北京雁栖湖应用数学研究院

尤瓦尔•佩雷斯 , 阿尔坦·谢什马尼 , 侯赛因·亚瓦尔塔努

吴杰

2024年12月09日 17:00 至 17:45

A6-101

Zoom 388 528 9728 (BIMSA)

The high-order interaction phenomena occur popularly in data analytics. The good progress for scientific and mathematical understanding on high order interaction complex system may highly influence the future development of the artificial intelligence. Guided by this scientific problem, various new topological theories have been recently developed from GLMY homology of digrahs as topological tools for analysing high order structures of complex networks, which enrich GLMY theory---a new-born research field in algebraic topology---that has achieved fruitful successful applications in complex diseases, microbiology, molecular and materials sciences. In this talk, we will give an introduction to the topological approaches to the mathematical modelings for high-order interaction complex systems, particularly the GLMY homology and its variants as effective tools in analysing topological structures of mathematical modelings beyong traditional simplicial complex modeling such as hypergraph modeling and the newly proposed statistical modelings of IdopNetwork and HyperNetwork. The talk will aim to general audience with highlingting how the interdisciplinary research collaboration with the statistics team would lead to the successful applications of topology with receiving returns to mathematics for developing GLMY theory.

BIMSA研究员，美国罗切斯特大学数学系博士，加州大学伯克利分校数学研究所博士后，前新加坡国立大学数学系终身教授，2021年12月入职北京雁栖湖应用数学研究院（BIMSA）。研究方向为代数拓扑与应用拓扑，在代数拓扑理论研究上的主要成就是建立了同伦群与辫子群理论的基础性关系，以及回路空间同伦论与置换群模表示论的基础性关系；在应用拓扑方面，他带领研究团队以复杂系统高阶互作拓扑基础为目标、生物医学与材料科学等领域科学问题为导向，发展有向图与超图的代数拓扑学，推动拓扑数据分析的新型拓扑理论及其应用，取得了一系列成果。在Journal of American Mathematical Society, Proceedings of the National Academy of Sciences of the United States of America, Advances in Mathematics等数学顶尖期刊发表学术论文100余篇。2007年获得新加坡国家科学奖。2014年获得国家自然科学基金海外联合基金（杰青B）的资助。