UBC Discrete Math Seminar: Semin Yoo

Let A and B be compact sets in ℝd. One of the fundamental problems in geometric measure theory is to study the relations between the Hausdorff dimensions of A, B, and A∩f(B), where f runs through a set of transformations. This type of question has been studied intensively by many mathematicians such as Bishop, Elekes, Falconer, Mattila, Kahane, Keleti, and Peres. In this talk, we discuss our recent results on the discrete analog of such questions arising from geometric measure theory. Our approach is based on several techniques including algebraic methods and discrete Fourier analysis. This is joint work with Thang Pham.