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:20260404T110823Z UID:MatPhySem/1 DESCRIPTION:Title: Formulation of metric compatibility of a connection in noncommuta tive geometry\nby Jyotishman Bhowmick (Indian Statistical Institute\, Kolkata) as part of Mathematical Physics Seminar\n\n\nAbstract\nThe goal o f the talk is to formulate the notion of Levi-Civita connections in noncom mutative geometry. More precisely\, we will work in the set up of differen tial calculus over a ( possibly ) noncommutative algebra. Given a pseudo- Riemannian metric g on the calculus\, a connection on the space of one-for ms will be called a Levi-Civita connection for g if the connection is tors ionless and compatible with g. The torsion of a connection in noncommutat ive geometry is well-known. So our main focus would be to define metric co mpatibility condition of a connection. We need the calculus to satisfy som e conditions to make sense of our metric compatibility condition and also the symmetry of the pseudo-Riemannian metric g. It turns out that these co nditions are also sufficient to ensure the existence of a unique Levi-Civi ta connection for any bilinear pseudo-Riemannian metric. Examples of such calculus include the fuzzy 3-sphere\, the quantum Heisenberg manifold and a class of Rieffel deformations of classical manifolds under free and isom etric toral actions. The talk is based on a joint work with D. Goswami and G. Landi.\n LOCATION:https://stable.researchseminars.org/talk/MatPhySem/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Debashish Goswami (ISI\, Kolkata) DTSTART:20200520T101500Z DTEND:20200520T111500Z DTSTAMP:20260404T110823Z UID:MatPhySem/2 DESCRIPTION:Title: Levi-Civita connections for a class of spectral triples.\nby Debashish Goswami (ISI\, Kolkata) as part of Mathematical Physics Seminar\ n\n\nAbstract\nWe give a new definition of Levi-Civita connection for a no ncommutative pseudo-Riemannian metric on a noncommutative manifold given b y a spectral triple. We prove the existence-uniqueness result for a class of modules of one-forms over a large class of noncommutative manifolds\, i ncluding the matrix geometry of the fuzzy 3-sphere\, the quantum Heisenber g manifolds and Connes-Landi deformations of spectral triples on the Conne s-Dubois 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. Mukhopadhyay.\n LOCATION:https://stable.researchseminars.org/talk/MatPhySem/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Fawad Hassan (Stockholm University) DTSTART:20200526T130000Z DTEND:20200526T140000Z DTSTAMP:20260404T110823Z UID:MatPhySem/3 DESCRIPTION:Title: Interactions of multiple spin-2 fields: bimetric and multimetric theories\nby Fawad Hassan (Stockholm University) as part of Mathematic al Physics Seminar\n\n\nAbstract\nClassical and quantum fields are classif ied in terms of their\n"spin" which not only specifies their behavior unde r rotations\, but also\ndetermines the basic structure of their field equa tions. The Standard\nModel describes particle physics in terms of fields o f 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 descri bable by local field\ntheories at all\, leaving theories of multiple spin- 2 fields as the main\npossible extensions of the familiar field theories. Hence\, a long standing\nquestion has been if GR could be extended to cont ain extra spin 2 fields\nof potential relevant to new physics. The main di fficulty in constructing\nsuch theories is the appearance of "ghost" insta bilities. Some such\ntheories have been found in recent years and are high ly constrained by\nconsistency conditions. This talk describes theories of two and multiple\nspin-2 fields commonly known as ghost-free bimetric and multimetric\ntheories. In particular I will focus on the structure of gho st free\nbimetric and multimetric interactions\, their physical interpreta tion\, and\non the notions of space and time in bimetric theories.\n\nWEBI NAR ON FRIDAY WAS CANCELLED DUE TO TECHNICAL PROBLEMS\n LOCATION:https://stable.researchseminars.org/talk/MatPhySem/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Shahn Majid (Queen Mary\, University of London) DTSTART:20200527T111500Z DTEND:20200527T121500Z DTSTAMP:20260404T110823Z UID:MatPhySem/4 DESCRIPTION:Title: Quantum gravity on the fuzzy sphere\nby Shahn Majid (Queen Ma ry\, University of London) as part of Mathematical Physics Seminar\n\n\nAb stract\nWe study the quantum geometry of the fuzzy sphere defined as the a ngular momentum algebra $[x_i\,x_j]=2\\imath\\lambda_p \\epsilon_{ijk}x_k$ modulo setting $\\sum_i x_i^2$ to a constant\, using a recently introduc ed 3D rotationally invariant differential structure. Metrics are given by symmetric 3×3 matrices g and we show that for each metric there is a uniq ue quantum Levi-Civita connection with constant coefficients\, with scalar curvature $\\frac{1}{2}({\\rm Tr}(g^2)-\\frac{1}{2}{\\rm Tr}(g)^2)/\\det( g)$. As an application\, we construct Euclidean quantum gravity on the fuz zy unit sphere. We also calculate the charge 1 monopole for the 3D differe ntial structure. Joint work with E. Lira Torres.\n\nLivestream platform: W EBEX\n LOCATION:https://stable.researchseminars.org/talk/MatPhySem/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Edwin Beggs (Swansea University) DTSTART:20200610T111500Z DTEND:20200610T121500Z DTSTAMP:20260404T110823Z UID:MatPhySem/5 DESCRIPTION:Title: Quantum geodesics in quantum mechanics\nby Edwin Beggs (Swans ea University) as part of Mathematical Physics Seminar\n\n\nAbstract\nWe s how that the standard Heisenberg algebra of quantum mechanics admits a non commutative 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 q uantum formulation of autoparallel curves (or `geodesics') reduces to Schr ödinger's equation. The connection is compatible with a natural quantum s ymplectic structure and associated generalised quantum metric. A remnant o f our approach also works on any symplectic manifold where\, by extending the calculus\, we can encode any hamiltonian flow as `geodesics' for a cer tain connection with torsion which is moreover compatible with an extended symplectic structure. Thus we formulate ordinary quantum mechanics in a w ay that more resembles gravity rather than the more well-studied idea of f ormulating geometry in a more quantum manner. We then apply the same appro ach to the Klein Gordon equation on Minkowski space with a background elec tromagnetic field\, formulating quantum `geodesics' on the relevant relati vistic Heisenberg algebra. Examples include a proper time relativistic fre e particle wave packet and a hydrogen-like atom. based on a joint work wit h Shahn Majid.\n LOCATION:https://stable.researchseminars.org/talk/MatPhySem/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Satyajit Guin (IIT Kanpur) DTSTART:20210622T120000Z DTEND:20210622T130000Z DTSTAMP:20260404T110823Z UID:MatPhySem/6 DESCRIPTION:Title: Equivariant spectral triple for the compact quantum group $U_q(2) $ for complex deformation parameters\nby Satyajit Guin (IIT Kanpur) as part of Mathematical Physics Seminar\n\n\nAbstract\nLet $q=|q|e^{i\\pi\\t heta}$ be a nonzero complex number such that $|q|\\neq 1$\, and consider t he compact quantum group $U_q(2)$. In this talk\, we discuss a complete li st of inequivalent irreducible representations of $U_q(2)$ and its Peter-W eyl decomposition. 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 ac tion of $U_q(2)$. The spectral triple obtained here is even\, $4^+$-summab le\, non-degenerate\, and the Dirac operator acts on two copies of the $L^ 2$-space of $U_q(2)$. The Chern character of the associated Fredholm modul e is nontrivial.\n\nThis is a joint work with Bipul Saurabh.\n LOCATION:https://stable.researchseminars.org/talk/MatPhySem/6/ END:VEVENT END:VCALENDAR