Description

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Recent years have seen an enormous growth in the applications of topology to other disciplines from the biological sciences to materials science, and from dynamical systems to cosmology and engineering. Many of these are factored through “topological data analysis” (TDA), but not all, with notable exceptions among those from dynamics and from engineering. All of these applications are due to topology’s capacity to define precise invariants from imprecise data: topological invariants (like the winding number of a curve around a point) are usually discrete and have some stability properties (here, to arbitrary perturbations that don’t move points as much as their distance to that point) that make them attractive.

However, topological stability is quite different from ordinary statistical stability. A single outlier can completely change the apparent topology of a space. One of the ways of dealing with this, persistence, has had numerous applications within pure math in recent years (in differential geometry, group theory, and approximation theory, to name three). The study of topology of random processes, and how the randomness perturbs topology is thus arising as an important scientific issue with potentially very wide significance. This workshop will bring together workers who have been dealing with this in different settings and in different ways, which should lead to progress in both application domains, and in a longer run, on the fundamental problems.

This workshop will include a poster session. In order to propose a poster, you must first register for the workshop, and then submit a poster proposal using the form that will become available on this page after you register. The registration form should not be used to propose a poster. The deadline for proposing a poster is March 3, 2023.

Organizers

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S M
Sayan Mukherjee Duke Statistics, University of Leipzig CS, Max Planck Institute for Mathematics in the Sciences
K T
Katharine Turner Mathematical Sciences Institute, Australian National University
S W
Shmuel Weinberger University of Chicago, Mathematics

Speakers

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O B
Omer Bobrowski Technion – Israel Institute of Technology
F C
Fred Chazal INRIA
L C
Lorin Crawford Microsoft
H E
Herbert Edelsbrunner ISTA – Institute of Science and Technology Austria
T H
Teresa Heiss ISTA – Institute of Science and Technology Austria
M K
Matthew Kahle Ohio State University
F M
Facundo Mémoli Ohio State University
W M
Washington Mio Florida State University
K M
Konstantin Mischaikow Rutgers University
A M
Anthea Monod Imperial College London
L M
Liz Munch Michigan State University
T O
Takashi Owada Purdue University
D P
Daniel Perez École normale supérieure – ENS
V R
Vanessa Robins Australian National University
B S
Benjamin Schweinhart George Mason University
P S
Primoz Skraba Queen Mary University of London and Jozef Stefan Institute, Slovenia
A S
Alex Strang University of Chicago
J T
Jonathan Taylor Stanford University
S T
Sarah Tymochko University of California, Los Angeles (UCLA)
B W
Bei Wang University of Utah
Y W
Yusu Wang University of California, San Diego (UCSD)
E W
Erin Wolf-Chambers St. Louis University

Schedule

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Monday, March 20, 2023
9:00-9:45 CDT
The correspondence of max-flow to the absolute permeability of porous systems

Speaker: Vanessa Robins (The Australian National University)

10:00-10:30 CDT
Coffee Break
10:30-11:15 CDT
Large deviation principle for geometric and topological functionals and associated point processes

Speaker: Takashi Owada (Purdue University)

11:30-12:30 CDT
Lunch
12:30-13:15 CDT
Distortion, on the Average and in Expectation

Speaker: Herbert Edelbrunner (ISTA – Institute of Science and Technology Austria)

13:35-2:10 CDT
Identifying Nonlinear Dynamics with High Confidence from Sparse Data

Speaker: Konstantin Mishaikow (Rutgers University)

14:35-15:00 CDT
Coffee Break
15:00-15:45 CDT
Data Analysis in Metric Spaces Through Metric Observables

Speaker: Washington Mio (Florida State University)

Tuesday, March 21, 2023
9:00-9:45 CDT
Exploring the Topology of Word Embeddings

Speaker: Bei Wang (University of Utah)

10:00-10:30 CDT
Coffee Break
10:30-11:15 CDT
On Complexity of Computing Bottleneck and Lexicographic Optimal Cycles in a Homology Class

Speaker: Erin Wolf-Chambers (St. Louis University)

11:30-12:30 CDT
Lunch
12:30-13:15 CDT
Topology and Local Geometry of the Eden Model

Speaker: Benjamin Schweinhart (George Mason University)

13:35-14:20 CDT
Homology of Gaussian random chain complexes

Speaker: Matthew Kahle (Ohio State University)

14:35-15:00 CDT
Coffee Break
15:00-15:45 CDT
Persistence Diagrams, Euler Characteristics, and Mobius Inversion

Speaker: Primoz Skraba (Queen Mary University of London and Jozef Stefan Institute, Slovenia)

Wednesday, March 22, 2023
9:00-9:45 CDT
Universality in Random Persistence Diagrams

Speaker: Omer Bobrowski (Technion – Israel Institute of Technology)

10:00-10:30 CDT
Coffee Break
10:30-11:15 CDT
Random fields beyond the null: building models from critical points

Speaker: Jonathan Taylor (Stanford University)

11:30-12:30 CDT
Lunch
12:30-13:15 CDT
Combining network analysis and persistent homology for classifying behavior of time series

Speaker: Liz Munch (Michigan State University)

13:35-14:20 CDT
Approximating Persistent Homology for Large Datasets

Speaker: Anthea Monod (Imperial College)

14:30-15:30 CDT
Hybrid Poster Session
Thursday, March 23, 2023
9:00-9:45 CDT
Persistent Homology of Periodic Maps

Speaker: Teresa Heiss (Institute of Science and Technology Austria (IST Austria))

10:00-10:30 CDT
Coffee Break
10:30-11:15 CDT
Curvature Sets Over Persistence Diagrams

Speaker: Facundo Mémoli (Ohio State University)

11:30-12:30 CDT
Lunch
12:30-13:15 CDT
Probabilistic Generative Frameworks for Sampling 3D Complex Shapes and Images

Speaker: Lorin Crawford (Microsoft Research)

13:35-14:20 CDT
Some topological properties of subgaussian fields of Riemannian manifolds

Speaker: Daniel Perez (École normale supérieure – ENS)

14:30-15:15 CDT
Clustering of discrete measures via mean measure quantization: application to unsupervised vectorization of persistence diagrams

Speaker: Fred Chazal (INRIA)

Friday, March 24, 2023
9:00-9:45 CDT
Using Zigzag Persistence for Bifurcation Detection

Speaker: Sarah Tymochko (University of California, Los Angeles (UCLA))

10:00-10:30 CDT
Coffee Break
10:30-11:15 CDT
Erdos-Renyi perturbed random geometric graphs

Speaker: Yusu Wang (University of California, San Diego (UCSD))

11:30-12:15 CDT
Multi-Scale Analysis of Random Functions on Graphs

Speaker: Alex Strang (University of Chicago)

12:30-13:30 CDT
Lunch

Poster Session

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The posters that have been submitted for the poster session are available on the poster session page.

Videos

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The correspondence of max-flow to the absolute permeability of porous systems

Vanessa Robins
March 20, 2023

Large deviation principle for geometric and topological functionals and associated point processes

Takashi Owada
March 20, 2023

Distortion, on the Average and in Expectation

Herbert Edelbrunner
March 20, 2023

Identifying Nonlinear Dynamics with High Confidence from Sparse Data

Konstantin Mishaikow
March 20, 2023

Data Analysis in Metric Spaces Through Metric Observables

Washington Mio
March 20, 2023

Exploring the Topology of Word Embeddings

Bei Wang
March 21, 2023

On Complexity of Computing Bottleneck and Lexicographic Optimal Cycles in a Homology Class

Erin Wolf-Chambers
March 21, 2023

Topology and Local Geometry of the Eden Model

Benjamin Schweinhart
March 21, 2023

Homology of Gaussian random chain complexes

Matthew Kahle
March 21, 2023

Persistence Diagrams, Euler Characteristics, and Mobius Inversion

Primoz Skraba
March 21, 2023

Universality in Random Persistence Diagrams

Omer Bobrowski
March 22, 2023

Random fields beyond the null: building models from critical points

Jonathan Taylor
March 22, 2023

Approximating Persistent Homology for Large Datasets

Anthea Monod
March 22, 2023

Persistent Homology of Periodic Maps

Teresa Heiss
March 23, 2023

Curvature Sets Over Persistence Diagrams

Facundo Mémoli
March 23, 2023

Probabilistic Generative Frameworks for Sampling 3D Complex Shapes and Images

Lorin Crawford
March 23, 2023

Some topological properties of subgaussian fields of Riemannian manifolds

Daniel Perez
March 23, 2023

Clustering of discrete measures via mean measure quantization: application to unsupervised vectorization of persistence diagrams

Fred Chazal
March 23, 2023

Using Zigzag Persistence for Bifurcation Detection

Sarah Tymochko
March 24, 2023

Erdos-Renyi perturbed random geometric graphs

Yusu Wang
March 24, 2023

Multi-Scale Analysis of Random Functions on Graphs

Alex Strang
March 24, 2023