Publications associées à Close-packing of equal spheres

Some Mordell-Weil lattices and applications to sphere packings

We provide new explicit examples of lattice sphere packings in dimensions 54, 55, 162, 163, 486 and 487 that are the densest known so far, using Kummer families of elliptic curves over global function fields. In some cases, these families of elliptic curve ...

EPFL2024

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

Six-dimensional sphere packing and linear programming

Maryna Viazovska, Matthew De Courcy-Ireland, Maria Margarethe Dostert

We prove that the Cohn-Elkies linear programming bound for sphere packing is not sharp in dimension 6. The proof uses duality and optimization over a space of modular forms, generalizing a construction of Cohn- Triantafillou [Math. Comp. 91 (2021), pp. 491 ...

Amer Mathematical Soc2024

Incommensurate phases

Gervais Chapuis

Incommensurately modulated crystalline phases are part of a more general family called aperiodic crystals. Their symmetry is treated within the theoretical framework of superspace groups that is a generalization of the 3D space groups that are used for con ...

Academic Press2024

Lattice packings through division algebras

Nihar Prakash Gargava

In this text, we will show the existence of lattice packings in a family of dimensions by employing division algebras. This construction is a generalization of Venkatesh's lattice packing result Venkatesh (Int Math Res Notices 2013(7): 1628-1642, 2013). In ...

SPRINGER HEIDELBERG2023

Dense Packings via Lifts of Codes to Division Rings

Vlad Serban, Nihar Prakash Gargava

obtain algorithmically effective versions of the dense lattice sphere packings constructed from orders in Q-division rings by the first author. The lattices in question are lifts of suitable codes from prime characteristic to orders O in Q-division rings a ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2023

Colloidal self-assembly of soft neural interfaces from injectable photovoltaic microdevices

Mahmut Selman Sakar, Zhangjun Huang, Murat Kaynak, Haiyan Jia

Biomimetic retinas with a wide field of view and high resolution are in demand for neuroprosthetics and robot vision. Conventional neural prostheses are manufactured outside the application area and implanted as a complete device using invasive surgery. He ...

2023

On the Mordell-Weil lattice of y(2) = x(3) + bx plus t(3n+1) in characteristic 3

Gauthier Leterrier

We study the elliptic curves given by y(2) = x(3) + bx + t(3n+1) over global function fields of characteristic 3 ; in particular we perform an explicit computation of the L-function by relating it to the zeta function of a certain superelliptic curve u(3) ...

SPRINGER INT PUBL AG2022

Crystallization kinetics of atomic crystals revealed by a single-shot and single-particle X-ray diffraction experiment

Christoph Bostedt, Alessandro Colombo, Giorgio Rossi

Crystallization is a fundamental natural phenomenon and the ubiquitous physical process in materials science for the design of new materials. So far, experimental observations of the structural dynamics in crystallization have been mostly restricted to slo ...

National Academy of Sciences2021

New dense superball packings in three dimensions

Maria Margarethe Dostert

We construct a new family of lattice packings for superballs in three dimensions (unit balls for the l(3)(p) norm) with p epsilon (1, 1.58]. We conjecture that the family also exists for p epsilon (1.58, log(2) 3 = 1.5849625 ...]. Like in the densest latti ...

WALTER DE GRUYTER GMBH2020