# Autumn 2018 at 1:45 PM in CH 240

Aug 30. Woojin Kim ; Multiscale analysis of dynamic metric spaces via Cosheaves.

Sep 6. Planning for Autumn 2018 and Spring 2019.

Sep 13. Ling Zhou ; Interval Decomposition of Infinite Zigzag Persistence Modules

Sep 20. Anastasios Stefanou ; "Dynamics on Categories" to include introductory material on monoidal actions on categories, also categories with a flow and equivariant functors, and also methods from TDA that can be realized as such. "The Functoriality of the Interleaving Distance" where I will define the interleaving distance and show it is an extended pseudometric, show that flow equivariant functors are 1-Lipschitz and give examples of interleaving distances and stability results from TDA along the way.

Sep 27. Ying Yin ; Persistent homology on teeth classification, Osman Okutan ; Hyperbolic Metric Spaces 1

Oct 4. Zhengchao Wan ; Geometry of the Space of Phylogenetic Trees

Oct 11. Autumn Break

Oct 18. Ying Yin ; Persistent homology on teeth classification, Anastasios Stefanou ; "The Geometry of Phylogenetic Networks" where I will discuss a recent result that the $\ell^infty$-cophenetic metric on phylogenetic trees can be realized as an interleaving distance and discuss future directions for research, e.g. define properly a category of phylogenetic networks and devising a metric for comparison for these structures which is an important open problem in computational biology.

Oct 25. Scott Newton ; Universality of the Homotopy Interleaving Distance

Nov 1. Ying Yin ; Persistent homology on teeth classification, Sunhyuk Lim ; Metric thickenings of Euclidean submanifolds, Metric reconstruction via optimal transport

Nov 8. Woojin Kim ; Generalized persistence analysis based on stable rank invariant, Multidimensional Persistence and Noise, Stable Invariants for Multidimensional Persistence

Nov 15. Ying Yin ; Persistent homology on teeth classification, Kritika Singhal ; Hyperbolic Metric spaces 2

Nov 29. Samir Chowdhury ; Graph distance from the topological view of non-backtracking cycles.

Dec 6. Ying Yin ; Persistent homology on teeth classification, Ling Zhou ; TBA

# Spring 2019

Sunhyuk Lim ; Limit theorems for persistence diagrams

Kritika Singhal ; Borsuk-Ulam type theorems for metric spaces.

Zhengchao Wan ; Spectral stability of metric-measure Laplacians

Simon Zhang ; Dualities in persistent (co) homology

Scott Newton ; A derived isometry theorem for constructible sheaves on R

# Spring, Summer 2018

Jan 15, 2018. Osman Okutan ; Approximating metric spaces with Reeb type graphs

Jan 22, 2018. (1) Ying Yin ; Persistent homology on teeth classification, (2) Woojin Kim ; Algebraic stability of zigzag persistence modules. Note

Jan 29, 2018. (1) Sunhyuk Lim ; Equiarea partition of general Riemannian manifolds, (2) Woojin Kim ; Algebraic stability of zigzag persistence modules. Note

Feb 5, 2018. (1) Ying Yin ; Persistent homology on teeth classification, (2) Osman Okutan ; Tight spans of metric spaces,

Feb 12, 2018. (1) Osman Okutan ; Tight spans of metric spaces.

Feb 19, 2018. (1) Ying Yin ; Persistent homology on teeth classification, (2) Tom Needham ; Injectivity Properties of Distance Distributions,

Feb 26, 2018. (1) Woojin Kim ; Algebraic Stability of Zigzag persistence modules Note ; (2) Osman Okutan ; Tight span of metric spaces.

Mar 5, 2018. (1) Woojin Kim ; Stable Siganature for Dynamic Metric Spaces via Zigzag Persistence Homology; (2) Osman Okutan ; Reeb Posets and Tree Approximations; (3) Ying Yin ; Persistent homology on teeth classification.

Mar 19, 2018. Samir Chowdhury ; A generalization of Gromov's reconstruction theorem.

Mar 26, 2018. (1) Xiao Zha; Topological data analysis on road network data, (2) Ying Yin ; Persistent homology on teeth classification, (3) Woojin Kim ; Algebraic Stability of Zigzag persistence modules.

April 2, 2018. (1) Woojin Kim ; Algebraic Stability of Zigzag persistence modules, (2) Sunhyuk Lim ; Overview of general Markov processes.

April 9, 2018. (1) Ying Yin ; Persistent homology on teeth classification, (2) Sunhyuk Lim ; Overview of general Markov processes, (3) Zhengchao Wan ; Categorification of Gromov-Hausdorff Distance and Interleaving of Functors;

April 16, 2018. Samir Chowdhury ; Geodesics in the space of persistence diagrams Frechet means for distributions of persistence diagrams (In "Frechet Means for Distributions of Persistence Diagrams", one of the main results is that the space of persistence diagrams equipped with a certain L2 norm has nonnegative curvature in the sense of Alexandrov. An implicit claim in the proof of this theorem is that all geodesics in this space arise as a straight line interpolation. We supply a detailed proof of this claim, using results about the convexity of Lp norms. )

April 23, 2018. (1) Ying Yin ; Persistent homology on teeth classification, (2) Sunhyuk Lim ; Overview of general Markov processes.

April 30, 2018. Sunhyuk Lim ; Overview of general Markov processes.

May 7, 2018. (1) Ying Yin ; Persistent homology on teeth classification, (2) Sunhyuk Lim ; Overview of general Markov processes, (3) Kritica Singhal ; Sketching and Clustering Metric Measure Spaces

May 28, 2018. (1) Alex Elchesen ; Reflection distance between Zigzag modules and stability, (2) Sunhyuk Lim ; Overview of general Markov processes.

June 4, 2018. at 1 PM (1) Kritica Singhal ; Fractal Dimension and Lower Bounds for Geometric Problems, (2) Ying Yin ; Persistent homology on teeth classification, (3) Sunhyuk Lim ; Overview of general Markov processes, (4) Zhengchao Wan ; Interleaving and Gromov-Hausdorff distance.

June 11, 2018. at 1:30 PM (1) Zhengchao Wan ; Interleaving and Gromov-Hausdorff distance.

June 18, 2018. at 1:30 PM (1) Samir Chowdhury ; Persistent homology methods for asymmetric networks (30 mins), (2) Tom Needham ; Gromov-Hausdorff distance between metric graphs.

June 25, 2018. at 1:30 PM Tom Needham ; Local Uniqueness of the Circular Integral Invariant.

July 2, 2018. at 1:30 PM Sunhyuk Lim ; Heat kernel on fractal sets.

July 9, 2018. at 1:30 PM in MW 154 (1) Simon Zhang ; GPU spectral sequence algorithm with software GPUPH

July 16, 2018. at 1 PM (1) Woojin Kim ; Formigrams- Clustering summary of dynamic data (20 mins), (2) Simon Zhang ; GPU spectral sequence algorithm with software GPUPH Three References: (1) Spectral Sequences, Exact Couples and Persistent Homology of filtrations , (2) You could have invented spectral sequences , (3) Spectral sequences via examples

July 23, 2018. (1) Woojin Kim ; Formigrams- Clustering summary of dynamic data (20 mins), (2) Simon Zhang ; GPU spectral sequence algorithm with software GPUPH

July 30, 2018. (1) Woojin Kim ; Formigrams- Clustering summary of dynamic data (20 mins), (2) Osman Okutan ; Spectral Sequences induced from the Vietories Rips filtrations.

August 6, 2018. at 4 PM in CH 240 Bowen Dai ; The Importance of Forgetting: Limiting Memory Improves Recovery of Topological Characteristics from Neural Data

August 20, 2018. at 1:30 PM in CH 240 Sunhyuk Lim ; On Alexandrov curvature.