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Applied and Computational Topology Seminar

  • Southern University of Science and Technology

About

This is a reading seminar on applied/computational topology. We will be working from Edelsbrunner and Harer's Computational topology: an introduction. To supplement presentations by participants, we will also invite experts in the field to speak.

Computational topology has become a subject that applies to a wide range of topics. This includes pattern recognition in data science, notably through the method of persistent homology. It also employs computer softwares to study questions internal to topology and geometry. We aim to gain an overview of the subject, learn its basic theory and examples, with an emphasis on persistent homology and its applications.

The prerequisite is an undergraduate topology course. Familiarity with computer programming will be a plus, as well as English proficiency. For student participants, we encourage you to informally discuss the material with faculty participants prior to your presentations.

Our focus in Spring 2021 is recent research with specific applications as well as further theoretical aspects.

Talks in Spring 2021 (mostly Mondays 9–12 in Huiyuan 3-415)

Jan 12, '21, Yifan Wu, Topological time series analysis, applications in the literature

Jan 19, '21, Xiabing Ruan, Extended persistence, spectral sequences

Mar 1, '21, Siheng Yi, Topological morphology descriptors and persistence images

Mar 8, '21, Siheng Yi, Stability of persistence

Mar 15, '21, Siyu Cen, Evolutionary de Rham-Hodge method

Mar 22, '21, Xiabing Ruan, Applications of extended persistence to shape recognition and protein docking

Mar 29, '21, Jizhang Liu, Quiver representations and persistent homology

Apr 12, '21, Siheng Yi, More on sliding window embeddings, persistent homology, and applications to audio signal processing

Apr 19, '21, Yifan Wu, Reproducing results of the wheeze detection paper

Apr 26, '21, Siheng Yi and Yifan Wu, More on reproducing wheeze detection via persistent homology; subsampling through landmarks and witness complexes

May 10, '21, Siyu Cen, Persistent homology for geospatial data of voting

May 17, '21, Xiabing Ruan, Persistent homology for data of syntactic structures of world languages

May 24, '21, Yuqing Xing, Persistent homology for data of plant morphology

Talks in Fall 2020 (mostly Tuesdays 9–12 in Huiyuan 3-415)

Sep 15 '20, Yifei Zhu and Ingrid Irmer, Overview and organization

Sep 22 '20, Xiabing Ruan, Graphs and planar graphs

Sep 27 '20, Xiabing Ruan and Ingrid Irmer, Plane curves, knots and links; examples

Oct 13 '20, Zhen Zhang and Siyu Cen, Graph application examples; triangulation of surfaces

Oct 20 '20, Siyu Cen, Self-intersection and simplification of surfaces

[Slides] Oct 23 '20 (Friday, 4:30–5:30 pm, zoom: 685 0623 5836), Jie Wu (Hebei Normal University), Topological data analysis and topological approaches to drug design and discovery

Oct 27 '20, Jizhang Liu, Simplicial complexes

Nov 3 '20, Jizhang Liu, Čech, Vietoris–Rips, and Delaunay complexes

Nov 6 '20 (Friday, 11:00 am–12:00 pm, zoom: 642 0299 8817), Andrew Blumberg (University of Texas at Austin), How to do science with topological data analysis

Nov 10 '20, Yifan Wu, Homology and matrix reduction

Nov 17 '20, Yifan Wu, Cohomology, dual block decompositions, and Poincaré duality

Nov 24 '20, Yifan Wu, Lefschetz and Alexander dualities

Dec 1 '20, Xiabing Ruan and Wenbo Liao, Persistent homology, persistence diagrams, and matrix reduction; introduction to Morse theory

Dec 8 '20, Wenbo Liao, More Morse theory

Dec 15 '20, Yifei Zhu and Xiabing Ruan, Piecewise linear Morse theory; efficient implementations of persistent homology

Dec 22 '20, Xiabing Ruan, Efficient implementations of persistent homology (cont'd)

References

  • Henry Adams et al, Persistence images: a stable vector representation of persistent homology
  • Pankaj K. Agarwal, Herbert Edelsbrunner, John Harer, and Yusu Wang, Extreme elevation on a 2-manifold
  • Gunnar Carlsson, Topology and data
  • Gunnar Carlsson, Topological modeling of complex data
  • Jiahui Chen, Rundong Zhao, Yiying Tong, and Guo-Wei Wei, Evolutionary de Rham-Hodge method
  • Vin de Silva and Gunnar Carlsson, Topological estimation using witness complexes
  • Michelle Feng and Mason A. Porter , Persistent homology of geospatial data: a case study with voting
  • Cohen-Steiner, Edelsbrunner, and Harer, Stability of persistence diagrams
  • Michael L. Connolly, Molecular surface triangulation
  • Herbert Edelsbrunner and John L. Harer, Computational topology: an introduction
  • Saba Emrani, Thanos Gentimis, and Hamid Krim, Persistent homology of delay embeddings and its application to wheeze detection
  • Hitesh Gakhar and Jose A. Perea, Sliding window persistence of quasiperiodic functions
  • Ingrid Irmer, Some references for computational topology
  • Lida Kanari et al, A topological representation of branching neuronal morphologies
  • Lida Kanari et al, Objective morphological classification of neocortical pyramidal cells
  • Mao Li et al, Characterizing 3D inflorescence architecture in grapevine using X-ray imaging and advanced morphometrics: implications for understanding cluster density
  • Mao Li et al, The persistent homology mathematical framework provides enhanced genotype-to-phenotype associations for plant morphology
  • Mao Li et al, Topological data analysis as a morphometric method: using persistent homology to demarcate a leaf morphospace
  • Washington Mio, Topological analysis of structural and functional data
  • Steve Y. Oudot, Persistence theory: from quiver representations to data analysis
  • Jose A. Perea, Topological time series analysis
  • Alexander Port, Taelin Karidi, and Matilde Marcolli, Topological analysis of syntactic structures
  • Raúl Rabadán and Andrew J. Blumberg, Topological data analysis for genomics and evolution: topology in biology
  • Michael T. Schaub et al, Random walks on simplicial complexes and the normalized Hodge 1-Laplacian
  • Guowei Wei, Mathematical AI for drug discovery
  • Jie Wu, Topological data analysis and topological approaches to drug design and discovery
  • Yifan Wu, Persistent homology in time series analysis and its application to wheeze detection
  • Zhen Zhang, Examples of graph data




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