Dung The Tran

activity

20222026

collaborators

5 papers

math.OC2026

Existence of Quantum Splines via Fourth-Order Gradient Flows

Chun-Chi Lin, Yang-Kai Lue, Dung The Tran

We establish a rigorous existence theory for the quantum splines introduced by Brody, Holm, and Meier in Physical Review Letters (2012). These curves arise as solutions of a variat…

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.OC2023

Higher-order Riemannian spline interpolation problems: a unified approach by gradient flows

Chun-Chi Lin, Dung The Tran

This paper addresses the problems of spline interpolation on smooth Riemannian manifolds, with or without the inclusion of least-squares fitting. Our unified approach utilizes grad…

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…

Existence of Quantum Splines via Fourth-Order Gradient Flows

Additive structures imply more distances in Fqd​

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

Higher-order Riemannian spline interpolation problems: a unified approach by gradient flows

The Erdos-Falconer distance problem in the tree setting

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