Let X be a complex projective K3 surface and let T-X be its transcendental lattice; the characteristic polynomials of isometries of T-X induced by automorphisms of X are powers of cyclotomic polynomials. Which powers of cyclotomic polynomials occur? The ai ...
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 ...
The “Multivariate Ring Learning with Errors” problem was presented as a generalization of Ring Learning with Errors (RLWE), introducing efficiency improvements with respect to the RLWE counterpart thanks to its multivariate structure. Nevertheless, the rec ...
The Ring Learning with Errors (RLWE) problem has become one of the most widely used cryptographic assumptions for the construction of modern cryptographic primitives. Most of these solutions make use of power-of-two cyclotomic rings mainly due to its simpl ...
We explore a few algebraic and geometric structures, through certain questions posed by modern cryptography. We focus on the cases of discrete logarithms in finite fields of small characteristic, the structure of isogeny graphs of ordinary abelian varietie ...
The worst-case hardness of finding short vectors in ideals of cyclotomic number fields (Ideal-SVP) is a central matter in lattice based cryptography. Assuming the worst-case hardness of Ideal-SVP allows to prove the Ring-LWE and Ring-SIS assumptions, and t ...
We establish several results towards the two-variable main conjecture of Iwasawa theory for elliptic curves without complex multiplication over imaginary quadratic fields, namely (i) the existence of an appropriate p-adic L-function, building on works of H ...
A set of low-strain commensurate interface structures for epitaxial graphene on SiC(0001) are obtained by combining rotated graphene supercells with m x m or m root 3 x m root 3R30 degrees SiC cells. For two among the interfaces with lowest strain, corresp ...
Let u(q)(g) be the small quantum group associated with a complex semisimple Lie algebra g and a primitive root of unity q, satisfying certain restrictions. We establish the equivalence between three different actions of g on the center of u(q)(g) and on th ...
We present a technique for the approximation of a class of Hilbert space--valued maps which arise within the framework of model order reduction (MOR) for parametric partial differential equations, whose solution map has a meromorphic structure. Our MOR str ...
