CRM: Centro De Giorgi
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ERC Research Period on Diophantine Geometry

Counting lattice points and o-minimal structures (30')

speaker: Martin Widmer (Scuola Normale Superiore)

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


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