Palestras e Seminários
05/11/2024
16:00
Auditório Luiz Antônio Fávaro
Palestrante: Sinai Robins
Responsável: Ali Tahzibi (Este endereço de email está sendo protegido de spambots. Você precisa do JavaScript ativado para vê-lo.)
Colóquio de Matemática
Abstract. We extend the Bombieri-Siegel formula from the geometry of numbers, by studying a lattice sum of the cross-covariogram of any two bounded sets A, B ⊂ R^d . Using Poisson summation, our extension also refines the summation index of the Bombieri-Siegel formula, allowing us to obtain some interesting applications. One of the consequences of these results is a new characterization of multi-tiling Euclidean space by translations of a compact set. Another consequence is a spectral formula for the volume of a compact set.
Finally, we give an application to arithmetic combinatorics, namely an identity for finite sums of discrete covariograms over any set of integer points in Z^d . As a consequence, we arrive at an equivalent condition for multi-tiling Z^d by any finite set of integer points. This is joint work with Michel Faleiros Martins.
