BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Shahn Majid (Queen Mary University) DTSTART:20221010T140000Z DTEND:20221010T150000Z DTSTAMP:20260423T035611Z UID:EQuAL/1 DESCRIPTION:Title: Qu antum Riemannian Geometry of the A_n graph\nby Shahn Majid (Queen Mary University) as part of European Quantum Algebra Lectures (EQuAL)\n\n\nAbs tract\nWe solve for quantum Riemannian geometries on the finite lattice in terval • − • − · · · − • with $n$ nodes (the Dynkin graph o f type $A_n$) and find that they are necessarily $q$-deformed with $q$ a r oot of unity. This comes out of the intrinsic geometry and not by assuming any quantum group in the picture. Specifically\, we discover a novel ‘b oundary effect’ whereby\, in order to admit a quantum-Levi Civita connec tion\, the ‘metric weight’ at any edge is forced to be greater pointin g towards the bulk compared to towards the boundary\, with ratio given by $(i + 1_)q/(i)_q$ at node $i$\, where $(i)_q$ is a $q$-integer. The Christ offel symbols are also $q$-deformed. The limit $q \\to 1$ is the quantum R iemannian geometry of the natural numbers $N$ with rational metric multipl es $(i + 1)/i$ in the direction of increasing $i$. In both cases there is a unique metric up to normalisation with zero Ricci scalar curvature. Elem ents of QFT and quantum gravity are exhibited for $n = 3$ and for the cont inuum limit of the geometry of $N$. The Laplacian for the scaler-flat metr ic becomes the Airy equation operator $(1/ x) d^2/ dx^2$ in so far as a li mit exists. The talk is based on joint work with J. Argota-Quiroz availabl e on arXiv: 2204.12212 (math.QA).\n LOCATION:https://researchseminars.org/talk/EQuAL/1/ END:VEVENT END:VCALENDAR