CTRG

Stanford's Computational Topology Reading Group (CTRG)

The computational topology reading group is no longer meeting. But we had quite a run back in the day! Here is the archive of our discussions.

Winter 2015

Date Topic Discussion leader
February 6 Area Exam talk (persistent homology) Jacek Skryzalin
February 13 Area Exam talk (mapper) Jacek Skryzalin
February 20 Mayer-Vietoris sequence Ryan Lewis
February 27 Introduction to Morse Theory (Forman) Amr Mohamed

Fall 2014

Date Topic Discussion leader
October 10 Topology and Data (Homology, pages 1-18) by Carlsson Amr Mohamed and Ansh Shukla
October 24 Nerve Complexes of Circular Arcs by Adamaszek, Adams, Frick, Peterson and Previte-Johnson Henry Adams
November 7 Zigzag Persistence by Carlsson and de Silva Jacek Skryzalin
November 14 Multidimensional Persistence (excerpts from Pawin's PhD thesis) Pawin Vongmasa

Spring 2014

Date Topic Discussion leader
April 25 Topological Pattern Recognition for Point Cloud Data (Homology, pages 1-18) by Carlsson Eric Yi
May 2 Computing Persistent Homology by Carlsson and Zomorodian Hao Su
May 16 Stability of Persistence Diagrams by Cohen-Steiner, Edelsbrunner, and Harer Hao Su
May 30 Zigzag persistence by Carlsson and de Silva Pawin Vongmasa

Spring 2013

Date Topic Discussion leader
April 17 A geometric framework for sparse matrix problems by Carlsson and de Silva Ryan Lewis
May 8 Algorithmic complexity of finding cross-cycles in flag complexes by Adamaszek and Stacho Michael Kerber
May 15 Statistical topology via Morse theory, persistence and nonparametric estimation by Bubenik, Carlsson, Kim, and Luo Michele Intermont
May 29 The Theory of Multidimensional Persistence by Carlsson and Zomorodian Sara Kalisnik
May 29 The Theory of Multidimensional Persistence by Carlsson and Zomorodian, Part II Sara Kalisnik

Winter 2013

Date Topic Discussion leader
January 31 Euler Integration of Gaussian Random Fields and Persistent Homology by Bobrowski and Borman Henry Adams
February 7 The structure and stability of persistence modules by Chazal, de Silva, Glisse, and Oudot Sara Kalisnik
February 28 The Computational Complexity of Knot and Link Problems by Hass, Lagarias, and Pippenger Michael Kerber
March 14 Euler Calculus with Applications to Signals and Sensing by Curry, Ghrist, and Robinson Daniel Müllner

Fall 2012

Date Topic Discussion leader
October 23 Computational topology for configuration spaces of hard disks by Carlsson, Gorham, Kahle, and Mason Michele Intermont
November 6 The structure and stability of persistence modules by Chazal, de Silva, Glisse, and Oudot Sara Kalisnik
November 27 Fréchet means for distributions of persistence diagrams by Turner, Mileyko, Mukherjee, and Harer Michael Kerber
December 11 Sheaf Theory Anthony Bak

Spring 2012

Date Topic Discussion leader
April 24 Conley index theory (chapters 1 and 2) by Mischaikow Henry Adams
May 8 Alexander duality for functions: the persistent behavior of land and water and shore by Edelsbrunner and Kerber Sara Kalisnik

Winter 2012

Date Topic Discussion leader
February 3 Topology of cyclo-octane energy landscape by Martin, Thompson, Coutsias, and Watson
Non-manifold surface reconstruction from high dimensional point cloud data by Martin and Watson		 Anthony Bak
February 17 Topological De-Noising: Strengthening the Topological Signal by Kloke and Carlsson Daniel Müllner
March 2 Linear-Size Approximations to the Vietoris-Rips Filtration by Sheehy Andrew Tausz
March 16 Vines and vineyards by updating persistence in linear time by Cohen-Steiner, Edelsbrunner, and Morozov Yang Li

Fall 2011

Date Topic Discussion leader
October 11 Computing persistent homology by Zomorodian and Carlsson Henry Adams
October 18 Topology-based simplification for feature extraction from 3D scalar fields by Gyulassy, Natarajan, Pascucci, Bremer, and Hamann Daniel Müllner
November 8 Local Homology Transfer and Stratification Learning by Bendich, Mukherjee, and Wang Daniel Chen
November 15 Target enumeration via Euler characteristic integrals by Baryshnikov and Ghrist Sara Kalisnik
November 29 A spectral algorithm for learning hidden Markov models by Hsu, Kakade, and Zhang Jonathan Huang
December 6 Persistent cohomology and circular coordinates by de Silva, Morozov, and Vejdemo-Johansson Anthony Bak

Spring 2011

Date Topic Discussion leader
April 13 Geometric inference for measures based on distance functions by Chazal, Cohen-Steiner, and Mérigot Henry Adams
April 20 Witnessed k-distance by Guibas, Mérigot, and Morozov Daniel Chen
April 27 Reeb graphs: approximation and persistence by Dey and Wang Daniel Müllner
May 4 Provable surface reconstruction from noisy samples by Dey and Goswami Aravind Babu
May 18 Multidimensional persistence Michael Lesnick
May 25 Optimal homologous cycles, total unimodularity, and linear programming by Dey, Hirani, and Krishnamoorthy Nan Hu
June 8 Algebraic topology and concurrency by Fajstrup, Raußen, Goubault
Detecting deadlocks in concurrent systems by Fajstrup, Goubault, Raußen
Directed homotopy theory, I. The fundamental category by Grandis 		Anthony Bak and Anton Dochtermann

Winter 2011

Date Topic Discussion leader
January 19 A weak definition of Delaunay triangulation by de Silva
Topological estimation using witness complexes by de Silva and Carlsson		 Henry Adams
January 26 Limit theorems for Betti numbers of random simplicial complexes by Kahle and Meckes Aravind Babu
February 2 Part II of the above Aravind Babu
February 9 Classifying clustering schemes by Carlsson and Mémoli
Persistent clustering and a theorem of J. Kleinberg by Carlsson and Mémoli
Characterization, stability, and convergence of hierarchical clustering methods by Carlsson and Mémoli		 Facundo Mémoli
February 23 A kernel view of the dimensionality reduction of manifolds by Ham, Lee, Mika, and Schölkopf Daniel Müllner
March 2 Diffusion maps by Coifman and Lafon
Vector diffusion maps and the connection Laplacian by Singer and Wu		 Adrian Butscher
March 9 Part II of the above Adrian Butscher
March 16 Gromov-Hausdorff stable signatures for shapes using persistence by Chazal, Cohen-Steiner, Guibas, Mémoli, and Oudot Michael Lesnick

Fall 2010

Date Topic Discussion leader
September 27 Analysis of scalar fields over point cloud data by Chazal, Guibas, Oudot, and Skraba
Persistent homology for kernels, images, and cokernels by Cohen-Steiner, Edelsbrunner, Harer, and Morozov		 Dmitriy Morozov
October 4 Hierarchical Morse-Smale complexes for piecewise linear 2-manifolds by Edelsbrunner, Harer, and Zomorodian Henry Adams
October 11 Geometric and topological guarantees for the WRAP reconstruction algorithm by Ramos and Sadri Daniel Chen
October 18 A user's guide to discrete Morse theory by Forman Sara Kalisnik
October 25 An algorithmic approach to chain recurrence by Kalies, Mischaikow, and VanderVorst
Vector field editing and periodic orbit extraction using morse decomposition by Chen, Mischaikow, Laramee, Pilarczyk, and Zhang		 Adrian Butscher
November 1 Approximating loops in a shortest homology basis from point data by Dey, Sun, and Wang Nan Hu
November 8 On a topological generalization of a theorem of Tverberg by Bárány, Shlosman, and Szücs Anton Dochtermann
November 15 Computing multidimensional persistence by Carlsson, Singh, and Zomorodian Michael Lesnick
November 22 Zigzag persistence by Carlsson and de Silva
Zigzag persistent homology and real valued functions by Carlsson, de Silva, and Morozov		 Aravind Babu
November 29 An impossibility theorem for clustering by Kleinberg
A uniqueness theorem for clustering by Zadeh and Ben-David		 Reza Zadeh
December 13 Persistence-based clustering in Riemannian manifolds by Chazal, Guibas, Oudot, and Skraba Daniel Müllner

Spring 2010

Date Topic Discussion leader
April 8 Random geometric complexes by Kahle
A statistical approach to persistent homology by Bubenik and Kim 		Matthew Kahle and
Aravind Babu
April 15 Alpha-beta witness complexes by Attali, Edelsbrunner, Harer, and Mileyko
The tidy set: a minimal simplicial set for computing homology of clique complexes by Zomorodian		 Daniel Chen and
Jonathan Jiang
April 22 Lipschitz functions have Lp-stable persistence by Cohen-Steiner, Edelsbrunner, Harer, and Mileyko
Proximity of persistence modules and their diagrams by Chazal, Cohen-Steiner, Glisse, Guibas, and Oudot		 Henry Adams
April 29 Boosting margin based distance functions for clustering by Hertz, Bar-Hillel, and Weinshall
Distance metric learning for large margin nearest neighbor classification by Weinberger, Blitzer, and Saul
Distance metric learning, with applicaiton to clustering with side-information by Xing, Ng, Jordan, and Russel		 Adrian Butscher
May 6 Discussion about data sets Daniel Müllner and
Facundo Mémoli
May 13 Laplace-Beltrami eigenfunctions: towards an algorithm that "understands" geometry by Lévy
Spectral mesh processing by Zhang, van Kaick, and Dyer		 Maks Ovsjanikov
May 20 Disease specific genomic analysis: identifying the signature of pathologic biology by Nicolau, Tibshirani, Børresen-Dale, and Jeffrey
and ongoing research		 Monica Nicolau
May 27 Spectral methods for dimensionality reduction by Saul, Weinberger, Sha, Ham, and Lee
Laplacian eigenmaps for dimensionality reduction and data representation by Belkin and Niyogi
Diffusion maps by Coifman and Lafon		 Mirela Ben-Chen
June 3 Laplace-Beltrami spectra as 'shape-DNA' of surfaces and solids by Reuter, Wolter, and Peinecke
Drums that sound the same by Chapman		 Katarzyna Gebal
June 10 Embedding riemannian manifolds by their heat kernel by Bérard, Besson, and Gallot Facundo Mémoli

Winter 2010

Date Topic Discussion leader
January 14 Persistent clustering and a theorem of J. Kleinberg by Carlsson and Mémoli
Multiparameter hierarchical clustering methods by Carlsson and Mémoli		 Aravind Babu
January 21 A topological view of unsupervised learning from noisy data by Niyogi, Smale, and Weinberger
Geometric inference for measures based on distance functions by Chazal, Cohen-Steiner, and Mérigot		 Quentin Mérigot
January 25 Measuring and computing natural generators for homology groups by Chen and Freedman
Localized homology by Zomorodian and Carlsson		 Mridul Aanjaneya
February 1 Persistent cohomology and circular coordinates by de Silva, Morozov, and Vejdemo-Johansson
Möbius voting for surface correspondence by Lipman and Funkhouser		 Mikael Vejdemo-Johansson
February 8 On the local behavior of spaces of natural images by Carlsson, Ishkhanov, de Silva, and Zomorodian
and ongoing research		 Jose Perea
February 22 Target enumeration via Euler characteristic integrals by Baryshnikov and Ghrist Henry Adams
March 1 Optimal reconstruction might be hard by Attali and Lieutier
Persistence-sensitive simplification of functions on surfaces in linear time by Attali, Glisse, Hornus, Lazarus, and Morozov		 Andrew Yarmola
March 8 The theory of multidimensional persistence by Carlsson and Zomorodian
and ongoing research		 Michael Lesnick