155 citations · 967 across the 61 of their papers we have counts for
63 papers
The complexity of computing the covering radius of a Euclidean lattice
Frank Vallentin
In this note, we prove that the covering radius problem for Euclidean lattices is complete for the second level of the polynomial hierarchy. The note also documents the author's fi…
Sums of squares in polynomial time
Nikolas Gärtner, Victor Magron, Frank Vallentin
In this paper, we analyze the bit complexity of deciding whether a given polynomial can be represented as a sum of squares of polynomials. We show that the weak membership problem…
Bounding the density of spherical polygon packings
Fernando Mário de Oliveira Filho, Andreas Spomer, Frank Vallentin
We determine putative optimal packings of regular spherical polygons via optimization on smooth manifolds. For several cases, we establish maximality by extending the Lovász theta…
Conic optimization for extremal geometry
Frank Vallentin
The aim of this paper is to highlight recent progress in using conic optimization methods to study geometric packing problems. We will look at four geometric packing problems of di…
Critical modular lattices in the Gaussian core model
Arian Joharian, Frank Vallentin, Marc Christian Zimmermannn
We discuss the local analysis of Gaussian potential energy of modular lattices. We present examples of -modular lattices -- such as the -dimensional Barnes-Wall lattice -- a…
Polarization of lattices: Stable cold spots and spherical designs
Christine Bachoc, Philippe Moustrou, Frank Vallentin +1
We consider the problem of finding the minimum of inhomogeneous Gaussian lattice sums: Given a lattice and a positive constant , the goal is to find t…