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, INRIA Stability and Convergence Properties of Persistence Diagrams in Topological Data Analysis |
9:40-10:00 | Break |
10:00-10:40 | Yusu Wang, Ohio State University Data Sparsification in Inferring Topology of Manifolds |
10:40-11:00 | Break |
11:00-11:40 | Peter Bubenik, Cleveland State University Statistical 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 Carolina Some Uniformity Results for Dynamical Systems |
2:40-3:00 | Break |
3:00-3:40 | Larry Wasserman, Carnegie Mellon University Statistical 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 Illinois What is the Dimension of the Internet? |
9:40-10:00 | Break |
10:00-10:40 | Katharine Turner, University of Chicago Can Topological Summary Statistics be Sufficient? |
10:40-11:00 | Break |
11:00-11:40 | Giseon Heo, University of Alberta Topological and Statistical Data Analysis |
11:40-1:00 | Lunch (provided at SAMSI) |
1:00-1:40 | Facundo Memoli, Ohio State University Curvature Sets over Persistence Diagrams |
1:40-2:00 | Break |
2:00-2:40 | Paul Bendich, Duke University Persistent Local Homology: Theory, Algorithms, Applications, New Directions |
2:40-3:00 | Break |
3:00-3:40 | Lek-Heng Lim, University of Chicago Hodge 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 University Statistical Inference for Persistence Diagrams |
9:40-10:00 | Break |
10:00-10:40 | Elizabeth Munch, Institute for Mathematics and its Applications Categorification of Reeb Graphs |
10:40-11:00 | Break |
11:00-11:40 | J.S. Marron, University of North Carolina OODA 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 University Persistent Homology of Time-delay Embeddings |
9:40-10:00 | Break |
10:00-10:40 | Jessi Cisewski, Carnegie Mellon University Persistent Homology of the Intergalactic Medium via the Lyman-alpha Forest |
10:40-11:00 | Break |
11:00-11:40 | Bei Wang, University of Utah Geometric Inference on Kernel Density Estimates |
11:40-1:00 | Lunch (provided at SAMSI) |
1:00-1:40 | Brittany Fasy, Tulane University Local Homology Based Distance Between Maps |
1:40-2:00 | Break |
2:00-2:40 | Harish Chintakunta, North Carolina State University Distributed Homology using Harmonics |
2:40-3:00 | Break |
3:00-3:40 | Vic Patrangenaru, Florida State University Neighborhood 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 University Phase Transitions in Random Čech Complexes |
9:40-10:00 | Break |
10:00-10:40 | Jennifer Gamble, North Carolina State University Quantifying Coverage in Dynamic Sensor Networks with Zigzag Persistent Homology |
10:40-11:00 | Break |
11:00-11:40 | Peter Kim, University of Guelph Pyrosequencing and Computational Topology: A tale of two homologies |
11:40-12:00 | Discussion |
12:00 | Lunch (provided at SAMSI) Adjourn |