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What and Who
Title:Persistent Nerves in Topological Inference and Data Analysis
Speaker:Don Sheehy
coming from:University of Connecticut
Speakers Bio:Don Sheehy received his B.S.E. from Princeton University and his Ph.D. in Computer Science from Carnegie Mellon University under Gary Miller. He spent two years as a postdoc with the Geometrica group at Inria Saclay in France. He is now Assistant Professor of Computer Science at The University of Connecticut. His research is in algorithms and data structures in computational geometry and topological data analysis.
Event Type:AG1 Mittagsseminar (own work)
Visibility:D1, D2, D3, D4, D5, RG1, SWS, MMCI
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Level:AG Audience
Date, Time and Location
Date:Tuesday, 17 March 2015
Duration:30 Minutes
Building:E1 4
One of the most powerful tools for computational geometers and topologists to move between continuous and discrete objects is the so-called Nerve Theorem. It gives a simple condition that guarantees a certain simplicial complex has the same topological type as a continuous set it is meant to approximate. For algorithms, this is invaluable as it allows us to guarantee that a discretization is correct. Example of uses of the Nerve Theorem and its variants include surface reconstruction, topological data analysis, and topological inference. In this talk, I will discuss a more recent version of the Nerve Theorem of Chazal and Oudot that connects the Nerve Theorem to persistent homology. I will then show some of my recent work on how the "Persistent Nerve Lemma" (PNL) can be used to greatly simplify several known results including work on sparse filtrations and homological sensor networks. The key idea in both of these cases is use the (PNL) as a way to use geometric arguments rather than combinatorial arguments, leading to both shorter proofs and more general results.
Name(s):Michael Kerber
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Created:Michael Kerber, 02/02/2015 02:37 PM Last modified:halma/MPII/DE, 04:39 PM Today
  • Michael Kerber, 03/02/2015 03:52 PM
  • Michael Kerber, 02/02/2015 02:37 PM -- Created document.