报 告 人：Volkmar Welker 教授
报告题目：Partial orders on decompositions of combinatorial structures
报告时间：2024年09月23日（周一）下午4：00
报告地点：分测中心102会议室
主办单位：数学与统计学院、数学研究院、科学技术研究院
报告人简介：
Volkmar Welker，德国马尔堡大学教授。主要从事代数组合、离散几何、组合交换代数等领域的研究。研究成果多次发表在Mem. Amer. Math. Soc.，Adv. Math.，Math. Z.，Trans. Amer. Math. Soc.，J. Algebra等高水平期刊上。
报告摘要：
For a combinatorial object which has a subobject poset we present conditions under which one can define meaningful posets or partial or full decompositions of the object and ordered analogs thereof. A classical example for such an object is a finite set and its subset poset which then leads to the posets of partial or full set partitions andtheir ordered analogs, all ordered by refinement. Similarly, one can start with a finite dimensional vectorspace over a finite field, its poset of subspaces and consider posets of partial or full direct sum decompositions of the vectorspace ordered by refinement.We show that there are many other structures for which these constructions make sense.In all cases we ask for enumerative invariants, such as the M\obius number of the posets, and consider geometric invariants (e.g., homotopy type) defined through theorder complex of the posets. The talk will contain many examples, some with complete solutions and some with challenging questions.