoting by

ω_K

the number of roots of unity in

K

, we ...

arXiv2023

Phase of Topological Lattice with Leaky Guided Mode Resonance

Kirsten Emilie Moselund, Chang Won Lee

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 ...

Basel2023

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

Vital role of magnetocrystalline anisotropy in cubic chiral skyrmion hosts

Henrik Moodysson Rønnow, Jonathan White

Magnetic anisotropy is anticipated to govern the formation of exotic spin textures reported recently in cubic chiral magnets, like low-temperature tilted conical and skyrmion lattice (SkL) states and metastable SkLs with various lattice geometry. Motivated ...

NATURE RESEARCH2021

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

Unimodular lattice

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

Single-Mode Laser in the Telecom Range by Deterministic Amplification of the Topological Interface Mode

Computer-assisted proof of kernel inequalities

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

Moments of the number of points in a bounded set for number field lattices

Phase of Topological Lattice with Leaky Guided Mode Resonance

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

Almost impossible E_8 and Leech lattices

Vital role of magnetocrystalline anisotropy in cubic chiral skyrmion hosts

Automorphisms of even unimodular lattices and equivariant Witt groups

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

Computer-assisted proof of kernel inequalities

Almost impossible E_8 and Leech lattices

Phase of Topological Lattice with Leaky Guided Mode Resonance

Automorphisms of even unimodular lattices and equivariant Witt groups

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

Vital role of magnetocrystalline anisotropy in cubic chiral skyrmion hosts

Moments of the number of points in a bounded set for number field lattices

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

Single-Mode Laser in the Telecom Range by Deterministic Amplification of the Topological Interface Mode