活动时间：2026年08月10日（周一）10：00

活动地点：西校区信息学院1号楼336英慧学术报告厅

报告人：刘华宁

报告人简介：

刘华宁，西北大学数学学院教授、博士生导师，剑桥大学与山东大学博士后。目前担任《纯粹数学与应用数学》期刊执行编委。研究方向为解析数论及其应用，发表论文100余篇。先后主持多项国家自然科学基金和1项陕西省杰出青年基金项目，曾获得钟家庆数学奖、全国优秀博士学位论文提名、霍英东教育基金会青年教师奖、陕西省青年科技新星以及两项陕西省科学技术奖。

报告摘要：

Thistalkis concerned with the fundamental scaling laws of quasi-complementary sequence sets (QCSSs) by understanding how large the set size (denoted by $M$) can grow with the flock size ($K$) and the sequence length ($N$). We first establish a geometric framework that transforms a QCSS into a complex unit-norm codebook through which certain polynomial upper bounds of the QCSS set size are obtained by exploiting the density thresholds of the codebooks. Sharp quadratic and cubic scaling laws are then introduced. Specifically, we show that asymptotically optimal QCSSs with tightness factor $\rho=1$ satisfy $M \leq (1+o(1))K^2N$, while asymptotically near-optimal QCSSs satisfy $M\leq(1+o(1))K^3N^2$ for $\rho<{(1+\sqrt{5})}/{2}$. To validate these upper bounds, we further propose explicit additive-character and mixed-character based constructions for QCSSs that achieve $M=K^2N+K$ and $M=K^3N^2+2K^2N+K$, respectively, thereby showing that the quadratic and cubic scaling laws are asymptotically tight. Our proposed constructions admit flexible parameter choices, and their maximum correlation estimates are shown to be tight through explicit extremal examples. Additionally, it is conjectured that the cubic scaling law is universal for all $1<\rho\leq 2$, i.e., any asymptotically near-optimal QCSSs should satisfy $M\leq (1+o(1))K^3N^2$, which identifies a fundamental cubic barrier for QCSS scalability. This is a joint work with Lirong Guo and Zilong Liu.

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