The school will introduce participants to a wide range of geometric methods for analyzing data. Data points often come with some notion of distance between them, or can be arranged into a graph, a simplicial complex or a hypergraph, and that allows for the application of quantitative geometric methods. Topological data analysis looks at the dependence of the Betti numbers (certain topological invariants) on a metric scale parameter. Other methods consider the statistics of graph curvatures, concepts in discrete geometry formulated in analogy to Riemannian geometry, and these deliver local invariants that are easy to compute, but indirectly encode much global information. Such discrete curvatures will constitute a particular focus of the school, but we shall also cover a range of other methods, and in particular, applications in many diverse fields, from neuroscience to image analysis or robotics
Organizers
| Emil Saucan, Braude College | Jürgen Jost, MPI MIS, Leipzig |
Speakers
| Anthea Monod, Imperial College | Omer Bobrowski, Technion & Queen Mary University |
| Florentin Münch, MPI MIS, Leipzig | Michael Farber, Queen Mary University |
| Emil Saucan, Braude College | Matthias Keller, Postdam University |
| Areejit Samal, IMSc, Chennai | Jürgen Jost, MPI MIS, Leipzig |
| Kelin Xia, Nanyang Technological University | David Gu, Stony Brook University |
Program
Monday, February 13, 2023
9:30-10:00 Registration and Opening
10:00-11:30 Jürgen Jost Discrete Ricci and sectional curvatures for metric spaces and networks 1
11:30-12:00 Coffee break
12:00-13:30 Jürgen Jost Discrete Ricci and sectional curvatures for metric spaces and networks 2
13:30-14:30 Lunch
14:30-16:00 Omer Bobrowski Universality in Random Persistence Diagrams
16:00-16:30 Coffee break
16:30-17:00 Yinon Nachshon & Paz Naim Ricci curvature and the stream of associations
17:00-18:30 Emil Saucan Metric curvatures for networks
Tuesday, February 14, 2023
9:30-11:00 Michael Farber Algebraic topology and autonomous robot motion 1
11:00-11:30 Coffee break
11:30-13:00 Michael Farber Algebraic topology and autonomous robot motion 2
13:00-14:00 Lunch
14:00-19:00 Excursion and festive dinner
Wednesday, February 15, 2023
9:30-11:00 Florentin Münch Discrete Ricci curvature and semigroup estimates
10:30-11:30 Coffee break
11:30-13:00 Florentin Münch Discrete Ricci curvature and homology
13:00-14:00 Lunch
14:00-16:00 Posters and short talks session:
Anna Song Signed distance persistence homology and Morse Theory for porous shape analysis
Yohai Reani Cycle Registration in Persistent Homology with Applications in Topological Bootstrap
Roan Talbut Wasserstein Distances on Tropical Projective Torii of Different Dimensions
16:00-16:30 Coffee break
16:30-18:00 David Gu Abel-Jacobi theory for meshing
Thursday, February 16, 2023
9:30-11:00 Arejit Samal Geometry-inspired measures with wide applications in network science
11:00-11:30 Coffee break
11:30-13:00 Emil Saucan Metric curvatures for networks
13:00-14:00 Lunch
14:00-15:30 Anthea Monod Some ideas for algebraic topology and tropical geometry in statistics and machine learning
15:30-16:00 Coffee break
16:00-17:30 David Gu Optimal transport for generative model
17:30-18:00 Alon Katz Distance Function for MEG Numerical Cognitive Tasks Trials
Friday, February 17, 2023
9:30-11:00 Kelin Xia Mathematical AI for molecular data analysis
11:00-11:30 Coffee break
11:30-13:00 Matthias Keller Dirichlet forms on graphs, intrinsic metrics and the heat equation
13:00-13:15 Closing & Good Bye
PhD students, Postdocs and all researchers in Mathematics and Computer Science are invited.
A Poster Session will be organized – The interested participants are invited to present their research.
Qualified applications will be accepted until all places are filled.
Local Organizing Committee: Aviv Gibali, Mark Elin, Lavi Karp, Emil Saucan
Important notice:
Dear Participants,
Please notice that when entering Israel you need to have proof of international health insurance (preferably in English), which must be presented upon entry, which will cover the costs in the event of a Covid19 illness. This foreign health insurance is mandatory! See, e.g. Allgemeine Informationen
Lodging Information: The Scool’s hotel is Rimonim Madison Hotel Nahariya
Contact: Ella Dechter, Email ellade@braude.ac.il, Phone +972-4-9901801