BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ákos Nagy (University of California\, Santa Barbara) DTSTART:20210705T160000Z DTEND:20210705T170000Z DTSTAMP:20260423T005816Z UID:QM3/50 DESCRIPTION:Title: Con centrating Majorana fermions\nby Ákos Nagy (University of California\ , Santa Barbara) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\ nAbstract\nI will begin by defining a canonical family of perturbations of the Dirac equation. These perturbations are complex anti-linear\, thus gr ound states only form a real vector space. A special case of this theory i s known as the Jackiw–Rossi theory\, which models surface excitations on the surface of a topological insulator placed in proximity to an s-wave s uperconductor. While the physics of the theory is relatively well-understo od\, the mathematical side has not been studied\, even on surfaces\, not t o mention its generalizations to higher dimensional and on nontrivial mani folds. I call these equations the ``generalized Jackiw–Rossi equations'' .\n\nAfter the definitions and connections to physics\, I will present my current work on the generalized Jackiw–Rossi equations. My main result i s a concentration phenomenon which proves the physical expectation that su ch Majorana fermions concentrate around the vortices of the superconductin g order parameter. Moreover\, I provide approximate solutions that are exp onentially sharp in the large coupling limit.\n\nIf time permits\, then I will show how these Majorana fermions define a bundle of projective spaces over the ``simple'' part of vortex moduli spaces. The holonomies of such bundles give rise to projective representations of (surface) braid groups\ , and thus\, speculatively\, can be of interest to quantum information the orists.\n LOCATION:https://researchseminars.org/talk/QM3/50/ END:VEVENT END:VCALENDAR