Monday, August 13, 2018 - 4:00pm - 5:00pm
Gregory Henselman (University of Pennsylvania)
This talk will introduce the central ideas of discrete Morse theory in high-performance (persistent) homology computation. Historically rooted in deep and beautiful structures from smooth geometry, this theory may be viewed, from a computational standpoint, as a very direct means of organizing cellular data to improve efficiency. Time permitting, we will discuss how the method of homological Morse reduction may be extended to the calculation of barcodes.
Monday, August 13, 2018 - 9:00am - 10:00am
Matthew Wright (St. Olaf College)
This talk will summarize the basics of persistent homology, including Rips and Cech complexes, filtrations, homology, the structure theorem for persistence modules, and barcodes.
This introductory talk is designed to reinforce the mathematical foundations of persistent homology, preparing participants for the subsequent talks in this workshop.
Tuesday, June 16, 2009 - 9:00am - 10:30am
Gunnar Carlsson (Stanford University)
No Abstract
Wednesday, March 5, 2014 - 9:00am - 9:50am
Henry Adams (University of Minnesota, Twin Cities)
Suppose ball-shaped sensors wander in a bounded domain. A sensor doesn't know its location but does know when it overlaps a nearby sensor. We say that an evasion path exists in this sensor network if a moving intruder can avoid detection. Vin de Silva and Robert Ghrist give a necessary condition, depending only on the time-varying connectivity data of the sensors, for an evasion path to exist. Using zigzag persistent homology, we provide an equivalent condition that moreover can be computed in a streaming fashion.
Tuesday, February 11, 2014 - 10:15am - 11:05am
Thomas Wanner (George Mason University)
Homology has long been accepted as an important computational tool for
quantifying complex structures. In many applications these structures arise as
nodal domains or excursion sets of real-valued functions, and are therefore
amenable to a numerical study based on suitable discretizations. Such an
approach immediately raises the question of how accurately the resulting
homology can be computed. In this talk we present a probabilistic algorithm for
correctly determining the topology of two-dimensional excursion sets. The
Wednesday, October 23, 2013 - 1:30pm - 2:30pm
Mikael Vejdemo-Johansson (Royal Institute of Technology (KTH))
We describe a topos of sheaves with the property that classical persistent homology of a filtered complex (should) be the internal simplicial homology functor of the logic specified by the base space of the sheaves. All relevant background to understand definitions and their ramifications will be provided in the talk.
Wednesday, October 30, 2013 - 9:00am - 9:50am
Tamal Dey (The Ohio State University)
The efficiency of extracting topological information from point data depends largely on the complex that is built on top of the data points. From a computational viewpoint, the most favored complexes for this purpose have so far been Vietoris-Rips and witness complexes. While the Vietoris-Rips complex
Thursday, October 10, 2013 - 9:00am - 9:50am
Jose Perea (Duke University)
We present in this talk a theoretical framework for studying the
persistent homology of point clouds from time-delay (or sliding window)
embeddings. We will show that maximum 1-d persistence yields a suitable
measure of periodicity at the signal level, and present theorems which
relate the resulting diagrams to the choices of window size, embedding
dimension and field of coefficients. If time permits, we will
demonstrate how this methodology can be applied to the study of
periodicity on time series from gene expression data.
Tuesday, June 4, 2013 - 2:00pm - 2:30pm
Yasu Hiraoka (Kyushu University)
Persistent homology and persistent diagrams have been developed as tools of topological data analysis. They provide a robust topological characterization of a given (discrete) geometrical data. In this talk, I will present our recent researches on applying persistent diagrams to protein structural analysis. Topological characterizations of protein compressibilities and H/D exchanges will be explained in detail.
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