– Europe/Lisbon
Room P3.10, Mathematics Building
— Online
![Alan Chang](https://math.tecnico.ulisboa.pt/seminars/uploads/82/17167464102952_photoNormal_alanchang_h180.webp)
Alan Chang, Washington University in St. Louis
Venetian blinds, digital sundials, and efficient coverings
Davies's efficient covering theorem states that we can cover any measurable set in the plane by lines without increasing the total measure. This result has a dual formulation, known as Falconer's digital sundial theorem, which states that we can construct a set in the plane to have any desired projections, up to null sets. The argument relies on a Venetian blind construction, a classical method in geometric measure theory. In joint work with Alex McDonald and Krystal Taylor, we study a variant of Davies's efficient covering theorem in which we replace lines with curves. This has a dual formulation in terms of nonlinear projections.