# Spring 2023

** January 12th. Organizational meeting. **

** January 19th. Alex McCleary, ** Higher Categories.

** January 26th. Alex McCleary, ** Higher Category Theory and Cohomology; ** Mario Gomez Flores, ** pre-talk: Keeping it Sparse; ** Aziz Burak Guelen, ** Simplicial Maps.

** February 2nd. Mario Gomez Flores, ** Keeping it Sparse; ** Nate Clause, ** pre-talk: Edit Distance and Persistence Diagrams over Lattices.

** February 9th. ** TBD.

** February 16th. Aziz Burak Guelen, ** Simplicial Maps; ** Ranthony Edmonds, ** pre-talk: Gromov-Wasserstein Gaussians.

** February 23rd. Nate Clause, ** Edit Distance and Persistence Diagrams over Lattices; ** Aziz Burak Guelen, ** pre-talk: Harmonic Persistent Homology.

** March 2nd. ** TBD.

** March 9th. Ling Zhou, ** Thesis defense practice; ** Mario Gomez Flores, ** Thesis defense practice.

** March 23rd. Ranthony Edmonds, ** Gromov-Wasserstein Gaussians.

** March 30th. Aziz Burak Guelen, ** Harmonic Persistent Homology.

** April 6th. Ranthony Edmonds, ** Seminar practice talk, TBD.

** April 13th. Ling Zhou, ** Hall's Marriage Theorem.

** April 20th. ** TBD.

# Autumn 2022

** Aug 25th. Organizational meeting. **

** Sep 1st. Qingsong Wang, ** Career development -- applying for postdoc positions; ** Aziz Burak Guelen, ** Pre-talk: Harmonic Persistent Homology; ** Nate Clause, ** Pre-talk: On the bottleneck stability of rank decompositions of multi-parameter persistence modules.

** Sep 8th. Mario Gomez Flores, ** Pre-talk: Average Gromov hyperbolicity and the Parisi ansatz; ** Fabian Roll, **A Unified View on the Functorial Nerve Theorem and its Variations.

** Sep 15th. Shreya Arya, **"A survey of Shape Spaces", and ** Arnab Auddy, **"Statistical and Computational Limits for Orthogonally Decomposable Tensors".

** Sep 22nd. Ranthony Edmonds, ** Pre-talk: Geometry of Graph Partitions via Optimal Transport; ** Alex McCleary, ** Strassen's Theorem.

** Sep 29th. Ling Zhou, ** From Discrete to Persistent Homotopy.

** Oct 6th. Brantley Vose, ** Pre-talk: "Geometry of the Space of Spaces"; ** Fabian Roll, ** "The many faces of discrete Morse theory".

** Oct 13th. Fall Break. **

** Oct 20th. Mario Gomez Flores, ** Average Gromov hyperbolicity and the Parisi ansatz.

** Oct 27th. Alex McCleary, ** "Strassen's Theorem part 2".

** Nov 3rd. Ranthony Edmonds, ** Geometry of Graph Partitions via Optimal Transport

** Nov 10th. Vanessa Robins, ** Evolution of local motifs and topological proximity in self-assembled quasi-crystalline phases.

** Nov 17th. Vanessa Robins, ** Tile-Transitive Tilings of the Euclidean and Hyperbolic Planes by Ribbons

** Nov 24th. Thanksgiving Break. **

# Summer 2022

** Apr 28th. Organizational meeting. **

** May 2nd. Musashi Koyama, ** Randomly Weighted $d$-Complexes: Minimal Spanning Acycles and Persistence Diagrams.

** May 12th. joint seminar. **

** May 26th. Qingsong Wang, ** Thesis defense practice: the persistent topology of geometric filtrations; ** Tyson Trauger, ** Pretalk on persistent homology.

** Jun 9th. joint seminar. **

** Jul 7th. Aziz Burak Guelen, ** Persistent Laplacian.; ** Tyson Trauger, ** Persistent homology.

** Jul 14th. joint seminar. **

** Aug 10th (Wed, 1:00pm). Brantley Vose, **TBD.

** Aug 11th. joint seminar **.

** Aug 18th. Tyson Trauger ** TBD.

# Spring 2022

** Jan 20th. Organizational meeting. **

** Jan 27th. Facundo Memoli and Ling Zhou, ** Career development -- how to improve your slides; ** Brantley Vose, ** Pre-talk: The Basics of Information Geometry; ** Nate Clause, ** Pre-talk: Updating Zigzag Persistence and Maintaining Representatives over Changing Filtrations.

** Feb 3rd. Aziz Burak Guelen, ** Pre-talk: Saecular persistence; ** Ranthony Edmonds, ** Pre-talk: Characterization, Stability, and Convergence of Hiearchical Clustering Methods and Classifying Clustering Schemes; ** Qingsong Wang, ** Pre-talk: Discrete curvature.

** Feb 10th. joint seminar. **

** Feb 17th. Mario Gomez Flores, ** Pre-talk: Contractions in persistence and metric graphs; ** Ling Zhou, ** Pre-talk: finiteness theorems.

** Feb 24th. Nate Clause, **Updating Zigzag Persistence and Maintaining Representatives over Changing Filtrations; **Alex McCleary, ** Pre-talk: Output-sensitive Computation of Generalized Persistence Diagrams for 2-filtrations.

** Mar 3rd. Ranthony Edmonds, **Characterization, Stability, and Convergence of Hiearchical Clustering Methods and Classifying Clustering Schemes; **Alex McCleary, ** Output-sensitive Computation of Generalized Persistence Diagrams for 2-filtrations (Part 1).

** Mar 10th. joint seminar. **

** Mar 17th. Spring Break. **

** Mar 24th. Qingsong Wang, **Discrete curvature; ** Ranthony Edmonds, ** TBD.

** Mar 31st. Aziz Burak Guelen, **Saecular persistence; **Alex McCleary, ** Output-sensitive Computation of Generalized Persistence Diagrams for 2-filtrations (Part 2).

** Apr 7th. Brantley Vose, **The Basics of Information Geometry.

** Apr 14th. joint seminar.**

** Apr 21st. Mario Gomez Flores, **Contractions in persistence and metric graphs; ** Ling Zhou, ** Finiteness theorems.

# Autumn 2021

** Sep 2nd. Organizational meeting. **

** Sep 9th. Alex McCleary, ** About Möbius inversion (Part 1).

** Sep 16th. Alex McCleary, ** About Möbius inversion (Part 2); ** Ling Zhou, ** Topological invariants and their computational complexity. [References 1, 2]

** Sep 23rd. Nate Clause, ** On Interval Decomposability of 2D Persistence Modules.

** Sep 30th. (Vietoris-Rips -- Tight Span joint CSU-OSU seminar). Mario Gomez Flores, ** On Vietoris-Rips Complexes of Hypercube Graphs; ** Alex McCleary, ** The Mobius Inversion in Practice.

** Oct 7th. Aziz Burak Guelen, ** Generalized Persistence diagrams; ** Qingsong Wang, ** Linkage-based hierarchical clustering methods. [References 1, 2]

** Oct 14th. ** Autumn Break

** Oct 21st. Zhengchao Wan, ** PhD thesis defense practice.

** Oct 28th. Tigran Ishkhanov** (invited speaker from Facebook Research), Career development talk; ** Musashi Koyama,** Theory and Algorithms for Constructing Discrete Morse Complexes from Grayscale Digital Images.

** Nov 4th. (Vietoris-Rips -- Tight Span joint CSU-OSU seminar). Henry Adams (CSU),** Conjectured connections between Vietoris-Rips complexes of spheres and Gromov-Hausdorff distances.

** Nov 11th. Ranthony Edmonds and Natalia Kravtsova, **Gromov-Hausdorff and Gromov-Wasserstein distances: main results [References 1, 2]; ** Aziz Burak Guelen, ** Bottleneck Stability for Generalized Persistence Diagrams.

** Nov 18th. Natalia Kravtsova and Ranthony Edmonds, **Gromov-Wasserstein distance: additional results and applications [References 1, 2]; ** Nate Clause, ** Signed Barcodes for Multi-Parameter Persistence via Rank Decompositions and Rank-Exact Resolutions.

** Dec 2nd. Marco Contessoto, ** PhD thesis defense practice.

** Dec 9th. (Vietoris-Rips -- Tight Span joint CSU-OSU seminar). Johnathan Bush (CSU), ** On Borsuk-Ulam theorems and convex sets; ** Brantley Vose, ** TBD.

# Summer 2021

** May 6th. Organizational meeting. **

** May 20th. Marco Contessoto, ** Computing Zigzag Persistent Cohomology; ** Ranthony Edmonds, ** Career development.

** May 27th. (Vietoris-Rips -- Tight Span joint CSU-OSU seminar). Michael Moy (CSU), ** Persistence Stability for Metric Thickenings.

** Jun 3rd. Brantley Vose (~30 mins), ** Three proofs of the interval decomposition (References: 1, 2 and 3 ); ** Facundo Memoli, ** Overview of projects in NDA group.

** Jun 10th. Mario Gomez Flores, ** Curvature sets over persistence diagrams.

** Jun 17th. Zhengchao Wan, ** Harmonic Persistent Homology.

** Jun 24th. (Vietoris-Rips -- Tight Span joint CSU-OSU seminar). Henry Adams (CSU), ** An introduction to Barvinok-Novik orbitopes, cyclic polytopes, and the sparsity-promoting L1 norm.

** Jul 1st. Ling Zhou, ** An algebra for patterns on a complex.

** Jul 8th. Brantley Vose (~30 mins), ** Three Metrics: Gromov-Hausdorff, Bottleneck, and Interleaving; ** Woojin Kim (Duke), ** Career development -- Beamer and presentation skills.

** Jul 15th. Woojin Kim (Duke), ** Local Characterizations for decomposability of 2-parameter persistence modules -Part 1; ** Nate Clause, ** Part 2.

** Jul 22nd. Nate Clause, ** An introduction to RIVET; ** Qingsong Wang, ** Footprints of geodesics in persistent homology.

** Jul 29th. ** Break

** Aug 5th. Brantley Vose (~45 mins), ** Estimating the Gromov-Hausdorff Distance with RIVET.

** Aug 12th. Kun Jin, ** Thesis defense practice: Optimal Transport with its Applications in Data Analysis and Machine Learning.

** Aug 19th. Alex McCleary, ** Persistence Diagrams Over Finite Lattices.

** Aug 26th. (Vietoris-Rips -- Tight Span joint CSU-OSU seminar) Sunhyuk Lim, ** The Gromov-Hausdorff distance between spheres.

# Spring 2021

** Jan 14th. Organizational meeting. **

** Jan 21st. Woojin Kim (Duke), ** Career development; ** Musashi Koyama, ** Persistent and Zigzag Homology: A Matrix Factorization Viewpoint.

** Jan 28th (Vietoris-Rips -- Tight Span joint CSU-OSU seminar). Mario Gomez Flores, ** VR and metric glueing & Kunneth formulas for persistence; ** Joshua Mirth (MSU), ** Geodesic homotopies in metric thickenings.

** Feb 4th. Ling Zhou, ** Filtered chain complex and its invariants (Paper 1, Paper 2).

** Feb 11th. Zhengchao Wan, ** Persistent Laplacians: properties, algorithms and implications.

** Feb 18th. Musashi Koyama, ** Simplicial matrix tree theorems.

** Feb 25th (Vietoris-Rips -- Tight Span joint CSU-OSU seminar). Qingsong Wang, ** Bestvina-Brady discrete Morse theory and Vietoris-Rips complexes; ** Henry Adams (CSU), ** Vietoris-Rips thickenings of spheres.

** Mar 4th. Nate Clause, ** Candidacy Practice: Topological Data Analysis in the Dynamic Setting; ** Shreyas Samaga, ** Algorithm to compute Zigzag persistence.

** Mar 11th. Alex Elchesen ** (invited speaker from University of Florida), Virtual persistence diagrams, signed measures, and Wasserstein distance.

** Mar 18th. Sunhyuk Lim, ** Geometry, Topology, and Spectral Methods in Data Analysis: from Injective Metric Spaces, through Gromov-type Distances, to Generalized MDS.

** Mar 25th. **

** Apr 1st. Instructional break. **

** Apr 8th. Ranthony Edmonds, ** Topological Data Analysis and Electoral Redistricting; ** Nate Clause, ** On the complexity of zero-dimensional multiparameter persistence.

** Apr 15th. Anastasios Stefanou (25 mins), ** Career development -- writing research statement, and multirank invariant; ** Marco Contessoto, ** Computing Zigzag Persistent Cohomology.

** Apr 22nd (Vietoris-Rips -- Tight Span joint CSU-OSU seminar). Johnathan Bush (CSU),** Maps of Vietoris-Rips metric thickenings into Euclidean spaces; ** Woojin Kim (Duke), ** Interleaving by parts for persistence in a poset.

# Autumn 2020

** Sep 10th. Sunhyuk Lim, ** Convex regions on the n-dimensional spherical surface; ** Facundo Memoli, ** Remarks and ideas about Vietoris-Rips complexes.

** Sep 17th. Qingsong Wang, ** Rips complexes as nerves and a Functorial Dowker-Nerve Diagram.

** Sep 24th. Mario Gomez Flores, ** Diameter-Extremal Subsets of Spheres.

** Oct 1st. Marco Contessoto, ** Persistent Cohomology and Circular Coordinates.

** Oct 8th. Musashi Koyama, ** Algorithm for persistent homology.

** Oct 15th. Ling Zhou, ** Ripser: efficient computation of Vietoris–Rips persistence barcodes.

** Oct 22nd. Mario Gomez Flores (20 mins), ** Some properties of Vietoris-Rips complexes; **Kun Jin, ** NLP overview.

** Oct 29th. ** Cancelled.

** Nov 5th. Nate Clause (~1hr), ** Coxeter Functors and Gabriels Theorem.

** Nov 12th. Nate Clause (~30 mins), ** Coxeter Functors and Gabriels Theorem (continued); ** Anastasios Stefanou (~1 hr), ** Hausdorff stability of higher dimensional barcodes with convex intervals.

** Nov 19th. Anastasios Stefanou (~30 mins), ** Universality of persistence diagrams and the bottleneck and Wasserstein distances; ** Marco Contessoto (~1 hr), ** Generalized persistence diagrams.

** Dec 3rd. Luis Scoccola ** (invited speaker from MSU), Metric properties and weakenings of interleaving distances.

# Summer 2020

** May 28th. Musashi Koyama, ** Persistence by Parts: Multiscale Feature Detection via Distributed Persistent Homology.

** Jun 4th. Nate Nathaniel, ** On rectangle-decomposable 2-parameter persistence modules.

** Jun 11th. Musashi Koyama, ** Persistence by Parts: Multiscale Feature Detection via Distributed Persistent Homology.

** Jun 18th. Woojin Kim, ** Elder-Rule-Staircodes for Augmented Metric
Spaces

** Jun 25th. Marco Contessoto, ** Persistent cohomology and cup length invariant.

** Jul 2nd. Anastasios Stefanou and Woojin Kim, ** Modules over posets: commutative and homological algebra.

** Jul 9th. Musashi Koyama (candidacy practice), ** Methods of calculating homology in a distributed fashion; ** Anastasios Stefanou, ** Research lecture overview.

** Jul 16th. Anastasios Stefanou, ** Research Lecture.

** Jul 23rd. Sunhyuk Lim, ** Topological representation of the geometry of metric spaces.

** Aug 6th. Zhengchao Wan and Kun Jin, ** Ricci flow.

** Aug 13th. Mario Gomez Flores and Qingsong Wang, ** Finite subset spaces of S^1.

** Aug 20th. Marco Contessoto,** Persistent diagrams as diagrams.

** Aug 27th. Ling Zhou, ** Multiplicative persistent distances.

# Spring 2020 at 1:45 PM in JH 382

** Jan 9th. Zhengchao Wan, ** Ultrametics and monoidal metric spaces.

** Jan 16th. Marco Contessoto (20 mins), ** State of the art on persistent co-homology; ** Sunhyuk Lim, ** Brief review of classical MDS.

** Jan 23rd. Qingsong Wang, ** Persistent barcode and Laplace eigenfunction on surface.

** Jan 30th. Alessandro Gregorio (20 mins), ** A concept of weak isometry for finite metric spaces and related invariants; ** Musashi Koyama, ** Spectral Sequence.

** Feb 6. Marco Contessoto (20 mins), ** Why is persistent cohomology faster than persistent homology? ** Anastasios Stefanou, ** A_\infty persistent homology estimates the topology from point cloud datasets.

** Feb 13th. Anastasios Stefanou, ** A_\infty persistent homology estimates the topology from point cloud datasets. ** Nate Nathaniel, ** Random coagulation/fragmentation process.

** Feb 20th. Ling Zhou, ** Persistent homotopy groups of metric spaces.

** Feb 27th. Marco Contessoto (20 mins), ** TBD. ** Kun Jin, ** The Gaussian Transform.

** Mar 5th. Marco Contessoto, ** Why is persistent cohomology faster than persistent homology?

** Mar 12th. ** Spring Break.

** Mar 19th. Marco Contessoto (20 mins), ** TBD; ** Mario Gomez Flores, ** Persistence as an approach to curvature sets.

** Mar 26th. Woojin Kim, ** Metrics and Persistent Homology for Dynamic Geometry; ** Kritika Singhal, ** Methods of Simplification of Metric spaces, and Lower bounds on the Gromov-Hausdorff distance.

** Apr 2nd. Marco Contessoto (20 mins), ** TBD; ** Zhengchao Wan, ** Ricci flow.

** Apr 9th. Zhengchao Wan, ** Ricci flow (Continued).

** Apr 16th. Musashi Koyama, ** Distributing persistent homology via spectral sequences.

** Apr 23th. Marco Contessoto, ** TBD.

** Apr 30th. Ling Zhou, ** Rational homotopy and Sullivan minimal models.

** May 7th. Musashi Koyama, ** Distributing persistent homology via spectral sequences (Continued).

** May 14th. Marco Contessoto (20 mins), ** TBD; ** Zhengchao Wan, ** Gromov Hausdorff geodesic are Hausdorff realizable.

# 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) **; Nash equilibrium.

** October 31. Kritika Singhal (1 hour) **; A Mass Transform.

** November 7. In Caldwell Lab 0183 Nate Nathaniel (30 mins) **; Computational implementation of the erosion diatance, ** Kun Jin (~ 30 mins) **; Updates in his project, ** Sunhyuk Lim (~ 30 mins) ; ** Intersection of balls on the constant curvature spaces.

** 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.