**abstract:**
Abstract: Let \(\Lambda\) be a lattice in \(\mathbb{R}^n\), and let
\(Z\subseteq \mathbb{R}^{m+n}\) be a
parameterized family of subsets \(Z_T\) of \(\mathbb{R}^n\). We are
interested in the cardinality \(|\Lambda\cap Z_T|\).
Using o-minimal structures from model theory we prove for fairly general
families \(Z\) an estimate which is also quite precise in terms
of the successive minima of the lattice, and the \(j\)-dimensional
volumes of the projections of \(Z_T\) to the \(j\)-dimensional coordinate
spaces
(where \(1\leq j\leq n-1\)). This is joint work with Fabrizio Barroero.

Fri 21 Sep, 11:20 - 11:50, Sala Conferenze Centro De Giorgi

Abstract

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