Academic Report
Title: Finite topological number and P group action
Reporter: Prof. ZHANG Ying
Time: Oct 18, 2019 (Friday) PM 16:20-17:00
Location: A1101# room, Innovation Park Building
Contact: Prof. LEI Fengchun (tel:84708360)
Abstract: Let t (n) and t_ (n) be the number of all different topologies and all different t_topologiesthat can be defined on an n-ary set, respectively. In the work of Russian mathematician borevich in the early 1980s, the periodicity of T (n) and t_ (n) moduli was studied. In the cooperation with Li Xiangfei, we get some arithmetical properties of T (n) and t_ (n) by properly constructing some p group actions. Specifically, we get the formula of power p ^ m of T (n + P ^ k) module prime number expressed by some special Topological Numbers and the periodicity of power p ^ m of T (n) module prime number (and therefore any positive integer) as inference; similarly, we also get the periodicity of power P ^ m of T (n) module prime number (and therefore any positive integer). This solves the problems left over by borevich's work. In addition, we also obtain the unexpected recurrence formula of the prime power of T (n) and t_ (n) modules.
The brief introduction to the reporter: Zhang Ying, professor and doctoral supervisor of School of mathematics science, Suzhou University, is engaged in geometric topology research. He has published academic papers in adv. math., Amer. J. math., J. diff. geom., math. Res. letters and other domestic and foreign mathematical magazines, and has achieved some research results that have attracted the attention of his peers.
