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Catégorie

Géométrie discrète

Publications associées (12)

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

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

Some Mordell-Weil lattices and applications to sphere packings

Gauthier Leterrier

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

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

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

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

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

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

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

Sharp sphere packings

Maryna Viazovska

In this talk we will speak about recent progress on the sphere packing problem. The packing problem can be formulated for a wide class of metric spaces equipped with a measure. An interesting feature of this optimization problem is that a slight change of ...

World Scientific Publishing2018

Scaling for hard-sphere colloidal glasses near jamming

Eric DeGiuli

Hard-sphere colloids are model systems in which to study the glass transition and universal properties of amorphous solids. Using covariance matrix analysis to determine the vibrational modes, we experimentally measure here the scaling behavior of the dens ...

IOP Publishing - EPL Association2016

Optical Mirror from Laser-Trapped Mesoscopic Particles

Johann Rohner

Trapping of mesoscopic particles by optical forces usually relies on the gradient force, whereby particles are attracted into optical wells formed by landscaping the intensity of an optical field. This is most often achieved by optical Gaussian beams, inte ...

Amer Physical Soc2014

Publications associées (12)