BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Chris Kapulkin (Western University) DTSTART:20260511T130000Z DTEND:20260511T140000Z DTSTAMP:20260525T015500Z UID:BilTop/140 DESCRIPTION:Title: Topology\, graphs\, and data\nby Chris Kapulkin (Western University) as part of Bilkent Topology Seminar\n\nLecture held in Zoom.\n\nAbstract\n This talk will be an introduction to the emerging area of discrete homotop y theory\, which applies intuitions and techniques from the continuous set ting to discrete objects such as graphs. It has found a broad range of app lications\, both within and outside mathematics\, including to matroid the ory\, hyperplane arrangements\, and data analysis.\n\nI will discuss two o f my own contributions to discrete homotopy theory\, one more theoretical and one more applied. The first is a proof\, joint with D. Carranza (Compo s. Math.\, 2024)\, of the conjecture by E. Babson\, H. Barcelo\, M. de Lon gueville\, and R. Laubenbacher that discrete homotopy groups can be topolo gically realized. The second\, joint with N. Kershaw (arXiv:2506.15020)\, builds on this result and introduces a new method of data analysis\, which we call persistent discrete homology. We show that in addition to its uti lity for clustering\, it can detect other geometric features of a data set . It is furthermore highly noise resistant\, and as such provides a powerf ul alternative to the usual methods of (unsupervised) machine learning\, e specially in areas subject to high uncertainty\, such as seismology or cri me linkage.\n LOCATION:https://researchseminars.org/talk/BilTop/140/ END:VEVENT END:VCALENDAR