Seminar
Date and Time
-
Location
Math Sci 111
Organizers
Speaker
Alan Chang (Washington University St Louis)
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.