Speaker Introduction

Dr. Francesco Gallinaro got his PhD in 2022 at the University of Leeds, Actually, Dr. Francesco Gallinaro is a Postdoc in the Logic group at the University of Pisa working mostly on the model theory of the exponential function. On the side of exponential fields Dr. Francesco Gallinaro mostly interested in Zilber’s conjectures predicting that the complex exponential field is quasiminimal and exponentially algebraically closed. Moreover, on the side of valued fields, he is interested in the connections between model theory and tropical geometry.

Abstract

Let W be an algebraic subvariety of the complex multiplicative group Gn m, and H an algebraic subgroup of Gn m such that dim W + dim H is at least n. What can we say about intersections between W and cosets of H? We show that if W satisfies a condition known as geometrical non-degeneracy, there is a finite set S of subgroups, depending only on W, such that if H is not contained in any of the elements of S then every coset of H intersects W. The ingredients of the proof come from tropical geometry, equidistribution, and model theory. This is joint work with G. Dill.