Tuesday, November 1, 2022
Time | Items |
---|---|
All day |
|
4:00pm |
11/01/2022 - 4:00pm Abstract: Our previous multiscale graph basis dictionaries (e.g., Generalized Haar-Walsh Transform [GHWT], Hierarchical Graph Laplacian Eigen Transform [HGLET], Natural Graph Wavelet Packets [NGWPs], and their relatives) were developed for analyzing data recorded on nodes of a given graph. In this work, we propose their generalization for analyzing data recorded on edges or on faces (i.e., triangles) of a simplicial complex (e.g., a triangle mesh of a manifold). The key idea is to use the Hodge Laplacians and their variants for hierarchical partitioning of edges or faces, and then build localized basis functions on those subsets. We plan to demonstrate their usefulness for data approximation on simplicial complexes generated from a co-authorship/citation dataset and an ocean current/flow dataset. Location:
WTS A30
11/01/2022 - 4:15pm For an infinite, residually finite group, it is interesting to ask what properties of the group are captured by its finite quotients. We will discuss how to use ideas of Bridson-McReynolds-Reid-Spitler to show, for example, that the fundamental group of zero surgery on the knot 6_2 is completely determined (among all residually finite groups) by the collection of its finite quotients. Location:
LOM 214
11/01/2022 - 4:30pm I will report on a joint work in progress with Dan Ciubotaru, Time permitting I will discuss the relation of this result to characters Location:
LOM 205
|