The 53rd KMGS will be held on December 4, Thursday, at the Natural Science Building (E6-1) Room 1410. We invite a speaker Donghan Kim from the Dept. of Mathematical Sciences, KAIST.
The abstract of the talk is as follows.
[Speaker] 김동한(Donghan Kim) from Dept. of Mathematical Sciences, KAIST, supervised by Prof. 김우진 (Woojin Kim)
[Title] Persistent Homology is Complementary to the Weisfeiler–Leman Test
[Discipline] Algebraic Topology
[Abstract]
We analyze the expressive power of persistent homology obtained purely from Vietoris–Rips filtrations on the shortest-path metric of a graph, without using any node features. We show that the verbose diagram completely determines the clique numbers in all dimensions, demonstrating that persistent homology captures rich combinatorial structure. We further construct, for every integer k, explicit graph pairs that the k-dimensional Weisfeiler–Leman test cannot distinguish but persistent homology can. These results demonstrate that persistent homology and the Weisfeiler–Leman test are fundamentally incomparable.
[Language] Korean