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Practical algorithms in 3-manifold topology
Geometry/TopologySpeaker: | Alex He, Oklahoma State |
Location: | 2112 MSB |
Start time: | Tue, May 6 2025, 2:10PM |
Every compact 3-manifold can be triangulated in infinitely many ways. So given two 3-manifold triangulations, how can we algorithmically decide whether or not they triangulate the same 3-manifold? This is the 3-manifold homeomorphism problem, which is (to say the least) very hard. Much attention is therefore given to simpler problems known as recognition problems: after fixing a 3-manifold M, how can we algorithmically decide whether a given triangulation actually triangulates M? In other words, how can we algorithmically recognize triangulations of M? This talk will survey various 3-manifold recognition problems, and discuss how we can design "practical" algorithms to solve these problems; the challenge is that the algorithms need to be both simple enough to implement in software and efficient enough to actually execute.