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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
Language:English
Date, Time and Location
Date:Tuesday, 17 March 2015
Time:13:00
Duration:30 Minutes
Location:Saarbr├╝cken
Building:E1 4
Room:024
Abstract
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.
Contact
Name(s):Michael Kerber
Video Broadcast
Video Broadcast:NoTo Location:
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Created by:Michael Kerber, 02/02/2015 02:37 PMLast modified by:Uwe Brahm/MPII/DE, 11/24/2016 04:13 PM
  • Michael Kerber, 03/02/2015 03:52 PM
  • Michael Kerber, 02/02/2015 02:37 PM -- Created document.