Explore advanced topological data analysis methods and their applications in data science through this comprehensive conference featuring 18 hours of expert presentations from leading researchers in the field. Delve into cutting-edge topics beyond traditional TDA, including multidimensional persistence, Reeb graphs, discrete Morse theory, spectral complexes, and persistent functions. Learn how geometric, topological, and combinatorial models are applied across diverse domains such as materials science, chemistry, biology, sensor networks, and machine learning. Discover the four-stage framework of data transformation: from raw data to topological representations, feature extraction, and learning models. Gain insights from renowned speakers including Herbert Edelsbrunner on space filling diagrams, Ginestra Bianconi on topological Dirac operators, Konstantin Mischaikow on combinatorial homological algebra, and Guo-Wei Wei on mathematical AI applications in biosciences. Master advanced concepts including simplicial neural networks, multi-parameter persistence, network sheaves, and persistent homology characterization of rare events. Access comprehensive slides and materials to support your understanding of these sophisticated mathematical frameworks and their practical implementations in modern data analysis challenges.

Syllabus

Herbert Edelsbrunner: The intrinsic volumes of a space filling diagram and their derivatives
Ginestra Bianconi (8/28/21): The topological Dirac operator and the dynamics of topological signals
Vidit Nanda (8/28/21): Principal components along quiver representations
Konstantin Mischaikow (8/28/21): Solving systems of ODEs via combinatorial homological algebra
Guo-Wei Wei (8/28/21): How Math and AI are revolutionizing biosciences
Stefania Ebli (8/29/21): Simplicial Neural Networks
Claudia Landi (8/29/21): Discrete Morse Theory meets Multi-Parameter Persistence
Francesco Vaccarino (8/29/21): Parallel decomposition of persistence modules through interval bases
Mattia G. Bergomi (8/29/21): Comparing Neural Networks via Generalized Persistence
Jürgen Jost (8/29/21): Geometry and Topology of Data
Kelin Xia (8/29/21): Persistent function based machine learning for drug design
Robert Ghrist (8/29/21): Laplacians and Network Sheaves
Sayan Mukherjee (8/29/21): Modeling shapes and fields: a sheaf theoretic perspective
Farzana Nasrin (8/29/21): Random Persistence Diagram Generator
Hiraoka Yasuaki (8/30/21): On characterizing rare events in persistent homology
Wojciech Chachólski (8/30/21): Enabling a machine to sense geometry
Patrizio Frosini (8/30/21): On the role of group equivariant non-expansive operators in TDA
Marian Mrozek (8/30/21): Combinatorial vs. Classical Dynamics: Recurrence
Massimo Ferri (8/30/21): Selection of points in persistence diagrams
R. Levi: An application of neighborhoods in directed graphs in the classification of binary dynamics
Ling Zhou (8/30/21): Other Persistence Invariants: homotopy and the cohomology ring
Henry Adams (8/30/21): Vietoris-Rips complexes of hypercube graphs