Organized by: He Yunan,Liu Jian

Speaker: 毕婉莹（BIMSA）

Time: 9:00-10:00, Dec 12 , 2023

Venue: 数学中心研讨室（至善楼602）

Online: 腾讯会议：890-671-578

Title: The magnitude homology of a hypergraph

Abstract:  

The magnitude homology, introduced by R. Hepworth and S. Willerton, offers a topological invariant that enables the study of graph properties. Hypergraphs, being a generalization of graphs, serve as popular mathematical models for data with higher-order structures. In this talk, we focus on

describing the topological characteristics of hypergraphs by considering their magnitude homology. We begin by examining the distances between hyperedges in a hypergraph and establish the magnitude homology of hypergraphs. Additionally, we explore the relationship between the magnitude and the magnitude homology of hypergraphs. Furthermore, we derive several functorial properties of the magnitude homology for hypergraphs. Lastly, we present the K\"{u}nneth theorem for the simple magnitude homology of hypergraphs.

Speaker: 邸少波（BIMSA）

Time: 10:00-11:00, Dec 12 , 2023

Venue: 数学中心研讨室（至善楼602）

Online: 腾讯会议：890-671-578

Title: On GLMY homology of Cayley digraphs and covering digraphs

Abstract:  

We develop a theory of covering digraphs, similar to the theory of covering spaces. By applying this theory to Cayley digraphs, we build a

“bridge” between GLMY-theory and group homology theory, which helps to reduce path homology calculations to group homology. We show some cases where this approach allows us to fully express path homology in terms of group homology. To illustrate this method, we provide a path homology computation for the Cayley digraph of the additive group of rational numbers.