Research interest:

One of the most important questions in Geometric measure theory and Combinatorics is: How large does a given set in vector space (F_q^d or R^d) need to be to make sure that it contains copies of a given configuration of points?

For example, I am interested in Falconer distance conjecture and related problems.
Falconer distance conjecture says that for any compact set A ⊂ R^d of Hausdorff dimension greater than d/2, the distance set ∆(A) is of positive Lebesgue measure. The best-known result in plane due to Guth, Iosevich, Ou, and Wang (2019)  gave the exponent 5/4, and the conjecture is still open.

My Co-Authors (11)