Publications related to Automorphisms of even unimodular lattices and equivariant Witt groups

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

Four-Variable Expanders Over The Prime Fields

Adrian Claudiu Valculescu, Van Thang Pham

Let F-p be a prime field of order p > 2, and let A be a set in F-p with very small size in terms of p. In this note, we show that the number of distinct cubic distances determined by points in A x A satisfies vertical bar(A - A)(3) + (A - A)(3 vertical bar ...

AMER MATHEMATICAL SOC2018

The sphere packing problem in dimension 24

Maryna Viazovska, Abhinav Kumar

Building on Viazovska’s recent solution of the sphere packing problem in eight dimensions, we prove that the Leech lattice is the densest packing of congruent spheres in twenty-four dimensions and that it is the unique optimal periodic packing. In particul ...

2017

ON THE DISCRETE LOGARITHM PROBLEM IN FINITE FIELDS OF FIXED CHARACTERISTIC

Robert Granger, Thorsten Kleinjung, Jens Markus Zumbrägel

For~

q

a prime power, the discrete logarithm problem (DLP) in~

\F_{q}

consists in finding, for any

g \in \mathbb{F}_{q}^{\times}

and

h \in \langle g \rangle

, an integer~

x

such that

g^x = h

. We present an algorithm for computing discrete logarithm ...

2016

Fibre Products of Supersingular Curves and the Enumeration of Irreducible Polynomials with Prescribed Coefficients

Robert Granger

For any positive integers

n\geq 3, r\geq 1

we present formulae for the number of irreducible polynomials of degree

n

over the finite field

\mathbb{F}_{2^r}

where the coefficients of

x^{n-1}

,

x^{n-2}

and

x^{n-3}

are zero. Our proofs involve coun ...

Elsevier2016

Universe and Matter Conjectured as a 3-Dimensional Lattice with Topological Singularities

Gérard Gremaud

One fundamental problem of modern physics is the search for a theory of everything able to explain the nature of space-time, what matter is and how matter interacts. There are various propositions, as Grand Unified Theory, Quantum Gravity, Supersymmetry, S ...

2016

Universe and Matter conjectured as a 3-dimensional Lattice with Topological Singularities

Gérard Gremaud

One fundamental problem of modern physics is the search for a theory of everything able to explain the nature of space-time, what matter is and how matter interacts. There are various propositions, as Grand Unified Theory, Quantum Gravity, Supersymmetry, S ...

Amazon2016

On the discrete logarithm problem in finite fields of fixed characteristic

Robert Granger, Thorsten Kleinjung, Jens Markus Zumbrägel

For

q

a prime power, the discrete logarithm problem (DLP) in

\mathbb{F}_q

consists in finding, for any

g \in \mathbb{F}_{q}^{\times}

and

h \in \langle g \rangle

, an integer

x

such that

g^x = h

. We present an algorithm for computing discrete log ...

2015

Isometries of quadratic spaces

Eva Bayer Fluckiger

Let k be a global field of characteristic not 2, and let f is an element of k[X] be an irreducible polynomial. We show that a non-degenerate quadratic space has an isometry with minimal polynomial f if and only if such an isometry exists over all the compl ...

European Mathematical Soc2015

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

Automorphisms of even unimodular lattices and equivariant Witt groups

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On compact representations of Voronoi cells of lattices

Four-Variable Expanders Over The Prime Fields

The sphere packing problem in dimension 24

ON THE DISCRETE LOGARITHM PROBLEM IN FINITE FIELDS OF FIXED CHARACTERISTIC

Fibre Products of Supersingular Curves and the Enumeration of Irreducible Polynomials with Prescribed Coefficients

Universe and Matter Conjectured as a 3-Dimensional Lattice with Topological Singularities

Universe and Matter conjectured as a 3-dimensional Lattice with Topological Singularities

On the discrete logarithm problem in finite fields of fixed characteristic

Isometries of quadratic spaces

Hermitian Categories, Extension Of Scalars And Systems Of Sesquilinear Forms

The sphere packing problem in dimension 24

Fibre Products of Supersingular Curves and the Enumeration of Irreducible Polynomials with Prescribed Coefficients

ON THE DISCRETE LOGARITHM PROBLEM IN FINITE FIELDS OF FIXED CHARACTERISTIC

Universe and Matter conjectured as a 3-dimensional Lattice with Topological Singularities

Universe and Matter Conjectured as a 3-Dimensional Lattice with Topological Singularities

On the discrete logarithm problem in finite fields of fixed characteristic

Isometries of quadratic spaces

On compact representations of Voronoi cells of lattices

Hermitian Categories, Extension Of Scalars And Systems Of Sesquilinear Forms

Four-Variable Expanders Over The Prime Fields