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Organizers:
‪Massimo Ferri‬ (UNIBO, Italy)
Vidit Nanda (Oxford, UK)
Jie Wu (HEBTU, China)
Guowei Wei (MSU, USA)
Kelin Xia (NTU, Singapore)
 
Scope:
Topological data analysis (TDA) and TDA-based machine learning models have achieved great successes in various areas, such as materials, chemistry, biology, sensor networks, shape analysis, scientific visualization, dynamics systems, and image/text/video/audio/graph data analysis. Beyond TDA, various other geometric, topological and combinatorial models have been developed for representation, featurization, and analysis, including:
  • Multidimensional persistence, Zig-zag persistence, persistent local homology,
  • Reeb graph, discrete Morse theory, Conley index,
  • Path complex, Neighborhood complex, Dowker complex, hypergraph, and their persistent homology,
  • Geometric anomaly detection, discrete geometry, discrete exterior calculus, etc,
  • Spectral graph, spectral simplicial complex, spectral hypergraph, etc,
  • Graph/Hodge/Tarski Laplacian, p-Laplacian, topological Dirac,
  • Cellular Sheaves,
  • Persistent functions, persistent spectral, persistent Ricci curvature, etc.
The application of these models in data analysis can be generalized into four stages, i.e., data, topology, feature and learning. Essentially, data are transformed into certain topological representations. Intrinsic geometric/topological/combinatorial features are obtained from these representations and then further input into learning models. 

This workshop is supported by School of Physics and Mathematical Sciences, NTU.

Invited Speakers:
Henry Adams, Colorado State University
Mattia G. Bergomi, Veos Digital, Milano
Ginestra Bianconi, Queen Mary University of London
Wojtek Chacholski, KTH Royal Institute of Technology
Stefania Ebli, EPFL
Herbert Edelsbrunner, IST Austria
 ‪Massimo Ferri, University of Bologna
Patrizio Frosini, University of Bologna
Robert Ghrist, University of Pennsylvania
Jurgen Jost, Max Planck Institute
Claudia Landi, University of Modena and Reggio Emilia
Ran Levi, University of Aberdeen
Konstantin Mischaikow, Rutgers
Vasileios Maroulas, University of Tennessee
Facundo Mémoli, Ohio State University
Marian Mrozek, Jagiellonian University
Sayan Mukherjee, Duke University
Vidit Nanda, Oxford
Andreas Ott, Karlsruhe Institute of Technology (KIT)
Francesco Vaccarino, Politecnico di Torino
Guowei Wei, Michigan State University
Kelin Xia, Nanyang Technological University
‪Hiraoka Yasuaki‬, Kyoto University
Farzana Nasrin, University of Hawaii
Ling Zhou, Ohio State University

Workshop Schedule (Central European Time, CET) (Titles and Abstracts):
 




August 28, 13:50-18:25 (CET)
13:50-14:00  Opening Remarks
 Chair: Jurgen Jost
14:00-14:50   Herbert Edelsbrunner "The intrinsic volumes of a space filling diagram and their derivatives"
14:50-15:40   Ginestra Bianconi   "The topological Dirac operator and the dynamics of topological signals"
15:40-16:30  Vidit Nanda "Principal components along quiver representations"
                    15 Minutes Time Break
16:45-17:35   Konstantin Mischaikow "Solving systems of ordinary differential equations via combinatorial homological algebra"
17:35-18:25   Guowei Wei   "How Math and AI are revolutionizing biosciences"



August 29, 9:00-12:35 (CET)
Chair: Herbert Edelsbrunner
09:00-9:50     Stefania Ebli "Simplicial Neural Networks"
09:50-10:40   Claudia Landi "Discrete Morse Theory meets Multi-Parameter Persistence"
                    15 Minutes Time Break
10:55-11:45  Francesco Vaccarino "Parallel decomposition of persistence modules through interval bases"
11:45-12:35  Mattia G. Bergomi  "Comparing Neural Networks via Generalized Persistence"
 



August 29, 14:00-18:25 (CET)
 Chair: Konstantin Mischaikow
14:00-14:50   Jurgen Jost   "Geometry and topology of data"                  
14:50-15:40   Kelin Xia "Persistent function based machine learning for drug design"
15:40-16:30    Robert Ghrist  "Laplacians and Network Sheaves"
                    15 Minutes Time Break
16:45-17:35   Sayan Mukherjee "Modeling shapes and fields: a sheaf theoretic perspective"
17:35-18:25   Farzana Nasrin "Random Persistence Diagram Generator" (presenting on behalf of Vasileios Maroulas)



August 30, 9:00-12:35 (CET)
Chair: Marian Mrozek
09:00-09:50   ‪Hiraoka Yasuaki "On characterizing rare events in persistent homology"
09:50-10:40   Andreas Ott "A persistent topology approach for the surveillance of coronavirus mutations"
                    15 Minutes Time Break
10:55-11:45   Wojciech Chacholski  "Enabling a machine to sense geometry"
11:45-12:35   Patrizio Frosini  "On the role of group equivariant non-expansive operators in Topological Data  Analysis"
 



August 30, 14:00-18:25 (CET)
 Chair: Vidit Nanda
14:00-14:50  Marian Mrozek "Combinatorial vs. Classical Dynamics: Recurrence"
14:50-15:40  Massimo Ferri  "Selection of points in persistence diagrams"
15:40-16:30   Ran Levi "An application of neighbourhoods in directed graphs in the classification of binary dynamics"
                     15 Minutes Time Break
16:45-17:35   Ling Zhou "Other Persistence Invariants: homotopy and the cohomology ring" (presenting on behalf of Facundo Mémoli)
17:35-18:25  Henry Adams   "Vietoris-Rips complexes of hypercube graphs"

Zoom Link：
Meeting ID: 305 412 0115
Passcode: TDA2021
Join Zoom Meeting: https://ntu-sg.zoom.us/j/3054120115
Zoom meeting videos are available at on Youtube https://www.youtube.com/watch?v=C7gh5BeMa3Y&list=PL4kY-dS_mSmKCxQ66ZnjMDkdigTT5FHcZ


Slide Link：
https://drive.google.com/drive/folders/1Alw3_itAPGCQ63QXLxRYT-AFqiZsnjNv