Teng Zhang

activity

20222026

collaborators

11 papers

math.CV2026

Proof of the Agler--McCarthy entropy conjecture

Jialin Lei, Teng Zhang

In 2021, J.~Agler and J.~E. McCarthy proposed a two-step programme toward the celebrated Krzyż conjecture. The first step is to prove an entropy conjecture for polynomials whose ze…

math.CV2026

Intersections of Convex Hulls of Polynomial Shifts and Critical Points

Teng Zhang

Let $p (z)$ be a complex polynomial of degree $n \geq 2$ . For each $c \in C$ , let $K_{c}$ denote the convex hull of the zeros of $p (z) + c$ , and let $K^{'}$ denote the convex hull of…

math.FA2026

An operator triangle inequality for the quadratic symmetric modulus

Teng Zhang

50 years after Thompson's famous triangle inequality for the operator right modulus, we establish a triangle inequality for the quadratic symmetric modulus. We also discuss the cor…

math.FA2026

Johnson's determinantal identity for contiguous minors of Toeplitz matrices, with an accretive extension

Teng Zhang

Let $A$ be an $n \times n$ real Toeplitz matrix satisfying $A + A^{⊤} = 2 J_{n}$ , where $J_{n}$ is the all-ones matrix.If $A_{r} (i, j)$ denotes the $r \times r$ contiguous sub…

math.FA2026

Schur--Horn type inequalities for hyperbolic polynomials

Teng Zhang

We establish a Schur--Horn type inequality for symmetric hyperbolic polynomials. As an immediate consequence, we resolve a conjecture of Nam Q. Le on Hadamard-type inequalities for…

math.GT2026

Positive representations over real closed fields

Xenia Flamm, Nicolas Tholozan, Tianqi Wang +1

We develop the theory of $Θ$ -positive representations from general Fuchsian groups to linear groups over real closed fields. Our definition, which does not assume the boundary map…

math.GT2025

Topology of the space of $d$ -pleated surfaces

Sara Maloni, Giuseppe Martone, Filippo Mazzoli +1

Given a maximal geodesic lamination $λ$ on a closed oriented surface $S$ of genus $g$ , the space of $d$ -pleated surfaces with pleating locus $λ$ is an open subset of $\mathrm{Hom}(…

math.CV2025

Sharp Schoenberg type inequalities and the de Bruin--Sharma problem

Quanyu Tang, Teng Zhang

In this paper, we confirm two conjectures proposed by Georgiev, Gómez-Serrano, Tao, and Wagner~\cite{GGTW25} on Schoenberg type inequalities of order $4$ , thereby providing a compl…

math.FA2025

A new proof of Lee's conjecture on the Frobenius norm via the matrix Cauchy-Schwarz inequality

Teng Zhang

In 2010, Eun-Young Lee conjectured that if $A, B$ are two $n \times n$ complex matrices and $∣ A ∣, ∣ B ∣$ are the absolute values of $A, B$ , respectively, then \[…

math.FA2024

Proof of Audenaert-Kittaneh's Conjecture

Teng Zhang

By using the Three-lines theorem for a certain analytic function defined in terms of the trace and a duality argument method, we prove Audenaert-Kittaneh's conjecture related to $p…

math.ST2022

Theoretical Guarantees for Sparse Principal Component Analysis based on the Elastic Net

Teng Zhang, Haoyi Yang, Lingzhou Xue

Sparse principal component analysis (SPCA) is widely used for dimensionality reduction and feature extraction in high-dimensional data analysis. Despite many methodological and the…

Proof of the Agler--McCarthy entropy conjecture

Intersections of Convex Hulls of Polynomial Shifts and Critical Points

An operator triangle inequality for the quadratic symmetric modulus

Johnson's determinantal identity for contiguous minors of Toeplitz matrices, with an accretive extension

Schur--Horn type inequalities for hyperbolic polynomials

Positive representations over real closed fields

Topology of the space of d-pleated surfaces

Sharp Schoenberg type inequalities and the de Bruin--Sharma problem

A new proof of Lee's conjecture on the Frobenius norm via the matrix Cauchy-Schwarz inequality

Proof of Audenaert-Kittaneh's Conjecture

Theoretical Guarantees for Sparse Principal Component Analysis based on the Elastic Net

Topology of the space of $d$ -pleated surfaces