Distance problems; Incidence geometry; Falconer ; extension theorems; Finite fields
PhamVan Thang (2021), An asymmetric bound for sum of distance sets, in Proceedings of the Steklov Institute of Mathematics
, 314, 290-300.
PhamVan Thang (2021), Extension theorems and a connection to the Erd os-Falconer distance problem over finite fields, in Journal of Functional Analysis
, 281(8), 109137.
PhamVan Thang, Mattila–Sjolin type functions: A finite field model, in Vietnam Journal of Mathematics
PhamVan Thang, On the Finite Field Cone Restriction Conjecture in Four Dimensions and Applications in Incidence Geometry, in International Mathematics Research Notices
PhamVan Thang, On the Mattila-Sjolin distance theorem for product sets, in Mathematika
PhamVan Thang, On the pinned distances problem over finite fields, in Journal of London Mathematical Society
In this research project, the PI will focus on two topics: Erdos-Falconer distance conjecture and Extension/Restriction theorems over finite fields. These topics lie on the intersection of Discrete Geometry and Number Theory. The PI plans to study these topics by employing algebraic methods, Fourier analysis methods, probabilistic methods, tools from additive number theory, and incidence machinery.