Chieu-Minh Tran

activity

20172026

most citedInterpolative Fusions I

9 citations · 34 across the 22 of their papers we have counts for

collaborators

23 papers

math.LO2026

Almost-linear Zarankiewicz bounds in $1$ -semi-equational theories

Hongyi Gou, Mostafa Mirabi, Mihir Mittal +2

We study multipartite hypergraphs definable in $1$ -semi-equational theories and prove almost-linear Zarankiewicz bounds in every fixed arity $r \geq 2$ . If $T$ is a $1$ -semi-equation…

math.LO2026

Open Problems in Mathematical Logic

George Barmpalias, Su Gao, Jialiang He +8

These open problems were presented in the Problem Sessions held during the Tianyuan Workshop on Definability and Computation, June 22-26, 2026. The problems are organized into sect…

math.GR2026

A nonabelian Brunn-Minkowski inequality II

Yifan Jing, Chieu-Minh Tran

We prove that every unimodular locally compact group $G$ of noncompact Lie dimension $n$ satisfies the sharp Brunn--Minkowski inequality \[ μ_G(XY)^{1/n}\geμ_G(X)^{1/n}+μ_G(Y)^{1/n…

math.LO2026

On Zarankiewicz's bounds for valued vector spaces

Hongyi Gou, Mihir Mittal, Chieu-Minh Tran +1

We establish absolute and relative almost-linear Zarankiewicz bounds for semilinear relations in valued vector spaces. For every fixed arity and description complexity, a $K_{t,\ld…

math.LO2026

Categoricity without Power

Jun Le Goh, Chieu-Minh Tran

We prove an analogue of Morley's categoricity theorem where cardinality is replaced by the recursion-theoretic notion of arithmetic degree. We say that a complete arithmetically de…

math.LO2025

Large implies henselian

Will Johnson, Chieu-Minh Tran, Erik Walsberg +1

Fix a field $K$ . We show that $K$ is large if and only if some elementary extension of $K$ is the fraction field of a henselian local domain which is not a field. The proof uses a…

math.CO2025

On the shatter function of semilinear set systems

Abdul Basit, Chieu-Minh Tran

We show that the shatter function of a semilinear set system on $R^{m}$ is asymptotic to a polynomial. This confirms, for the structure $(R; +, <)$ , a conjecture of…

math.GR2024

Measure doubling in unimodular locally compact groups and quotients

Zuxiang Kong, Fei Peng, Chieu-Minh Tran

We consider a (possibly discrete) unimodular locally compact group $G$ with Haar measure $μ_{G}$ , and a compact $A \subseteq G$ of positive measure with $μ_{G} (A^{2}) \leq K μ_{G} (A)$ . Let $H…

math.LO2023

Of model completeness and algebraic groups

Daniel Max Hoffmann, Piotr Kowalski, Chieu-Minh Tran +1

We show that if G is a split semisimple algebraic group over a model complete field K, then the groups G(K) and G(K)' (the commutator group which is a ``Chevalley group'' as for ex…

math.LO2023

Model Theory of Complex Numbers with Polynomial Functions

Benjamin Castle, Chieu-Minh Tran

Let $C$ be the set of complex numbers, and let $P$ be a collection of complex polynomial maps in several variables. Assuming at least one $P \in P$ depends…

math.GR2023

Measure doubling of small sets in $SO (3, R)$

Yifan Jing, Chieu-Minh Tran, Ruixiang Zhang

Let $SO (3, R)$ be the 3D-rotation group equipped with the real-manifold topology and the normalized Haar measure $μ$ . Resolving a problem by Breuillard and Green,…

math.GR2023★ 1 cited

Measure growth in compact semisimple Lie groups and the Kemperman Inverse Problem

Yifan Jing, Chieu-Minh Tran

Suppose $G$ is a compact semisimple Lie group, $μ$ is the normalized Haar measure on $G$ , and $A, A^{2} \subseteq G$ are measurable. We show that $$μ(A^2)\geq \min\{1, 2μ(A)+ημ(A)(1-…

math.GR2021★ 3 cited

On the small measure expansion phenomenon in connected noncompact nonabelian groups

Jinpeng An, Yifan Jing, Chieu-Minh Tran +1

Suppose $G$ is a connected noncompact locally compact group, $A, B$ are nonempty and compact subsets of $G$ , $μ$ is a left Haar measure on $G$ . Assuming that $G$ is unimodular, and…

math.GR2021

A Cauchy-Davenport theorem for locally compact groups

Yifan Jing, Chieu-Minh Tran

We generalize the Cauchy-Davenport theorem to locally compact groups.

math.GR2021★ 4 cited

A nonabelian Brunn-Minkowski inequality

Yifan Jing, Chieu-Minh Tran, Ruixiang Zhang

Henstock and Macbeath asked in 1953 whether the Brunn-Minkowski inequality can be generalized to nonabelian locally compact groups; questions along the same line were also asked by…

math.CO2020

Zarankiewicz's problem for semilinear hypergraphs

Abdul Basit, Artem Chernikov, Sergei Starchenko +2

A bipartite graph $H = (V_{1}, V_{2}; E)$ with $∣ V_{1} ∣ + ∣ V_{2} ∣ = n$ is semilinear if $V_{i} \subseteq R^{d_{i}}$ for some $d_{i}$ and the edge relation $E$ consists of th…

math.LO2020★ 7 cited

The étale-open topology and the stable fields conjecture

Will Johnson, Chieu-Minh Tran, Erik Walsberg +1

For an arbitrary field $K$ and $K$ -variety $V$ , we introduce the étale-open topology on the set $V (K)$ of $K$ -points of $V$ . This topology agrees with the Zariski topology, Euclide…

math.CO2020★ 6 cited

Minimal and nearly minimal measure expansions in connected unimodular groups

Yifan Jing, Chieu-Minh Tran

Let $G$ be a connected unimodular group equipped with a (left and hence right) Haar measure $μ_{G}$ , and suppose $A, B \subseteq G$ are nonempty and compact. An inequality by Kemperm…

math.LO2020

Stable formulas in ordered structures

Daniel Max Hoffmann, Chieu-Minh Tran, Jinhe Ye

We classify the stable formulas in the theory of Dense Linear Orders without endpoints, the stable formulas in the theory of Divisible Abelian Groups, and the stable formulas witho…

math.LO2019★ 2 cited

Semialgebraic methods and generalized sum-product phenomena

Yifan Jing, Souktik Roy, Chieu-Minh Tran

For a bivariate $P (x, y) \in R [x, y] ∖ (R [x] \cup R [y])$ , our first result shows that for all finite $A \subseteq R$ , $|P(A,A)|\geq α|A|^{5…

math.CO2019

Expanding Polynomials and Pairs of Polynomials in Characteristic 0

Yifan Jing, Souktik Roy, Chieu-Minh Tran

We begin a generalized study of sum-product type phenomenon in different fields by considering pairs $P (x, y)$ and $Q (x, y)$ of two variable polynomials that simultaneously exhibit s…

math.LO2018★ 9 cited

Interpolative Fusions I

Alex Kruckman, Minh Chieu Tran, Erik Walsberg

We define the interpolative fusion $T_{\cup}^{*}$ of a family $(T_{i})_{i \in I}$ of first-order theories over a common reduct $T_{\cap}$ , a notion that generalizes many examples of random…

math.LO2017★ 2 cited

The additive groups of $Z$ and $Q$ with predicates for being square-free

Neer Bhardwaj, Minh Chieu Tran

We consider the four structures $(Z; Sqf^{Z})$ , $(Z; <, Sqf^{Z})$ , $(Q; Sqf^{Q})$ , and $(\mathbb{Q}; <, \…

Almost-linear Zarankiewicz bounds in 1-semi-equational theories

Open Problems in Mathematical Logic

A nonabelian Brunn-Minkowski inequality II

On Zarankiewicz's bounds for valued vector spaces

Categoricity without Power

Large implies henselian

On the shatter function of semilinear set systems

Measure doubling in unimodular locally compact groups and quotients

Of model completeness and algebraic groups

Model Theory of Complex Numbers with Polynomial Functions

Measure doubling of small sets in SO(3,R)

Measure growth in compact semisimple Lie groups and the Kemperman Inverse Problem

On the small measure expansion phenomenon in connected noncompact nonabelian groups

A Cauchy-Davenport theorem for locally compact groups

A nonabelian Brunn-Minkowski inequality

Zarankiewicz's problem for semilinear hypergraphs

The étale-open topology and the stable fields conjecture

Minimal and nearly minimal measure expansions in connected unimodular groups

Stable formulas in ordered structures

Semialgebraic methods and generalized sum-product phenomena

Expanding Polynomials and Pairs of Polynomials in Characteristic 0

Interpolative Fusions I

The additive groups of Z and Q with predicates for being square-free

Almost-linear Zarankiewicz bounds in $1$ -semi-equational theories

Measure doubling of small sets in $SO (3, R)$

The additive groups of $Z$ and $Q$ with predicates for being square-free