The section numbers correspond either to Munkres - Topology, or Edelsbrunner, Harer - Computational Topology.

Date | Topic |
---|---|

1/18 | Intro, Topological spaces (M. 12) |

1/20 | Bases, subspace topology (M. 13, 16) |

1/23 | Closed sets, limit points (M. 17) |

1/25 | Continuous functions (M. 18) |

1/27 | The metric topology (M. 20) |

1/30 | The quotient topology (M. 22) |

2/1 | Connected spaces (M. 23), Graphs (EH I.1) |

2/3 | Surfaces (EH II.1) |

2/6 | Simplicial complexes (EH III.1) |

2/8 | Convex set systems (EH III.2) |

2/10 | Homology (EH IV.1) |

2/13 | Homology (EH IV.1) |

2/15 | Induced maps on homology (EH IV.1) |

2/17 | Euler-Poincare formula (EH IV.2) Giusti et. al. - Clique topology reveals intrinsic geometric structure in neural correlations Masulli, Villa - The topology of the directed clique complex as a network invariant |

2/20 | Relative homology (EH IV.3) |

2/22 | Exact sequences (EH IV.4) |

2/24 | Exact sequence of a pair (EH IV.3) Homology of a genus g surface |

2/27 | The mapper algorithm Python Mapper - software implementation of mapper Singh, Mémoli, Carlsson - Topological Methods for the Analysis of High Dimensional Data Sets and 3D Object Recognition - original paper Kraft - Illustrations of Data Analysis Using the Mapper Algorithm and Persistent Homology - more detailed explanation |

3/1 | Persistent Homology (EH VII.1) |

3/3 | Persistent Homology (EH VII.1) |

3/6 | Stability Theorems (EH VIII.2) |

3/8 | Midterm - Covers sections III.1, IV.1, IV.2 (Euler-Poincaré formula), IV.3 in Edelsbrunner-Harer's bookPractice problems |

3/10 | Applications Persistent homology transform for modeling shapes and surfaces Sliding windows and persistence: an application of topological methods to signal analysis |

3/13-3/17 | Spring Break |

3/20 | Morse theory (EH VI.1) |

3/22 | Morse theory (EH VI.1) |

3/24 | Transversality (EH VI.2) |

3/27 | The Morse-Smale complex (EH VI.2) |

3/29 | CW complexes REU paper on cellular homology |

3/31 | Cellular homology |

4/3 | Cellular homology |

4/5 | Discrete Morse theory Forman - A user's guide to discrete Morse theory Forman - Morse theory for cell complexes |

4/7 | Discrete Morse theory |

4/10 | Discrete Morse theory |

4/12 | Discrete Morse theory |

4/14-4/17 | |

4/19 | |

4/21 | |

4/24 | |

4/26 | |

4/28 | Presentations 9:25 -- 9:35 Christian Gorski 9:40 -- 9:50 Shijie Jin 9:55 -- 10:05 Zhixing Zhang |

5/1 | Presentations 9:18 -- 9:28 Ariel Navotas 9:30 -- 9:40 Alex Sitaras 9:42 -- 9:50 Luke Vandertie 9:52 -- 10:02 Marissa Koscielski 10:04 -- 10:14 Erin Denison |

5/3 | Presentations 9:25 -- 9:35 Christian Hokaj / Matthew Drnevich 9:38 -- 9:48 Robert Black / Jonathan Baker 9:51 -- 10:01 Sean Kent 10:04 -- 10:14 Samantha Kerper |