Seminar| Institute of Mathematical Sciences
Time: Wednesday, January 7th, 2026,16:00-17:00
Location: RS408, IMS
Speaker: Erxiao Wang, Zhejiang Normal University
Abstract: In recent years, frequent breakthroughs have been achieved in the niche field of tiling (or tessellation). Notable advances reported in popular science journals include: convex pentagonal monotiles in the plane, densest sphere packings, rational tetrahedra, counter-examples of the periodic tiling conjecture, and the einstein (i.e., aperiodic monotiles). This talk will review these research progresses, including the speaker's own work on spherical tilings, discuss the connections of tiling with symmetries, topology, algebraic geometry, number theory, harmonic analysis, and dynamical systems, and briefly touch upon its applications in zero-waste manufacturing, modular construction, quasicrystals, music, AI etc.. (No math background required. All are welcome.)
近年来，“小众”的密铺（或镶嵌）领域取得了诸多突破性进展。科普期刊报道的代表性成果包括：平面凸五边形单形平铺、最密球堆积、有理四面体、周期性平铺猜想的反例以及“爱因斯坦”（即无循环单砖）。本报告将综述上述研究进展，涵盖报告人在球面密铺的分类，探讨密铺与对称性、拓扑、代数几何、数论、调和分析及动力系统等领域的关联，并简要提及其在无废料制造、模块化构建、准晶体、音乐、人工智能等领域的应用。
（无需数学背景。欢迎所有人。）
About the speaker: 王二小现为浙江师范大学双龙特聘教授，曾任职MSRI、UT Austin、NUS及中科院海外归国杰出青年，是TU Munich、HKUST访问学者。长期研究微分几何和可积系统交叉的环群方法领域，合作做出反常识的基础理论突破，证明了可积系统的解空间上的有理环群作用均由其导师Terng和Uhlenbeck推广的广义贝克隆变换生成，无需幂零元作用。又经过六年合作攻关和两年审稿，2022年成为我国首次同时发表三篇长文研究，现已彻底解决球面多边形边对边单密铺完整分类这个百年难题；正带领十余名本硕博探索着二维错棱、曲棱、双曲、多层、多原型、随机密铺，三维密铺，整数密铺等，及其与材料和人工智能等领域的交叉应用。