Nhan D. V. Nguyen

activity

20242026

collaborators

7 papers

math.AG2026

A Chow-Type theorem from asymptotic directions

Nhan Nguyen

Let $X \subset C^{n}$ be a closed pure $d$ -dimensional complex analytic set. We associate to $X$ its set of projective asymptotic directions $$ Σ_\infty(X) :=\{\ell \in \mathb…

math.PR2026

Real roots of non-centered random polynomials

Yen Q. Do, Nhan D. V. Nguyen, Sean O'Rourke

We study the fluctuations of the number of real roots of random polynomials with independent, nonzero-mean coefficients. Such non-centered ensembles arise naturally in signal-plus-…

math.AG2025

Bi-H"older invariants in o-minimal structures

An V. Q. Huynh, Minh B. Nguyen, Nhan X. V. Nguyen +1

We prove that for any two definable germs in a polynomially bounded o-minimal structure, there exists a critical threshold $I^\pm_{0} \in (0, 1)$ such that if these germs are bi- $I^\pm$ -H"o…

math.AG2025

Classification of Lipschitz unimodal function germs

Nhan Nguyen, Maria Ruas, Saurabh Trivedi

In this paper, we introduce the notion of Lipschitz modality for isolated singularities $f : (C^{n}, 0) \to (C, 0)$ and provide a complete classification of Lipschi…

math.PR2025

Real roots of random polynomials: asymptotics of the variance

Yen Q. Do, Nhan D. V. Nguyen

We compute the precise leading asymptotics of the variance of the number of real roots for a large class of random polynomials, where the random coefficients have polynomial growth…

math.AG2025

A bi-Lipschitz invariant for analytic function germs

Nhan Nguyen

In this paper, we introduce a new bi-Lipschitz invariant for analytic function germs in two variables, enhancing the Henry-Parusinski invariant.