Alex Rutar: Visible parts and lower bounds for incidences

The visibility problem concerns the extent to which compact subsets of Euclidean space can look "exceptionally large" when viewed from typical directions. I will discuss some history and recent progress (joint with Tuomas Orponen) on the visibility problem in the plane. The new observation is that the visibility problem can be formulated in terms of lower bounds for incidences: given a collection of spatially mixed geometric objects (say, points and tubes), under what conditions can we guarantee that there are non-trivial incidences?