BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ximena Fernández (Durham University\, UK) DTSTART:20231013T160000Z DTEND:20231013T170000Z DTSTAMP:20260423T041611Z UID:GEOTOP-A/53 DESCRIPTION:Title: The Fermat principle in Riemannian geometry\nby Ximena Fernández (D urham University\, UK) as part of GEOTOP-A seminar\n\n\nAbstract\nIn many situations in physics\, the path of light is determined not only by spatia l geometry but also by an underlying local density (e.g.\, mass concentrat ion in general relativity\, refractive index in optics). Consider a scenar io where a Riemannian manifold in Euclidean space is shaped by a density f unction\, with only a finite sample of points available. How can we infer the original metric and determine the manifold's topology?\n\nThis talk in troduces a density-based method for estimating topological features from d ata in high-dimensional Euclidean spaces\, assuming a manifold structure. The key to our approach lies in the Fermat distance\, a sample metric that robustly infers the deformed Riemannian metric. Theoretical convergence r esults and implications in the homology inference of the manifold will be presented. Additionally\, I will show practical applications in time serie s analysis with examples from real-world data.\n\nThis talk is based on th e article: X. Fernandez\, E. Borghini\, G. Mindlin\, and P. Groisman. "Int rinsic Persistent Homology via Density-Based Metric Learning." Journal of Machine Learning Research 24 (2023) 1-42.\n LOCATION:https://researchseminars.org/talk/GEOTOP-A/53/ END:VEVENT END:VCALENDAR