Phúc Võ Dang

activity

20152026

most citedOn a minimal set of generators for the polynomial algebra of five variables as a module over the Steenrod algebra

55 citations · 103 across the 26 of their papers we have counts for

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Showing 2025Show all

11 papers · 1 filter

math.AT2025

Low-degree mod 2 cohomology of classifying spaces of $G_{2}$ -gauge groups

Dang Vo Phuc

Let $G_{k}$ be the gauge group of the principal $G_{2}$ -bundle over $S^{4}$ classified by $k \in π_{4} (B G_{2}) ≅ Z$ . In this paper, we determine the first positive fibre row…

math.RT2025

Spectral Separation and Eigenvalue Labelling for Polynomial Tensor Representations of General Linear Groups

Dang Vo Phuc

Let $q = p^{f}$ be a prime power, $H \leq GL_{d} (q)$ a subgroup containing a genuine Singer cycle $s$ of order $q^{d} - 1$ , and $W$ an $F_{q} H$ -module whose scalar extension…

math.AT2025

The rank-five Peterson hit problem, the Singer transfer, and canonical Milnor-operation layers

Dang Vo Phuc

Let $V_{n} = (F_{2})^{n}$ , let $P_{n} = H^{*} (B V_{n}; F_{2}) = F_{2} [u_{1}, \dots, u_{n}]$ , and regard $P_{n}$ as an unstable module over the mod $2$ Steenrod algebra $A$ . We stu…

math.GR2025★ 1 cited

Jensen's Functional Equation on Involution-Generated Groups: A Square-Root Criterion, Rigidity Phenomena, and Obstruction Spaces

Dang Vo Phuc

Let $G$ be a group and $H$ an abelian group. We study normalized solutions $f : G \to H$ of the Jensen equation $f (x y) + f (x y^{- 1}) = 2 f (x)$ and its companion $f (x y) + f (x^{- 1} y) = 2 f (y)$ . Re…

math.AC2025

On modular invariants of the truncated polynomial ring in rank four

Dang Vo Phuc

We prove the rank-4 case of the conjecture of Ha-Hai-Nghia for the invariant subspace of the truncated polynomial ring $\mathcal{Q}_m(n)=\mathbb{F}_q[x_1,\dots,x_n]/(x_1^{q^m},\dot…

math.AC2025

Observation Nuclei in Affine Geometry: Symbolic Powers, Fat Points, and Infinitesimal Recovery

Dang Vo Phuc

This paper integrates point-dependent infinitesimal data into affine geometry through quantale nuclei and finitary weak ideal systems. For a subset $X \subseteq k^{n}$ and a bounded…

math.AT2025

Geometric realization via unoriented bordism and a counterexample to Singer's conjecture for the sixth algebraic transfer

Dang Vo Phuc

Let $A$ be the mod-2 Steenrod algebra acting in the usual way on $P_{q} = F_{2} [x_{1}, \dots, x_{q}]$ , and let $Q P_{q} = F_{2} \otimes_{A} P_{q}$ . Singer's…

math.AT2025

Normalized Derivations for Steenrod--Milnor Operations on the Dickson Algebra and Applications

Dang Vo Phuc

Computing higher iterates of the primitive Steenrod-Milnor operations $St^{\emptyset, Δ_{i}}$ on the Dickson algebra $D_{n}$ has historically been obstructed by severe combinat…

math.AT2025

Computing Invariant Spaces via Global Cluster Analysis and Representation Theory

Dang Vo Phuc

The Singer algebraic transfer is a fundamental homomorphism in algebraic topology, providing a bridge between the homology of classifying spaces and the cohomology of the Steenrod…

math.AT2025

A matrix criterion and algorithmic approach for the Peterson hit problem: Part I

Dang Vo Phuc

The Peterson hit problem in algebraic topology is to explicitly determine the dimension of the quotient space $Q P_{k} = F_{2} \otimes_{A} P_{k}$ in posit…

math.AT2025

On the computation of $Ext_{A}^{k, k +*} (Z /2, Z /2)$ for $k \leq 5$

Dang Vo Phuc

This Note presents a computational algorithm for determining a basis of the cohomology of the mod 2 Steenrod algebra, $\mathrm{Ext}_{\mathcal A}^{k, k+*}(\mathbb{Z}/2, \mathbb{Z}/2…

Low-degree mod 2 cohomology of classifying spaces of G2​-gauge groups

Spectral Separation and Eigenvalue Labelling for Polynomial Tensor Representations of General Linear Groups

The rank-five Peterson hit problem, the Singer transfer, and canonical Milnor-operation layers

Jensen's Functional Equation on Involution-Generated Groups: A Square-Root Criterion, Rigidity Phenomena, and Obstruction Spaces

On modular invariants of the truncated polynomial ring in rank four

Observation Nuclei in Affine Geometry: Symbolic Powers, Fat Points, and Infinitesimal Recovery

Geometric realization via unoriented bordism and a counterexample to Singer's conjecture for the sixth algebraic transfer

Normalized Derivations for Steenrod--Milnor Operations on the Dickson Algebra and Applications

Computing Invariant Spaces via Global Cluster Analysis and Representation Theory

A matrix criterion and algorithmic approach for the Peterson hit problem: Part I

On the computation of ExtAk,k+∗​(Z/2,Z/2) for k≤5

Low-degree mod 2 cohomology of classifying spaces of $G_{2}$ -gauge groups

On the computation of $Ext_{A}^{k, k +*} (Z /2, Z /2)$ for $k \leq 5$