# 2013-14: LDHD: Topological Data Analysis: February 3-7, 2014

## Workshop Information

This workshop was held at SAMSI.

Topological Data Analysis began a little more than 20 years ago with the introduction of persistence by Edelsbrunner, Lestcher and Zomorodian. Since that time the field has grown significantly. Many strong theorems, numerous algorithms, and pieces of software have been created in that period. More recently, the field has considered stochastic modeling and analysis, which has resulted in interactions with Statistics, Probability, and Computer Science. This workshop focused on the interaction of Statistics and Probability with this new area of Applied Mathematics. The goals were to familiarize people in both areas with techniques from the other and to understand what future directions are the most promising.

Topics included:

- Statistics and persistent homology
- Topological data analysis and inference in dynamical systems and time series
- Topological data analysis and shape statistics
- Topological data analysis and network models
- Probability models for random topology objects
- Statistical applications of Hodge theory

Schedule

Participant List

Speaker Title and Abstracts

Poster Titles

### Schedule

**Monday, February 3, 2014 at SAMSI, Room 150**

8:30-8:55 a.m. | Registration |

8:55-9:00 | Welcome |

9:00-9:40 | Frederic Chazal, INRIAStability and Convergence Properties of Persistence Diagrams in Topological Data Analysis |

9:40-10:00 | Break |

10:00-10:40 | Yusu Wang, Ohio State UniversityData Sparsification in Inferring Topology of Manifolds |

10:40-11:00 | Break |

11:00-11:40 | Peter Bubenik, Cleveland State UniversityStatistical Topological Data Analysis using Persistence Landscapes |

11:40-1:00 | Lunch (provided at SAMSI) |

1:00-1:40 | Megan Owen, Lehman College (CUNY)Mean and Variance of Metric Trees |

1:40-2:00 | Break |

2:00-2:40 | Andrew Nobel, University of North CarolinaSome Uniformity Results for Dynamical Systems |

2:40-3:00 | Break |

3:00-3:40 | Larry Wasserman, Carnegie Mellon UniversityStatistical Inference for Functional Summaries of Persistent Homology |

3:40-4:00 | Break |

4:00-5:00 | Discussion |

**Tuesday, February 4, 2014 at SAMSI, Room 150**

9:00-9:40 a.m. | Yuliy Baryshnikov, University of IllinoisWhat is the Dimension of the Internet? |

9:40-10:00 | Break |

10:00-10:40 | Katharine Turner, University of ChicagoCan Topological Summary Statistics be Sufficient? |

10:40-11:00 | Break |

11:00-11:40 | Giseon Heo, University of AlbertaTopological and Statistical Data Analysis |

11:40-1:00 | Lunch (provided at SAMSI) |

1:00-1:40 | Facundo Memoli, Ohio State UniversityCurvature Sets over Persistence Diagrams |

1:40-2:00 | Break |

2:00-2:40 | Paul Bendich, Duke UniversityPersistent Local Homology: Theory, Algorithms, Applications, New Directions |

2:40-3:00 | Break |

3:00-3:40 | Lek-Heng Lim, University of ChicagoHodge Theory in Data Analysis |

3:40-4:00 | Break |

4:00-5:00 | Discussion |

5:00-6:30 | Poster Session and Reception SAMSI will provide poster presentation boards and tape. The board dimensions are 4 ft. wide by 3 ft. high. They are tri-fold with each side being 1 ft. wide and the center 2 ft. wide. Please make sure your poster fits the board. The boards can accommodate up to 16 pages of paper measuring 8.5 inches by 11 inches. |

**Wednesday, February 5, 2014 at SAMSI, Room 150**

9:00-9:40 a.m. | Fabrizio Lecci, Carnegie Mellon UniversityStatistical Inference for Persistence Diagrams |

9:40-10:00 | Break |

10:00-10:40 | Elizabeth Munch, Institute for Mathematics and its ApplicationsCategorification of Reeb Graphs |

10:40-11:00 | Break |

11:00-11:40 | J.S. Marron, University of North CarolinaOODA of Tree-Structured Data Objects |

11:40-12:00 | Discussion |

12:00 | Box Lunch (provided at SAMSI) - Free Afternoon |

**Thursday, February 6, 2014 at SAMSI, Room 150**

9:00-9:40 a.m. | Jose Perea, Duke UniversityPersistent Homology of Time-delay Embeddings |

9:40-10:00 | Break |

10:00-10:40 | Jessi Cisewski, Carnegie Mellon UniversityPersistent Homology of the Intergalactic Medium via the Lyman-alpha Forest |

10:40-11:00 | Break |

11:00-11:40 | Bei Wang, University of UtahGeometric Inference on Kernel Density Estimates |

11:40-1:00 | Lunch (provided at SAMSI) |

1:00-1:40 | Brittany Fasy, Tulane UniversityLocal Homology Based Distance Between Maps |

1:40-2:00 | Break |

2:00-2:40 | Harish Chintakunta, North Carolina State UniversityDistributed Homology using Harmonics |

2:40-3:00 | Break |

3:00-3:40 | Vic Patrangenaru, Florida State UniversityNeighborhood Hypothesis Testing for Mean Contour Shapes of Corpus Callosum Mid Sections |

3:40-4:00 | Break |

4:00-5:00 | Discussion |

**Friday, February 7, 2014 at SAMSI, Room 150**

9:00-9:40 a.m. | Omer Bobrowski, Duke UniversityPhase Transitions in Random Čech Complexes |

9:40-10:00 | Break |

10:00-10:40 | Jennifer Gamble, North Carolina State UniversityQuantifying Coverage in Dynamic Sensor Networks with Zigzag Persistent Homology |

10:40-11:00 | Break |

11:00-11:40 | Peter Kim, University of GuelphPyrosequencing and Computational Topology: A tale of two homologies |

11:40-12:00 | Discussion |

12:00 | Lunch (provided at SAMSI) Adjourn |