Applied Algebraic Topology Methods, Computation, and Science - ATMCS/AATRN 2020

Applied Algebraic Topology Network via YouTube

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Explore advanced topics in applied algebraic topology through this comprehensive seminar series co-hosted by ATMCS (Algebraic Topology: Methods, Computation, and Science) and AATRN (Applied Algebraic Topology Research Network). Delve into cutting-edge research presentations covering persistence diagrams and optimal partial transport, differential calculus on persistence barcodes, density-based clustering algorithms, and embeddings in Tverberg-type problems. Examine homotopical decompositions of simplicial complexes, spatiotemporal persistent homology for dynamic metric spaces, and topological assembly methods for locally linear Euclidean models. Study sheaves as computable topological invariants, ephemeral persistence modules, and efficient approximation techniques for matching distances in multi-parameter persistence. Investigate limit theorems for Betti numbers in random simplicial complexes, comparative stability of zigzag bottleneck distances, and fundamental groups of random cubical complexes. Learn about data-driven torsion coordinates, Wasserstein stability, Conley-Morse-Forman theory for combinatorial multivector fields, and intrinsic topological transforms via distance kernel embedding. Discover generalized penalty methods for circular coordinate representation, hardness results in discrete Morse theory, statistical invariance of Betti numbers, and geometric analysis of enzyme kinetics. Explore nonembeddability properties of persistence diagrams, bifurcation detection using zigzag persistent homology, brain dynamics analysis through Mapper techniques, and topological simplification of voxelized data. Master theoretical foundations including limit theorems for topological invariants, intrinsic dimension inference for convex sensing data, interleaving techniques for persistence in posets, and quasiperiodicity analysis using persistent Künneth formulas.

Syllabus

Vincent Divol 5/25/20: Studying the space of persistence diagrams using optimal partial transport II
Théo Lacombe (5/25/20): Studying the space of persistence diagrams using optimal partial transport I
Jacob Leygonie (6/1/20): Differential calculus on persistence barcodes
Alexander Rolle (6/1/20): Stable and consistent density-based clustering
Marek Filakovský: Embeddings and Tverberg-Type Problems: New Algorithms and Undecidability Results
Francesca Tombari (6/8/20): Homotopical decompositions of simplicial and Vietoris Rips complexes
Woojin Kim (6/15/20): Spatiotemporal persistent homology for dynamic metric spaces
Joshua Mike (6/15/20): TALLEM: Topological Assembly of Locally Linear Euclidean Models
Nicolas Berkouk (6/22/20): Sheaves as computable and stable topological invariants for datasets:
François Petit (6/22/20): Ephemeral persistence modules and distance comparison
Arnur Nigmetov 6/29/20: Efficient approximation of the matching distance for 2-parameter persistence
Mickaël Buchet: Every nD persistence module is the restriction of an (n+1)D indecomposable module.
Shu Kanazawa (7/6/2020): A limit theorem for Betti numbers of random simplicial complexes
Killian Meehan (7/6/2020): Comparative Stability of Two Zigzag Bottleneck Distances
Érika Roldán Roa (7/13/20): The fundamental group of 2-dimensional random cubical complexes
Luis Polanco (7/13/20): Data driven torsion coordinates and Wasserstein stability
Michał Lipiński 7/20/20: Conley-Morse-Forman theory for generalized combinatorial multivector fields
Elchanan Solomon (7/20/20): Intrinsic Topological Transforms via the Distance Kernel Embedding
Hengrui Luo (7/27/20): Generalized penalty for circular coordinate representation
Abhishek Rathod (7/27/70): Hardness results in discrete Morse theory for 2-complexes
Siddharth Vishwanath (8/3/20): Statistical invariance of Betti numbers in the thermodynamic regime
Lewis Marsh (8/3/20): Geometric and topological data analysis of enzyme kinetics
Alexander Wagner (8/10/20): Nonembeddability of persistence diagrams into Hilbert spaces
Sarah Tymochko (8/10/20) Detecting bifurcations in dynamical systems with zigzag persistent homology
Samir Chowdhury (8/17/20): Exploring brain dynamics during ongoing cognition using Mapper
Hannah Schreiber (8/17/20): Topological simplification of voxelized data
Takashi Owada 1/11/20: Limit Thms for top. invariants of the dynamic multi-param. simplicial complex
Min-Chun Wu 1/11/2021: A Topological Approach to Inferring the Intrinsic Dim. of Convex Sensing Data
Anastasios Stefanou (1/12/21): Interleaving by parts for persistence in a poset
Hitesh Gakhar (1/12/21):A theoretical analysis of quasiperiodicity using persistent Künneth formulae
Tomoo Yokoyama (1/13/21):Generalizations of Morse graph of flows and Reeb graph of Hamiltonian flows
Nicola Quercioli (1/13/21): Group equivariant non-expansive operators and their use in Deep Learning
Alex Elchesen (1/14/21): Universality of Persistence Diagrams and Bottleneck & Wasserstein Distances
Anna Schenfisch (1/14/21): A Faithful Discretization of the Persistent Homology Transform
Ling Zhou (1/15/21): Persistent Homotopy Groups of Metric Spaces
Nathanael Cox (1/15/21): Effective Algorithms For Quotients of Semi-Algebraic Equivalence Relations
Zhengchao Wan (1/16/21): Computing Gromov-Hausdorff distances between ultrametric spaces
Luis Scoccola (1/16/21): Locally persistent categories & metric properties of interleaving distances