江苏省应用数学（中国矿业大学）中心系列学术报告
短期课程报告题目：Coset complexes in finite groups
报告人：孟沆洋
个人简历：孟沆洋，上海大学理学院数学系副教授，西班牙瓦伦西亚大学基础数学博士，主要研究领域为有限群论及其表示。相关结果发表于Trans. Amer. Math. Soc., J. Lond. Math. Soc.，Proc. Amer. Math.Soc.，J. Algebra等杂志。 获上海市2020年度扬帆计划项目、2020年度上海市引智人才XSC计划，2021年获 Baer Prize特别提名奖，主持国家自然科学基金青年项目一项，面上项目一项。
邀请人：张驰
报告 1：Posets and order complexes
报告时间：2024年11月25日（周一）上午9：30-10：30
报告地点：博1-A202
报告摘要：In this discourse, we will delve into the concept of partially ordered sets, commonly known as posets, and their corresponding order complexes. The study of posets is fundamental in various fields such as combinatorics, algebra, and theoretical computer science. We will then explore how these order complexes can be realized as geometric simplicial complexes in Euclidean space. This realization is crucial as it bridges the gap between combinatorial structures and topological spaces, enabling us to study the topological properties of posets through the lens of algebraic topology.
报告2： Order complexes of p-subgroups and Quillen’s conjecture
报告时间：2024年11月25日（周一）上午10：40-11：40
报告地点：博1-A202
报告摘要：In this talk, we will touch upon the famous Quillen's Conjecture, which is a deep and influential conjecture in algebraic topology and finite group theory. Although it remains unproven in general, it has inspired a wealth of research and has been confirmed in various special cases.
报告3： Order complexes of proper cosets in finite groups
报告时间：2024年11月25日（周一）下午16:00-17:00
报告地点：数学学院A310
报告摘要：In this talk, we will show some topological properties of proper coset posets in finite groups. Let G be a finite group and X be a subgroup of G. Denote by C_X(G) the set of all cosets Hx in G with X ≤ H < G. We will show that C_X(G) is non-contractible if G is solvable or N_G(X) contains a Sylow 2-subgroup and a Sylow 3-subgroup of G. This result follows J. Shareshian and R. Woodroofe’s work in Adv.Math(2016). We also give some divisibility properties of the Euler characteristic of C_X(G) when X is a p-group, which follows K. S. Brown’s classical result in J.Algebra (2000).