BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ergun Yalcin (Bilkent University) DTSTART:20240205T103000Z DTEND:20240205T113000Z DTSTAMP:20260422T135750Z UID:BilTop/75 DESCRIPTION:Title: TDA I: An Introduction to Topological Data Analysis\nby Ergun Yalcin ( Bilkent University) as part of Bilkent Topology Seminar\n\nLecture held in SB-Z11.\n\nAbstract\nTopological Data Analysis is an emerging area of mat hematics where topological\nmethods are used to analyze data. One of the m ost important tools for TDA is Persistent\nHomology. The input of this pro cess is a finite metric space (a data cloud) and the output\nis a barcode or a persistent diagram. Given a finite metric space\, using closed balls\ nof changing radius\, we build a filtered simplicial complex. The homology modules of these\nfiltered simplicial complexes are called persistent hom ology modules and they are\nexpressed using barcodes or persistent diagram s. What makes this method very useful\nis that the persistent homology cal culations can be done using a simple matrix algorithm\,\ncalled the reduct ion algorithm. I will introduce basic ideas behind persistent homology\nan d show how the reduction algorithm works. Most of the talk should be acces sible to\nan undergraduate student who has taken a linear algebra course.\ n\nPart I of a sequel on Topological Data Analysis (TDA).\n LOCATION:https://researchseminars.org/talk/BilTop/75/ END:VEVENT END:VCALENDAR