About: An online seminar focusing on Vietoris-Rips complexes and related topics (broadly interpreted), such as new connections between applied and quantitative topology, Čech complexes, nerve lemmas, manifold reconstruction, metric thickenings, the tight span, the filling radius, Gromov-Hausdorff distances, optimal transport, homotopies of bounded size, geometric group theory, topological combinatorics, geometric topology, equivariant topology, polytopes, configuration spaces, minimal homology generators, computational topology, algorithms, applications to data analysis, etc, and this is far from an exclusive list.
Organizers: Henry Adams (2021-present), John Bush (2022-present), Sunhyuk Lim (2022-present), and Facundo Mémoli (2021-present)
Logistics: We meet approximately every-other Friday at 11am Eastern Time (UTC-5 or UTC-4, depending on daylight savings), unless noted otherwise. Please join the Applied Algebraic Topology Research Network (AATRN) mailing list to receive email invitations to the Zoom talks. Recordings of most of the talks are posted to the AATRN YouTube Channel, in particular at this playlist.
Associated Workshop: You may interested in the associated Workshop on Bridging Applied and Quantitative Topology (and its associated YouTube playlist) that happened the week of May 9-13, 2022.
Ethics: "The correct attribution of mathematical results is essential, both because it encourages creativity, by benefiting the creator whose career may depend on the recognition of the work and because it informs the community of when, where, and sometimes how original ideas entered into the chain of mathematical thought." We ask that both attendees and also speakers of our seminar adhere to the Ethical Guidelines of the AMS, from where the previous sentence is quoted. See in particular Sections I and II. Results and ideas presented in this seminar should be treated in a similar way to papers posted online to the arXiv.
Videos can be cited (especially when no accompanying paper is currently available) via the following sample bibtex entry:
@misc{Barmak-VRtalk2021,
title = {Star clusters in clique complexes and the {V}ietoris--{R}ips complex of planar sets},
author = {Jonathan Barmak},
note = {AATRN Vietoris--Rips Online Seminar},
year = {2021},
howpublished = {\url{https://youtu.be/9ZGjyVBWUjg}},
}
Summer 2023
Friday June 9, Alexey Balitskiy, Urysohn width
Friday June 16, Melanie Weber, Exploiting geometric structure in matrix-valued optimization
Friday June 23, Shin-ichi Ohta, Barycenters and a law of large numbers in Gromov hyperbolic spaces
Friday July 21, Dominique Attali, Reconstructing manifolds by weighted l_1-norm minimization
Spring 2023
Friday January 20, Sergio Zamora, The lower semi-continuity of $\pi_1$ and nilpotent structures in persistence
Friday February 3, Urs Lang, Combinatorial dimension and higher-rank hyperbolicity
Friday February 24, Irina Gelbukh, How the Reeb graph of a smooth function encodes the class of the function and the type of the manifold
Friday March 3, Emilie Purvine, Applied Topology for Discrete Structures
Friday March 17, Nicolò Zava, Every stable invariant of finite metric spaces produces false positives
Friday March 31, Samir Shukla, Vietoris-Rips complexes of hypercube graphs
Friday April 14, Hubert Wagner, Topology of... surprisal: or how to combine information theory with Vietoris-Rips filtrations
Friday May 26, Uzu Lim, Strange random topology of the circle
Fall 2022
Thursday September 8, Vanessa Robins: The Extended Persistent Homology Transform for Manifolds with Boundary
Friday September 16, Dmitri Burago, A Mozaic from Geometry, Dynamics, PDEs, and maybe more
Friday September 30, Lori Ziegelmeier, Cycle Representatives in Persistent Homology using Linear Programming
Friday November 11, Abigail Hickok, Persistence Diagram Bundles: A multidimensional generalization of vineyards
Friday December 9, Éric Colin de Verdière, Optimal topological simplification of surfaces: Algorithms and hardness
Summer 2022
Friday June 10, Diego Mondéjar Ruiz, Approximation of compact metric spaces by finite samples
Friday July 22, Krystyna Kuperberg, Shape Theory: Vietoris-Čech approach to homotopy
Friday July 29, Simon Zhang, Recent uses of GPU accelerated computation of VR barcodes in evaluating Deep Learning models
Friday August 12, Alexander Rolle: Homology inference for the degree-Rips bifiltration
Friday August 19, Francisco Martinez Figueroa: Chromatic number of G-Borsuk graphs
Spring 2022
Friday January 21, Ling Zhou, Persistent homotopy groups of metric spaces
Friday February 4, Don Sheehy, Persistent Homology of Lipschitz Extensions
Friday February 18, Bradley Nelson, Parameterized Vietoris-Rips Filtrations via Covers
Friday March 4, Ulrich Bauer, Gromov hyperbolicity, geodesic defect, and apparent pairs in Rips filtrations
Friday March 18, Fedor Manin, Linear homotopies of maps to spheres
Friday April 1, Stéphane Sabourau, Macroscopic scalar curvature and local collapsing
Friday April 15, Hannah Alpert, Homology of sliding-squares configuration spaces
Friday April 29, Barbara Giunti, Average complexity of barcode computation for Vietoris-Rips filtrations
Week of May 9-13, Workshop on Bridging Applied and Quantitative Topology; see also the workshop's YouTube playlist
Friday May 27, Regina Rotman, Curvature bounds and the length of the shortest closed geodesic
Fall 2021
Friday September 10, Yevgeny Liokumovich, Urysohn width, isoperimetric inequalities and scalar curvature
Friday September 24, Sunhyuk Lim, The Gromov-Hausdorff distance between spheres
Friday October 29, Jürgen Jost, Geometry and Topology of Data
Friday November 5, Johnathan Bush, Maps of Čech and Vietoris–Rips complexes into euclidean spaces
Friday December 3, Luis Scoccola, Density-sensitive and robust Vietoris-Rips filtrations
Summer 2021
Friday June 4, Florian Frick, Rips complexes, projective codes, and zeros of odd maps
Friday June 18, Parvaneh Joharinad, Hyperconvex spaces and their associated Čech complexes
Friday July 2, Yusu Wang, Graph skeletonization of PCDs via topological methods
Wednesday July 14, Mikhail Katz, Collapsing surfaces
Friday August 13, Jonathan Barmak, Star clusters in clique complexes and the Vietoris-Rips complex of planar sets
Friday August 27, Francesca Tombari, Decomposing simplicial complexes (without losing pieces)
Spring 2021
Friday March 12, Henry Adams, Vietoris-Rips thickenings: Problems for birds and frogs
Friday March 26, Facundo Mémoli, Vietoris-Rips Persistent Homology, Injective Metric Spaces, and The Filling Radius
Friday April 9, Baris Coskunuzer, Geometric Approaches on Persistent Homology
Friday April 23, Žiga Virk, A counter-example to Hausmann's conjecture
Friday May 7, Bei Wang, Homotopy Types of Vietoris–Rips Complexes of Metric Gluings
Friday May 21, Matthew Zaremsky, Vietoris-Rips complexes and geometric group theory