Abstract

In this talk, first l will review the definition of singular cubic homologies of digraphs developed byGrigoryan, Jimenez and Muranov. Based on some geometric/topological consideration and someresults on the GJM's work, l will define the cellular homologies of digraphs in terms of the so-calledadmissible pairs and admissible relations. Also l will give several examples and properties of suchhomology theory. Finally, l will talk about some relations between cellular homologies and singulacubic homologies of digraphs and give some questions. This talk is based on the joint work with S.. Yau.

Speaker Intro

Xinxing Tang, received a bachelor's degree in basic mathematics from the School ofMathematics, Sichuan University in 2013, and received a doctorate from Beiing InternationaCenter for Mathematical Research, Peking University in 2018. From 2018 to 2021, he worked as apostdoctoral fellow at the Yau Mathematical Sciences Center, Tsinghua University, and joined YangLake Beijing Institute of Mathematical Sciences and Applications in 2021 as assistant professorResearch interests include: integrable systems, especially infinite-dimensional integrable systemsthat appear in GW theory and LG theory, and are interested in understanding the algebraicstructure of infinite symmetries and related calculations. Other interests include: mixed Hodgestructures, quantum groups and KZ equations, W algebra and W symmetry, Augmentationrepresentation.