BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jyotishman Bhowmick (Indian Statistical Institute\, Kolkata) DTSTART:20200513T101500Z DTEND:20200513T111500Z DTSTAMP:20260422T225800Z UID:MatPhySem/1 DESCRIPTION:Title: Formulation of metric compatibility of a connection in noncommutative ge ometry\nby Jyotishman Bhowmick (Indian Statistical Institute\, Kolkata ) as part of Mathematical Physics Seminar\n\n\nAbstract\nThe goal of the t alk is to formulate the notion of Levi-Civita connections in noncommutativ e geometry. More precisely\, we will work in the set up of differential ca lculus over a ( possibly ) noncommutative algebra. Given a pseudo-Riemann ian metric g on the calculus\, a connection on the space of one-forms will be called a Levi-Civita connection for g if the connection is torsionless and compatible with g. The torsion of a connection in noncommutative geo metry is well-known. So our main focus would be to define metric compatibi lity condition of a connection. We need the calculus to satisfy some condi tions to make sense of our metric compatibility condition and also the sym metry of the pseudo-Riemannian metric g. It turns out that these condition s are also sufficient to ensure the existence of a unique Levi-Civita conn ection for any bilinear pseudo-Riemannian metric. Examples of such calculu s include the fuzzy 3-sphere\, the quantum Heisenberg manifold and a class of Rieffel deformations of classical manifolds under free and isometric t oral actions. The talk is based on a joint work with D. Goswami and G. Lan di.\n LOCATION:https://researchseminars.org/talk/MatPhySem/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Debashish Goswami (ISI\, Kolkata) DTSTART:20200520T101500Z DTEND:20200520T111500Z DTSTAMP:20260422T225800Z UID:MatPhySem/2 DESCRIPTION:Title: Levi-Civita connections for a class of spectral triples.\nby Debashi sh Goswami (ISI\, Kolkata) as part of Mathematical Physics Seminar\n\n\nAb stract\nWe give a new definition of Levi-Civita connection for a noncommut ative pseudo-Riemannian metric on a noncommutative manifold given by a spe ctral triple. We prove the existence-uniqueness result for a class of modu les of one-forms over a large class of noncommutative manifolds\, includin g the matrix geometry of the fuzzy 3-sphere\, the quantum Heisenberg manif olds and Connes-Landi deformations of spectral triples on the Connes-Duboi s Violette-Rieffel-deformation of a compact manifold equipped with a free toral action. This is based on a joint work with J. Bhowmick and S. Mukhop adhyay.\n LOCATION:https://researchseminars.org/talk/MatPhySem/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Fawad Hassan (Stockholm University) DTSTART:20200526T130000Z DTEND:20200526T140000Z DTSTAMP:20260422T225800Z UID:MatPhySem/3 DESCRIPTION:Title: Interactions of multiple spin-2 fields: bimetric and multimetric theorie s\nby Fawad Hassan (Stockholm University) as part of Mathematical Phys ics Seminar\n\n\nAbstract\nClassical and quantum fields are classified in terms of their\n"spin" which not only specifies their behavior under rotat ions\, but also\ndetermines the basic structure of their field equations. The Standard\nModel describes particle physics in terms of fields of spin 0\, 1/2 and 1\,\nwhereas General Relativity (GR) is the theory of a single massless field\nof spin 2. Fields of higher spin may not be describable b y local field\ntheories at all\, leaving theories of multiple spin-2 field s as the main\npossible extensions of the familiar field theories. Hence\, a long standing\nquestion has been if GR could be extended to contain ext ra spin 2 fields\nof potential relevant to new physics. The main difficult y in constructing\nsuch theories is the appearance of "ghost" instabilitie s. Some such\ntheories have been found in recent years and are highly cons trained by\nconsistency conditions. This talk describes theories of two an d multiple\nspin-2 fields commonly known as ghost-free bimetric and multim etric\ntheories. In particular I will focus on the structure of ghost free \nbimetric and multimetric interactions\, their physical interpretation\, and\non the notions of space and time in bimetric theories.\n\nWEBINAR ON FRIDAY WAS CANCELLED DUE TO TECHNICAL PROBLEMS\n LOCATION:https://researchseminars.org/talk/MatPhySem/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Shahn Majid (Queen Mary\, University of London) DTSTART:20200527T111500Z DTEND:20200527T121500Z DTSTAMP:20260422T225800Z UID:MatPhySem/4 DESCRIPTION:Title: Quantum gravity on the fuzzy sphere\nby Shahn Majid (Queen Mary\, Un iversity of London) as part of Mathematical Physics Seminar\n\n\nAbstract\ nWe study the quantum geometry of the fuzzy sphere defined as the angular momentum algebra $[x_i\,x_j]=2\\imath\\lambda_p \\epsilon_{ijk}x_k$ modul o setting $\\sum_i x_i^2$ to a constant\, using a recently introduced 3D r otationally invariant differential structure. Metrics are given by symmetr ic 3×3 matrices g and we show that for each metric there is a unique quan tum Levi-Civita connection with constant coefficients\, with scalar curvat ure $\\frac{1}{2}({\\rm Tr}(g^2)-\\frac{1}{2}{\\rm Tr}(g)^2)/\\det(g)$. As an application\, we construct Euclidean quantum gravity on the fuzzy unit sphere. We also calculate the charge 1 monopole for the 3D differential s tructure. Joint work with E. Lira Torres.\n\nLivestream platform: WEBEX\n LOCATION:https://researchseminars.org/talk/MatPhySem/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Edwin Beggs (Swansea University) DTSTART:20200610T111500Z DTEND:20200610T121500Z DTSTAMP:20260422T225800Z UID:MatPhySem/5 DESCRIPTION:Title: Quantum geodesics in quantum mechanics\nby Edwin Beggs (Swansea Univ ersity) as part of Mathematical Physics Seminar\n\n\nAbstract\nWe show tha t the standard Heisenberg algebra of quantum mechanics admits a noncommuta tive differential calculus $Ω^1$ depending on the Hamiltonian $H=p^2/2m+V (x)$ and a flat quantum connection with torsion on it such that a quantum formulation of autoparallel curves (or `geodesics') reduces to Schrödinge r's equation. The connection is compatible with a natural quantum symplect ic structure and associated generalised quantum metric. A remnant of our a pproach also works on any symplectic manifold where\, by extending the cal culus\, we can encode any hamiltonian flow as `geodesics' for a certain co nnection with torsion which is moreover compatible with an extended symple ctic structure. Thus we formulate ordinary quantum mechanics in a way that more resembles gravity rather than the more well-studied idea of formulat ing geometry in a more quantum manner. We then apply the same approach to the Klein Gordon equation on Minkowski space with a background electromagn etic field\, formulating quantum `geodesics' on the relevant relativistic Heisenberg algebra. Examples include a proper time relativistic free parti cle wave packet and a hydrogen-like atom. based on a joint work with Shahn Majid.\n LOCATION:https://researchseminars.org/talk/MatPhySem/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Satyajit Guin (IIT Kanpur) DTSTART:20210622T120000Z DTEND:20210622T130000Z DTSTAMP:20260422T225800Z UID:MatPhySem/6 DESCRIPTION:Title: Equivariant spectral triple for the compact quantum group $U_q(2)$ for c omplex deformation parameters\nby Satyajit Guin (IIT Kanpur) as part o f Mathematical Physics Seminar\n\n\nAbstract\nLet $q=|q|e^{i\\pi\\theta}$ be a nonzero complex number such that $|q|\\neq 1$\, and consider the comp act quantum group $U_q(2)$. In this talk\, we discuss a complete list of i nequivalent irreducible representations of $U_q(2)$ and its Peter-Weyl dec omposition. Then\, for $\\theta\\notin\\mathbb{Q}\\setminus\\{0\,1\\}$ we discuss the $K$-theory of the underlying $C^*$-algebra $C(U_q(2))$\, and a spectral triple which is equivariant under the comultiplication action of $U_q(2)$. The spectral triple obtained here is even\, $4^+$-summable\, no n-degenerate\, and the Dirac operator acts on two copies of the $L^2$-spac e of $U_q(2)$. The Chern character of the associated Fredholm module is no ntrivial.\n\nThis is a joint work with Bipul Saurabh.\n LOCATION:https://researchseminars.org/talk/MatPhySem/6/ END:VEVENT END:VCALENDAR