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BEGIN:VEVENT
SUMMARY:Alex McCearly (The Ohio State University)
DTSTART:20210928T200000Z
DTEND:20210928T210000Z
DTSTAMP:20260404T111059Z
UID:TDGA/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/TDGA/
 1/">The Functoriality of Persistent Homology</a>\nby Alex McCearly (The Oh
 io State University) as part of Topology\, Geometry\, & Data Analysis (TGD
 A) Seminar\n\n\nAbstract\nThe pipeline that takes a filtration to its pers
 istence diagram is functorial: it takes morphisms of filtrations to morphi
 sms of persistence diagrams. We will analyze this structure\, focusing on 
 the one-parameter setting. We will start with an overview of the categorie
 s of filtrations and persistence diagrams followed by some examples of mor
 phisms between filtrations arising in practice and what the induced morphi
 sms between persistence diagrams can tell us.\n
LOCATION:https://stable.researchseminars.org/talk/TDGA/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhengchao Wan (The Ohio State University)
DTSTART:20211012T200000Z
DTEND:20211012T210000Z
DTSTAMP:20260404T111059Z
UID:TDGA/2
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/TDGA/
 2/">The Gromov-Hausdorff distance between ultrametric spaces</a>\nby Zheng
 chao Wan (The Ohio State University) as part of Topology\, Geometry\, & Da
 ta Analysis (TGDA) Seminar\n\n\nAbstract\nThe Gromov-Hausdorff distance $(
 d_GH)$ is a natural distance between metric spaces. However\, computing $d
 _GH$ is NP-hard\, even in the case of finite ultrametric spaces. We identi
 fy a one parameter family $\\{d_{GH\,p}\\}_{p\\in[1\,\\infty]}$ of Gromov-
 Hausdorff type distances on the collection of ultrametric spaces such that
  $d_{GH\,1}=d_{GH}$. The extreme case when $p=\\infty$\, which we also den
 ote by $u_{GH}$\, turns out to be an ultrametric on the collection of ultr
 ametric spaces. We discuss various geometric and topological properties of
  $d_{GH\,p}$ as well as some of its structural results. These structural r
 esults in turn allow us to study the computational aspects of the distance
 . In particular\, we establish that (1) $u_{GH}$ is computationally tracta
 ble and (2) when $p < \\infty$\, although $d_{GH\,p}$ is NP-hard to comput
 e\, we identify a fixed-parameter tractable algorithm for computing the ex
 act value of $d_{GH\,p}$ between finite ultrametric spaces.\n
LOCATION:https://stable.researchseminars.org/talk/TDGA/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Qingsong Wang (The Ohio State University)
DTSTART:20211005T200000Z
DTEND:20211005T210000Z
DTSTAMP:20260404T111059Z
UID:TDGA/3
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/TDGA/
 3/">The Persistent Topology of Optimal Transport Based Metric Thickenings<
 /a>\nby Qingsong Wang (The Ohio State University) as part of Topology\, Ge
 ometry\, & Data Analysis (TGDA) Seminar\n\n\nAbstract\nA metric thickening
  of a given metric space X is any metric space admitting an isometric embe
 dding of X. Thickenings have found use in applications of topology to data
  analysis\, where one may approximate the shape of a dataset via the persi
 stent homology of an increasing sequence of spaces. We introduce two new f
 amilies of metric thickenings\,  the p-Vietoris–Rips and p-Čech metric 
 thickenings for any p between 1 and infinity\, which include all measures 
 on X whose p-diameter or p-radius is bounded from above\, equipped with an
  optimal transport metric. These families recover the previously studied V
 ietoris–Rips and Čech metric thickenings when p is infinity. As our mai
 n contribution\, we prove a stability theorem for the persistent homology 
 of p-Vietoris–Rips and p-Čech metric thickenings\, which is novel even 
 in the case p is infinity. In the specific case p equals 2\, we prove a Ha
 usmann-type theorem for thickenings of manifolds\, and we derive the compl
 ete list of homotopy types of the 2-Vietoris–Rips thickenings of the sph
 ere as the scale increases. This is joint work with Henry Adams\, Facundo 
 Mémoli and Michael Moy.\n
LOCATION:https://stable.researchseminars.org/talk/TDGA/3/
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BEGIN:VEVENT
SUMMARY:Mario Gómez Flores (The Ohio State University)
DTSTART:20211109T210000Z
DTEND:20211109T220000Z
DTSTAMP:20260404T111059Z
UID:TDGA/4
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/TDGA/
 4/">Curvature Sets Over Persistence Diagrams</a>\nby Mario Gómez Flores (
 The Ohio State University) as part of Topology\, Geometry\, & Data Analysi
 s (TGDA) Seminar\n\n\nAbstract\nWe study an invariant of compact metric sp
 aces inspired by the Curvature Sets defined by Gromov. The (n\,k)-Persiste
 nce Set of X is the collection of k-dimensional VR persistence diagrams of
  any subset of X with n or less points. This research seeks to provide a c
 heaper persistence-like invariant for metric spaces\, as the computation o
 f the VR complex becomes prohibitive once the input reaches a certain size
 . I'll focus on the case n=2k+2\, where we can find a geometric formula to
  calculate the VR persistence diagram of a space with n points. We explore
  the application of this formula to the characterization of persistence se
 ts of several spaces\, including circles\, higher dimensional spheres\, an
 d surfaces with constant curvature. We also show that persistence sets can
  detect the homotopy type of a certain family of graphs.\n
LOCATION:https://stable.researchseminars.org/talk/TDGA/4/
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