Hong Wang

Given a set T of distinct \delta-tubes and a set P of disjoint \delta-balls in R^n, the set of incidences between T and P is defined as I(P,T)={(p,l)∈P×T:p∩l≠∅}. The well-known Szemeredi-Trotter theorem in combinatorics studies a discrete analogue...

We prove some Szemeredi-Trotter type estimates for tubes in the plane under some natural assumptions. Joint works with Ciprian Demeter and with Shukun Wu (in progress), which are based on the Furstenberg sets estimate proved by Orponen-Shmerkin, and...

If E is a compact set of Hausdorff dimension s > 1 on the plane, then its distance set was conjectured (by Falconer 1985) to have positive Lebesgue measure. Joint with Guth, Iosevich and Ou, we show that dim E > 5/4 is a sufficient condition. This...