Duc-Manh Nguyen

activity

20102026

most citedWeierstrass Prym eigenforms in genus four

14 citations · 98 across the 25 of their papers we have counts for

collaborators

28 papers

math.AG2026

Hilbert surfaces, modular forms, and Siegel-Veech constants

Duc-Manh Nguyen

We give the values of the Siegel-Veech constants associated with saddle connections having distinct endpoints on translation surfaces in Prym eigenform loci in $Ω\mathcal{M}_3(2,2)…

math.GT2025

Intersection theory and Siegel-Veech constants for Prym eigenform loci in $Ω M_{3} (2, 2)^{odd}$

Duc-Manh Nguyen

We compute the Siegel-Veech constants associated to saddle connections with distinct endpoints on Prym eigenforms for real quadratic orders with non-square discriminant in $Ω\mathc…

cs.CL2025

SLM-Bench: A Comprehensive Benchmark of Small Language Models on Environmental Impacts--Extended Version

Nghiem Thanh Pham, Tung Kieu, Duc-Manh Nguyen +3

Small Language Models (SLMs) offer computational efficiency and accessibility, yet a systematic evaluation of their performance and environmental impact remains lacking. We introdu…

math.GT2023

Representations of braid groups via cyclic covers of the sphere: Zariski closure and arithmeticity

Gabrielle Menet, Duc-Manh Nguyen

Let $d \geq 2$ and $n \geq 3$ be two natural numbers. Given any sequence $κ = (k_{1}, \dots, k_{n}) \in Z^{n}$ such that $g cd (k_{1}, \dots, k_{n}, d) = 1$ , we consider the family of Riemann…

math.AG2023★ 1 cited

Intersection theory and volumes of moduli spaces of flat metrics on the sphere (with an appendix by Vincent Koziarz and Duc-Manh Nguyen)

Duc-Manh Nguyen

Let $P Ω^{d} M_{0, n} (κ)$ , where $κ = (k_{1}, \dots, k_{n})$ , be a stratum of (projectivized) $d$ -differentials in genus $0$ . We prove a recursive formula which relates the v…

math.AG2022

On the volumes of linear subvarieties in moduli spaces of projectivized Abelian differentials

Duc-Manh Nguyen

For $k \in Z_{> 0}$ , let $H_{g, n}^{(k)}$ denote the vector bundle over $M_{g, n}$ whose every fiber consists of meromorphic $k$ -differentials with poles…

math.AG2021

The Incidence Variety Compactification of strata of d-differentials in genus 0

Duc-Manh Nguyen

Given $d \in Z_{\geq 2}$ , for every $κ = (k_{1}, \dots, k_{n}) \in Z^{n}$ such that $k_{i} \geq 1 - d$ and $k_{1} + \dots + k_{n} = - 2 d$ , denote by $Ω^{d} M_{0, n} (κ)$ and $\mathbb…

math.GT2020★ 10 cited

Variation of Hodge structure and enumerating tilings of surfaces by triangles and squares

Vincent Koziarz, Duc-Manh Nguyen

Let $S$ be a connected closed oriented surface of genus $g$ . Given a triangulation (resp. quadrangulation) of $S$ , define the index of each of its vertices to be the number of edge…

math.GT2019★ 4 cited

Volume forms on moduli spaces of d-differentials

Duc-Manh Nguyen

Given $d \in N$ , $g \in N \cup {0}$ , and an integral vector $κ = (k_{1}, \dots, k_{n})$ such that $k_{i} > - d$ and $k_{1} + \dots + k_{n} = d (2 g - 2)$ , let $Ω^{d} M_{g, n} (κ)$ denot…

math.GT2018

Topological Veech dichotomy and tessellations of the hyperbolic plane

Duc-Manh Nguyen

For every half-translation surface with marked points $(M, Σ)$ , we construct an associated tessellation $Π (M, Σ)$ of the Poincaré upper half plane whose tiles have finitely many side…

math.GT2018★ 14 cited

Weierstrass Prym eigenforms in genus four

Erwan Lanneau, Duc-Manh Nguyen

We prove that for each discriminant $D \equiv 0, 1 mod 4, D \neq \in {4, 9}$ , the corresponding Prym eigenform locus discovered by McMullen in the stratum $H (6)$ is connec…

math.GT2017

Existence of closed geodesics through a regular point on translation surfaces

Duc-Manh Nguyen, Huiping Pan, Weixu Su

We show that on any translation surface, if a regular point is contained in a simple closed geodesic, then it is contained in infinitely many simple closed geodesics, whose directi…

math.GT2016

Rank 2 Affine Manifolds in Genus 3

David Aulicino, Duc-Manh Nguyen

We complete the classification of rank two affine manifolds in the moduli space of translation surfaces in genus three. Combined with a recent result of Mirzakhani and Wright, this…

math.AG2016

Complex hyperbolic volume and intersection of boundary divisors in moduli spaces of genus zero curves

Vincent Koziarz, Duc-Manh Nguyen

We show that the complex hyperbolic metrics defined by Deligne-Mostow and Thurston on $M_{0, n}$ are singular Kähler-Einstein metrics when $M_{0, n}$ is embed…

math.GT2015★ 9 cited

Translation surfaces and the curve graph in genus two

Duc-Manh Nguyen

Let $S$ be a (topological) compact closed surface of genus two. We associate to each translation surface $(X, ω) \in H (2) ⊔ H (1, 1)$ a subgraph $\hat{\mathcal{…

math.DS2015

Finiteness of Teichmüller curves in non-arithmetic rank 1 orbit closures

Erwan Lanneau, Duc-Manh Nguyen, Alex Wright

We show that in any non-arithmetic rank 1 orbit closure of translation surfaces, there are only finitely many Teichmüller curves. We also show that in any non-arithmetic rank 1 orb…

math.GT2015★ 9 cited

Rank two affine submanifolds in $H (2, 2)$ and $H (3, 1)$

David Aulicino, Duc-Manh Nguyen

We classify all rank two affine manifolds in strata in genus three with two zeros. This confirms a conjecture of Maryam Mirzakhani in these cases. Several technical results are pro…

math.GT2014

Connected components of Prym eigenform loci in genus three

Erwan Lanneau, Duc-Manh Nguyen

This paper is devoted to the classification of connected components of Prym eigenform loci in the strata H(2,2)^odd and H(1,1,2) in the Abelian differentials bundle in genus 3. The…

math.GT2013★ 5 cited

GL^+(2,R)-orbits in Prym eigenform loci

Erwan Lanneau, Duc-Manh Nguyen

This paper is devoted to the classification of GL^+(2,R)-orbit closures of surfaces in the intersection of the Prym eigenform locus with various strata of quadratic differentials.…

math.DS2013★ 8 cited

Classification of higher rank orbit closures in H^{odd}(4)

David Aulicino, Duc-Manh Nguyen, Alex Wright

The moduli space of genus 3 translation surfaces with a single zero has two connected components. We show that in the odd connected component H^{odd}(4) the only GL^+(2,R) orbit cl…

math.DS2013★ 10 cited

Non-Veech surfaces in H^hyp(4) are generic

Duc-Manh Nguyen, Alex Wright

We show that every surface in H^hyp(4) is either a Veech surface or a generic surface, i.e. its GL^+(2,R)-orbit is either a closed or a dense subset of H^hyp(4) . The proof develop…

math.GT2013★ 10 cited

Complete periodicity of Prym eigenforms

Erwan Lanneau, Duc-Manh Nguyen

This paper deals with Prym eigenforms which are introduced previously by McMullen. We prove several results on the directional flow on those surfaces, related to complete periodici…

math.GT2012★ 3 cited

Volumes of the sets of translation surfaces with small saddle connections in rank one affine submanifolds

Duc-Manh Nguyen

We prove some estimates of the volumes of the sets of translation surfaces of unit area having several independent small saddle connections in a rank one affine submanifold.

math.GT2011★ 8 cited

Teichmueller curves generated by Weierstrass Prym eigenforms in genus three and genus four

Erwan Lanneau, Duc-Manh Nguyen

This paper is devoted to the classification of the infinite families of Teichmuller curves generated by Prym eigenforms of genus 3 having a single zero. These curves were discovere…

Hilbert surfaces, modular forms, and Siegel-Veech constants

Intersection theory and Siegel-Veech constants for Prym eigenform loci in ΩM3​(2,2)odd

SLM-Bench: A Comprehensive Benchmark of Small Language Models on Environmental Impacts--Extended Version

Representations of braid groups via cyclic covers of the sphere: Zariski closure and arithmeticity

Intersection theory and volumes of moduli spaces of flat metrics on the sphere (with an appendix by Vincent Koziarz and Duc-Manh Nguyen)

On the volumes of linear subvarieties in moduli spaces of projectivized Abelian differentials

The Incidence Variety Compactification of strata of d-differentials in genus 0

Variation of Hodge structure and enumerating tilings of surfaces by triangles and squares

Volume forms on moduli spaces of d-differentials

Topological Veech dichotomy and tessellations of the hyperbolic plane

Weierstrass Prym eigenforms in genus four

Existence of closed geodesics through a regular point on translation surfaces

Rank 2 Affine Manifolds in Genus 3

Complex hyperbolic volume and intersection of boundary divisors in moduli spaces of genus zero curves

Translation surfaces and the curve graph in genus two

Finiteness of Teichmüller curves in non-arithmetic rank 1 orbit closures

Rank two affine submanifolds in H(2,2) and H(3,1)

Connected components of Prym eigenform loci in genus three

GL^+(2,R)-orbits in Prym eigenform loci

Classification of higher rank orbit closures in H^{odd}(4)

Non-Veech surfaces in H^hyp(4) are generic

Complete periodicity of Prym eigenforms

Volumes of the sets of translation surfaces with small saddle connections in rank one affine submanifolds

Teichmueller curves generated by Weierstrass Prym eigenforms in genus three and genus four

Intersection theory and Siegel-Veech constants for Prym eigenform loci in $Ω M_{3} (2, 2)^{odd}$

Rank two affine submanifolds in $H (2, 2)$ and $H (3, 1)$