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NCTS Reading Seminar on Topological Data Analysis
Time: September 11 - December 25, 2019
Room: R440, Astronomy-Mathematics Building, NTU
Organizers: Chuan-Shen Hu ( National Taiwan Normal University) ,Yi-Sheng Wang ( NCTS)
一、 課程背景與目的:
Over the past decade, topological data analysis has undergone a rapid development and expansion; it has been proved effective in analyzing data sets, which traditional methods cannot cope with.
The main tool in topological data analysis is persistent homology, which is often defined and computed in terms of simplicial complex structures; namely, for every filtrated simplicial complex, one can compute its associated persistence diagram.   
In recent years, new interpretation of persistent homology from a more categorical point of view has been worked out by several authors, and this point of view provides a more general framework and allows us to define multidimentional persistence and could eventually lead to new methods of analyzing data sets that have more than one filtrations.  
 
This goal of the seminar is to understand the approach to multidimensional persistence and its theoretical foundation    laid out by J. M. Curry in his thesis “Sheaves, cosheaves, and applications”.  
 
二、 課程之大綱:
Week 1:  Multidimensional Persistence Diagrams via (co)sheaf Theory--Categorical Preliminaries
Week 2:  Sheaves and cosheaves
Week 3:  Examples
Week 4:  Cellular sheaves and cosheaves
Week 5:  Functors associated to maps
Week 6:  Homology and cohomology
Week 7:  Derived category theory
Week 8:  Persistence in terms of (co)sheaves I
Week 9:  Persistence in terms of (co)sheaves II
Week10: Multidimensional persistence
 
Talk List
10:00 - 11:00 , November 13 , 2019
( Wednesday )
Multidimensional Persistence Diagrams via (co)Sheaf Theory--applications in TDA
Chuan-Shen Hu ( National Taiwan Normal University )
10:00 - 11:00 , November 6 , 2019
( Wednesday )
Multidimensional Persistence Diagrams via (co)Sheaf Theory--the derived perspective
Hung-Yu Yeh ( Academia Sinica )
9:30 - 10:30 , October 16 , 2019
( Wednesday )
Multidimensional Persistence Diagrams via (co)Sheaf Theory--Cellular (co)sheaves
Yi-Sheng Wang ( NCTS )
10:00 - 11:00 , October 9 , 2019
( Wednesday )
Multidimensional Persistence Diagrams via (co)Sheaf Theory--Grothendieck Operations
Yi-Sheng Wang ( NCTS )
10:00 - 11:00 , October 2 , 2019
( Wednesday )
Multidimensional Persistence Diagrams via (co)sheaf Theory--Sheaves and Cosheaves
Yi-Sheng Wang ( NCTS )
10:00 - 11:00 , September 18 , 2019
( Wednesday )
Multidimensional Persistence Diagrams via (co)sheaf Theory--Categorical Preliminaries II
Chuan-Shen Hu ( National Taiwan Normal University )
10:00 - 11:00 , September 11 , 2019
( Wednesday )
Multidimensional Persistence Diagrams via (co)sheaf Theory--Categorical Preliminaries
Chuan-Shen Hu ( National Taiwan Normal University )
 
 
 
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 (C) 2019 National Center for Theoretical Sciences