Autumn 2019 at 1:45 PM in JH 382

August 22. Zhengchao Wan (1 hour); An estimate for the sum of Betti numbers Ling Zhou (15-20 mins); Vietoris-Rips complex of finite tree metric spaces. Qingsong Wang (40 mins) ; Loops in Reeb graphs

August 29.Ling Zhou (40 mins); Vietoris-Rips complex of finite tree metric spaces. Facundo (20mins); More remarks added to Zhengchao and Ling's talks, (20-30 mins) ; Optimal Transport Survey

September 5. Qingsong Wang (40 -50 mins) ; Loops in Reeb graphs Hao Xing (45 mins) ; Vector diffusion maps and the connection Laplacian ;

September 12. Sunhyuk Lim (1.5 hours) ; On the filling radius of positively curved manifolds

September 19. Anastasios Stefanou (30 mins) ; The Brouwer's Fixed point theorem and its applications, Qingsong Wang (30 mins) ; On homotopy types of Vietoris-Rips complexes of metric gluings, Ling Zhou (30 mins) ; Gromov-Hausdorff distances between cycle graphs and star graphs.

September 26 (JH 355) . Musashi Koyama (15 mins) ; Homological Algebra for Persistence Modules , Daryl DeFord ; TBD

October 3. Organization for the rest of the semester

October 10. Autumn Break

October 17. Musashi Koyama (15 mins) ; Homological Algebra for Persistence Modules , Kun Jin (20-30 mins) ; Updates in his project

October 24. Musashi Koyama ( ~ 30 mins) ; Homological Algebra for Persistence Modules , Mario Gomez Flores ( ~30 mins) ; TBD

October 31. Kritika Singhal (1 hour) ; TBD

November 7. Nate Nathaniel (30 mins) ; Computational implementation of the erosion diatance, Kun Jin (~ 30 mins) ; Updates in his project, Sunhyuk Lim (~ 30 mins) ; TBD

November 14. Ling Zhou ; Persistent Fundamental Groups of Metric Spaces

November 21. Mario Gomez Flores (~1 hour) ; TBD

December 5. Musashi Koyama (1 hour) ; Homological Algebra for Persistence Modules

Summer 2019

at 1:45 PM in CH 240

May 2. Woojin Kim ; Relationship between the rank functions and the barcodes for persistence modules over general posets.

May 9. Woojin Kim ; Conley index and Connection matrice

May 16. Osman Okutan ; Persistence, Metric Invariants and Simplification (Thesis defense practice)

June 6. Hao Xing ; UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction

June 13. Ling Zhou ; Spanning Trees and fundamental groups of graphs

June 20. Hao Xing ; PERSISTENCE BARCODES AND LAPLACE EIGENFUNCTIONS ON SURFACES

June 27. Zhengchao Wan ; Topology and Curvature of Metric Spaces

July 11. Nathaniel Clause ; Classification of Flocking Behavior via Zigzag Persistent Homology

July 18. Hao Xing ; Persistent homology and Floer-Novikov theory

July 24. Anastasios Stefanou ; Magnitude of metric spaces and magnitude homology 1 .

July 25. Kritika Singhal ; On hyperbolicity constant

July 26. Hao Xing ; Persistence modules with operators in Morse and Floer theory

August 1. Anastasios Stefanou ; Magnitude of metric spaces and magnitude homology 2.

In Jennings Hall 382 below

August 8. Kun Jin ; Comparisons of Meanshift, Gaussian Transform and Wasserstein Transform

August 15. Anastasios Stefanou ; Magnitude of metric spaces and magnitude homology 3. Zhengchao Wan ; An estimate for the sum of Betti numbers

Spring 2019 at 1:45 PM in CH 240

Jan 10. Samir Chowdhury ; Graph distance from the topological view of non-backtracking cycles

Jan 17. Sunhyuk Lim ; Metric thickenings of Euclidean submanifolds, Metric reconstruction via optimal transport

Jan 24. Zhengchao Wan ; A geometric study of Wasserstein spaces: isometric rigidity in negative curvature

Jan 31. Simon Zhang ; Dualities in persistent (co) homology

Feb 7. Amit Patel (Colorado State Univ) ; Smoothing Operator

Feb 14. Zhengchao Wan ; A geometric study of Wasserstein spaces, Kritika Singhal ; Borsuk-Ulam type theorems for metric spaces.

Feb 21. Scott Newton ; A derived isometry theorem for constructible sheaves on R

Feb 28. Anastasios Stefanou ; Computation of the interleaving distance between multidimensional persistence

Mar 7. Woojin Kim ; (1) Stable Persistent Homology Features of Dynamic Metric Spaces and (2) Rank Invariant for Zigzag Modules

Mar 14. Spring Break

Mar 28. (1) Hao Xing, ; Generalized Persistence Diagrams , (2) Kritika Singhal ; Box distance between special orthogonal groups

April 4. Anastasios Stefanou ; Computation of the interleaving distance between multidimensional persistence

April 11. Anastasios Stefanou ; Computation of the interleaving distance between multidimensional persistence

April 18. Plan for next semester; paper assignment

April 25. Guilherme Vituri Fernandes Pinto

TBD. Sunhyuk Lim ; Limit theorems for persistence diagrams

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. Guilherme Vituri Fernandes Pinto ; A persistent Kunneth formula for an unusual product of metric (or not) spaces.

Dec 6. Ying Yin ; Persistent homology on teeth classification, Ling Zhou ; The Structure and Stability of Persistence Modules

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.