Dung The Tran

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20222026

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math.CO2025

Additive structures imply more distances in $F_{q}^{d}$

Daewoong Cheong, Gennian Ge, Doowon Koh +3

For a set $E \subseteq F_{q}^{d}$ , the distance set is defined as $Δ (E) := {∥ x - y ∥ : x, y \in E}$ , where $∥ \cdot ∥$ denotes the stand…

math.CO2025

A functional Loomis-Whitney type inequality in the Heisenberg group and projection theorems over finite fields

Daewoong Cheong, Thang Pham, Dung The Tran

We establish functional Loomis--Whitney type inequalities in the finite Heisenberg group $H^{n} (F_{q})$ . For $n = 1$ , we determine the sharp region of exponents $(u_1,u…

math.CO2022

The Erdos-Falconer distance problem in the tree setting

Thang Pham, Steven Senger, Dung The Tran

The recent breakthrough of Guth, Iosevich, Ou, and Wang (2019) on the Falconer distance problem states that for a compact set $A \subset R^{2}$ , if the Hausdorff dimension of…

Additive structures imply more distances in Fqd​

A functional Loomis-Whitney type inequality in the Heisenberg group and projection theorems over finite fields

The Erdos-Falconer distance problem in the tree setting

Additive structures imply more distances in $F_{q}^{d}$