BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Toni Annala (University of British Columbia) DTSTART:20220328T160000Z DTEND:20220328T170000Z DTSTAMP:20260422T135612Z UID:BilTop/41 DESCRIPTION:Title: Topologically protected vortex knots and links\nby Toni Annala (Univer sity of British Columbia) as part of Bilkent Topology Seminar\n\n\nAbstrac t\nThe physical properties of condensed-matter systems can often be approx imated by a "mean field" which\, outside a small singular locus of the sys tem (defects)\, takes values in a topological space M called the order par ameter space. A topological vortex is a codimension two defect\, about whi ch the order parameter field winds in a way that corresponds to a non-cont ractible loop in M. If the fundamental group of the order parameter space is non-Abelian\, then these vortices exhibit a remarkable behavior: not al l pairs of topological vortices are free to pass through each other.\n\nIt is then a natural to wonder if such vortices could be employed in tying r obust linked structures in physical fields. As a minimum\, such a structur e should not untie via strand crossings and local reconnections\, which ar e the usual means of decay for knotted and linked vortex loops. In this ta lk\, we will present several examples of such structures. Our approach is based on the fact that if the second homotopy group of M is trivial\, then the order parameter field admits a combinatorial description\, which\, de pending on the fundamental group of M\, can be expressed graphically. Henc e\, finding topologically stable tangled structures reduces to constructin g nontrivial invariants for "colored" links\, which remain unchanged in st rand crossings and local reconnections.\n LOCATION:https://researchseminars.org/talk/BilTop/41/ END:VEVENT END:VCALENDAR