Fall 2026
Time & Location: All talks are on Monday in Gibson Hall ___ at _:00 PM unless otherwise noted.
Organizer: Komendarczyk, Rafal
August 27, 2026
Geometry & Topology
Title: Persistent Homology Learning Seminar
Speaker: Rafal Komendarczyk - Tulane
Abstract: We would like to gauge interest and work out logistics before committing to a regular schedule.
Please join us to discuss:
- Current status and topics covered so far
- Interest in continuing as a biweekly seminar
- Scheduling preferences
**Course Registration:** This seminar is offered as MATH-7760-02 (Persistent Homology) for 3 graduate credits it will meet on Thursdays 12:30 PM – 1:30 PM in Norman Mayer MA-104. The course just appeared in the roster and registration remains open through Friday, August 28, 2026. Students interested in registering for credit should do so before the deadline.
Location: Norman Mayer MA-104
Time: 12:30 PM
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September 03, 2026
Geometry & Topology
Title: Persistent Homology Learning Seminar
Speaker: Rafal Komendarczyk - Tulane University
Abstract: The Persistent Homology Learning Seminar (MATH-7760-02) resumes this week and meets weekly through the fall, Thursdays 12:30-1:30 PM in Gibson Hall GI-308.
Please note the room: this is not where we met on August 27.
The seminar is organized around one question: when are two metric spaces close, and which topological invariants respect that closeness? We take the
Gromov-Hausdorff distance as the measure of similarity between metric spaces and work toward the stability theorem
d_B(B(X), B(Y)) <= 2 d_GH(X, Y), which says that the persistence barcode is a Lipschitz invariant of the data.
All interested are welcome to attend. No prior exposure to persistent homology is assumed.
Location: Gibson Hall GI-308
Time: 12:30 PM
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September 10, 2026
Geometry & Topology
Title: Persistent Homology Learning Seminar (LSC)
Speaker: Rafal Komendarczyk - Tulane University
Abstract: Last week d_GH was defined as an infimum of Hausdorff distances over all isometric embeddings of two compact metric spaces into a common ambient space: conceptually clean, but an infimum over a proper class. This week we prove the correspondence formula d_GH(X,Y) = (1/2) inf_C dis(C), the infimum taken over correspondences C in X x Y. It removes the ambient space entirely and is the form in which d_GH enters every later estimate.
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The seminar is organized around one question: when are two metric spaces close, and which topological invariants respect that closeness? We take the Gromov-Hausdorff distance as the measure of similarity between metric spaces and work toward the stability theorem d_B(B(X), B(Y)) <= 2 d_GH(X, Y), which says that the persistence barcode is a Lipschitz invariant of the data.
Location: Gibson Hall GI-308
Time: 12:30 PM
_______________
September 17, 2026
Geometry & Topology
Title: Persistent Homology Learning Seminar (LSC)
Speaker: Rafal Komendarczyk - Tulane University
Abstract: We finish the Gromov-Hausdorff distance by showing that it is a genuine
metric on isometry classes of compact metric spaces: d_GH(X,Y) = 0 exactly
when X and Y are isometric.
We then begin a review of homology in the form the seminar needs: chain
complexes and simplicial homology over a field, and contiguity of simplicial
maps, the tool behind the stability of Rips persistence.
Location: Gibson Hall GI-308
Time: 12:30 PM
_______________
September 24, 2026
Geometry & Topology
Title: Persistent Homology Learning Seminar (LSC)
Speaker: Rafal Komendarczyk - Tulane University
Abstract: We begin the homology review: homology in the form the seminar needs it, developed from scratch, with no prior exposure assumed.
Chain complexes over a field, simplicial complexes and their homology, and a statement of the properties of singular homology we will use later. Time permitting, we reach contiguity of simplicial maps, the mechanism behind the stability of Rips persistence.
Location: Gibson Hall GI-308
Time: 12:30 PM
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