Masoud Zargar

activity

20172024

collaborators

9 papers

math.MG2024

Stiefel manifolds and upper bounds for spherical codes and packings

Masoud Zargar

We improve upper bounds on sphere packing densities and sizes of spherical codes in high dimensions. In particular, we prove that the maximal sphere packing densities $δ_{n}$ in $\ma…

math.CO2023

The union-closed sets conjecture for non-uniform distributions

Masoud Zargar

The union-closed sets conjecture, attributed to Péter Frankl from 1979, states that for any non-empty finite union-closed family of finite sets not consisting of only the empty set…

math.NT2022

Random flat bundles and equidistribution

Masoud Zargar

Each signature $λ (n) = (λ_{1} (n), \dots, λ_{n} (n))$ , where $λ_{1} (n) \geq \dots \geq λ_{n} (n)$ are integers, gives an irreducible representation $π_{\underlineλ(n)}:U(n)\rightarrow\text{…

math.MG2020

New upper bounds for spherical codes and packings

Naser T. Sardari, Masoud Zargar

We improve the previously best known upper bounds on the sizes of $θ$ -spherical codes for every $θ < θ^{*} \approx 62.99 7^{\circ}$ at least by a factor of $0.4325$ , in sufficiently high…

math.AG2019

Riemannian structures and point-counting

Masoud Zargar

Suppose $(X_{n})$ is a sequence of positive-dimensional smooth projective complete intersections over $F_{q}$ with dimensions bounded from above and with characteristic zero l…

math.NT2019

Ramanujan graphs and exponential sums over function fields

Naser T. Sardari, Masoud Zargar

We prove that $q + 1$ -regular Morgenstern Ramanujan graphs $X^{q, g}$ (depending on $g \in F_{q} [t]$ ) have diameter at most $\left(\frac{4}{3}+\varepsilon\right)\log_{q}|X^{q,g}|…

math.NT2019

Optimal strong approximation for quadrics over $F_{q} [t]$

Naser T. Sardari, Masoud Zargar

Suppose $q$ is a fixed odd prime power, $F (x)$ is a non-degenerate quadratic form over $F_{q} [t]$ of discriminant $Δ$ in $d \geq 5$ variables $x$ , and $f,g\in\mat…

math.AG2017

Integration of Voevodsky motives

Masoud Zargar

In this paper, we construct four different theories of integration, two that are for Voevodsky motives, one for mixed $ℓ$ -adic sheaves, and a fourth theory of integration for ra…

math.AG2017

Comparison of Stable Homotopy Categories and a Generalized Suslin-Voevodsky Theorem

Masoud Zargar

Let $k$ be an algebraically closed field of exponential characteristic $p$ . Given any prime $ℓ \neq = p$ , we construct a stable étale realization functor $$\underline{\text{Ét}}_{\…

Stiefel manifolds and upper bounds for spherical codes and packings

The union-closed sets conjecture for non-uniform distributions

Random flat bundles and equidistribution

New upper bounds for spherical codes and packings

Riemannian structures and point-counting

Ramanujan graphs and exponential sums over function fields

Optimal strong approximation for quadrics over Fq​[t]

Integration of Voevodsky motives

Comparison of Stable Homotopy Categories and a Generalized Suslin-Voevodsky Theorem

Optimal strong approximation for quadrics over $F_{q} [t]$