Speaker: Francesco Veneziano (ESI Vienna and TU Graz)
Title: Torsion-anomalous intersections
Anomalous Intersections are a fairly recent framework introduced by Bombieri, Masser and Zannier, which comprises and generalises a vast body of problems and conjectures
in Arithmetic Geometry. Let $V$ be a variety contained in a group variety $G$, which is usually taken to be an abelian variety or a torus.
When intersecting $V$ with an algebraic subgroup $B$, if the intersection $V\cap B$ has a component of dimension strictly greater than "expected", then such a component
is said to be torsion-anomalous. In analogy with many fundamental results in the field, there are conjectures giving geometrical conditions for the variety $V$ to have
only finitely many (maximal) torsion-anomalous subvarieties. The formulation of these conjectures generalises famous problems such as the Manin-Mumford Conjecture and is
related to the Mordell-Lang problem.