BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Christopher Fewster (University of York) DTSTART:20200525T140000Z DTEND:20200525T145000Z DTSTAMP:20260416T030430Z UID:IML-SMR/1 DESCRIPTION:Title: A nonlocal generalisation of Green hyperbolicity\nby Christopher Fewst er (University of York) as part of Scattering\, microlocal analysis and re normalisation\n\n\nAbstract\nI describe how Bär's theory of Green hyperbo lic partial differential operators can be generalized to nonlocal operator s\, where the nonlocality is confined to a compact spacetime region. Opera tors of this type arise in some models of the interaction between a field and a particle detector\, but they can also be used to model fields on non commutative spacetimes and "soft causality violation".\n\nIt is shown that the nonlocal Green hyperbolic operators enjoy (suitable generalizations o f) many of the properties of Green hyperbolic operators\; in particular\, they can be used as the starting point for a quantum field theory on curve d spacetimes.\n\nThe talk describes work in progress with Rainer Verch (Le ipzig).\n LOCATION:https://researchseminars.org/talk/IML-SMR/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Jan Dereziński (University of Warsaw) DTSTART:20200525T150000Z DTEND:20200525T155000Z DTSTAMP:20260416T030430Z UID:IML-SMR/2 DESCRIPTION:Title: The Feynman propagator on curved spacetimes\nby Jan Dereziński (Unive rsity of Warsaw) as part of Scattering\, microlocal analysis and renormali sation\n\n\nAbstract\nSpacetimes with an asymptotically stationary future and past possess a distinguished Feynman propagator\, a central ingredient of the evaluation of scattering amplitudes. I will describe its construct ion and the related question of self-adjointness of the Klein-Gordon opera tor.\n LOCATION:https://researchseminars.org/talk/IML-SMR/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Dmitri Vassiliev (University College London) DTSTART:20200528T090000Z DTEND:20200528T095000Z DTSTAMP:20260416T030430Z UID:IML-SMR/3 DESCRIPTION:Title: Geometric wave propagator on Riemannian manifolds\nby Dmitri Vassiliev (University College London) as part of Scattering\, microlocal analysis a nd renormalisation\n\n\nAbstract\nWe study the propagator of the wave equa tion on a closed Riemannian manifold M. We propose a geometric approach to the construction of the propagator as a single oscillatory integral globa l both in space and in time with a distinguished complex-valued phase func tion. This enables us to provide a global invariant definition of the full symbol of the propagator - a scalar function on the cotangent bundle - an d an algorithm for the explicit calculation of its homogeneous components. The central part of the talk is devoted to the detailed analysis of the s ubprincipal symbol\; in particular\, we derive its explicit small time asy mptotic expansion. We present a general geometric construction that allows one to visualise topological obstructions and describe their circumventio n with the use of a complex-valued phase function. We illustrate the gener al framework with explicit examples in dimension two.\n LOCATION:https://researchseminars.org/talk/IML-SMR/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Matteo Capoferri (Cardiff University) DTSTART:20200528T100000Z DTEND:20200528T105000Z DTSTAMP:20260416T030430Z UID:IML-SMR/4 DESCRIPTION:Title: Global propagator for the massless Dirac operator and spectral asymptotics \nby Matteo Capoferri (Cardiff University) as part of Scattering\, mic rolocal analysis and renormalisation\n\n\nAbstract\nWe construct the propa gator of the massless Dirac operator W on a closed Riemannian 3-manifold a s the sum of two invariantly defined oscillatory integrals\, global in spa ce and in time\, with distinguished complex-valued phase functions. The tw o oscillatory integrals – the positive and the negative propagators – correspond to positive and negative eigenvalues of W\, respectively. This enables us to provide a global invariant definition of the full symbols of the propagators (scalar matrix-functions on the cotangent bundle)\, a clo sed formula for the principal symbols and an algorithm for the explicit ca lculation of all their homogeneous components. Furthermore\, we obtain sma ll time expansions for principal and subprincipal symbols of the propagato rs in terms of geometric invariants. Lastly\, we use our results to comput e the third local Weyl coefficients in the asymptotic expansion of the eig envalue counting functions of W.\n LOCATION:https://researchseminars.org/talk/IML-SMR/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Wojciech Dybalski (TU München) DTSTART:20200601T140000Z DTEND:20200601T145000Z DTSTAMP:20260416T030430Z UID:IML-SMR/5 DESCRIPTION:Title: The Bisognano–Wichmann property for asymptotically complete massless QFT \nby Wojciech Dybalski (TU München) as part of Scattering\, microloca l analysis and renormalisation\n\n\nAbstract\nA novel algebraic criterion for the Bisognano-Wichmann property of one-particle nets was recently foun d by V. Morinelli. In this talk I will explain how to apply this criterion to the case of massless\, integer spin particles using the Mackey subgrou p theorem. In the next step the result will be lifted from the one-particl e nets to Haag-Kastler nets using the assumption of asymptotic completenes s. The argument relies on scattering theory of massless particles due to B uchholz and its recent simplifications. Also ideas from the massive case\, which had been solved by J. Mund\, enter into the discussion. The talk is based on a joint paper with V. Morinelli.\n LOCATION:https://researchseminars.org/talk/IML-SMR/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Pavel Kurasov (Stockholm University) DTSTART:20200601T150000Z DTEND:20200601T155000Z DTSTAMP:20260416T030430Z UID:IML-SMR/6 DESCRIPTION:Title: The additive structure of the spectra of quantum graphs and discrete measu res\nby Pavel Kurasov (Stockholm University) as part of Scattering\, m icrolocal analysis and renormalisation\n\n\nAbstract\nIt is proven that th e spectrum of the Laplacian on a metric graph $\\Gamma$ contains arithmeti c sequences if and only if the graph has a loop -- an edge connected to on e vertex\nby both end points. Moreover the length of the longest possible arithmetic subsequence\nis estimated using the corresponding discrete grap h $G$.\n \nOur main tool is diophantine analysis\, specifically ''Lang's $ G_m $ Conjecture'' concerning the intersection of the division group of a finitely generated subgroup of $(\\mathbb C^*)^N$ with a subvariety of $( \\mathbb C^*)^N$.\n On our way we prove recent Colin de Verdière's Conjec ture concerning structure\n of polynomials associated with metric graphs.\ n\n\n \n The trace formula connecting spectra of standard Laplacians on me tric graphs to the\n sets of periodic orbits allows us to construct a lar ge family of exotic crystalline measures\, studied recently\n by Y. Meyer. Crystalline measures are discrete measures with Fourier transform being a discrete measure as well.\n Our analysis in the first part imply that con structed measures are\n not just combinations of Poisson summation formula e.\n\n\n\n\nThis is a joint work with Peter Sarnak.\n LOCATION:https://researchseminars.org/talk/IML-SMR/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Alessio Marta (University of Milan) DTSTART:20200604T090000Z DTEND:20200604T095000Z DTSTAMP:20260416T030430Z UID:IML-SMR/7 DESCRIPTION:Title: Propagation of singularities on asymptotically AdS spacetimes with general boundary conditions\nby Alessio Marta (University of Milan) as part o f Scattering\, microlocal analysis and renormalisation\n\n\nAbstract\nWe c onsider a Klein-Gordon equation on asymptotically anti-de Sitter spacetime s subject to a very general class of boundary conditions implemented on th e conformal boundary by pseudodifferential operators. Using microlocal est imates\, we prove a propagation of singularities theorem along generalized broken bicharacteristics and we study the well-posedness of the problem\, proving existence and uniqueness theorems for a subset of the boundary co nditions considered that includes interesting cases: In particular among t his class of boundary conditions\, in addition to Neumann\, Dirichlet and Robin\, there are dynamical boundary conditions (e.g. of Wentzell kind).\n LOCATION:https://researchseminars.org/talk/IML-SMR/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Kasia Rejzner (University of York) DTSTART:20200608T140000Z DTEND:20200608T145000Z DTSTAMP:20260416T030430Z UID:IML-SMR/9 DESCRIPTION:Title: Symmetries and locality in perturbative algebraic quantum field theory \nby Kasia Rejzner (University of York) as part of Scattering\, microlocal analysis and renormalisation\n\n\nAbstract\nPerturbative algebraic quantu m field theory (pAQFT) is a rigorous framework for perturbative QFT\, appl icable also on curved spacetimes\, which makes heavy use of microlocal ana lysis. The key idea is that through constructing extensions of certain dis tributions\, one obtains time-ordered products of quantum fields. This bec omes more complicated when symmetries are involved\, e.g. in QED\, Yang-Mi lls theories and gravity. In this talk I will explain how the idea of loca lity and application of homological algebra naturally lead to a constructi on known as BV formalism.\n LOCATION:https://researchseminars.org/talk/IML-SMR/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Strohmaier (University of Leeds) DTSTART:20200608T150000Z DTEND:20200608T155000Z DTSTAMP:20260416T030430Z UID:IML-SMR/10 DESCRIPTION:Title: Spectral theory on stationary spacetimes\nby Alexander Strohmaier (Un iversity of Leeds) as part of Scattering\, microlocal analysis and renorma lisation\n\n\nAbstract\nFor compact Riemannian manifolds the Gutzwiller-Du istermaat-Guillemin trace formula is one of the standard tools to show Wey l laws\, investigate questions of quantum chaos\, and prove inverse spectr al problems. In this talk I am going to present a generalisation to the se tting of stationary spacetimes with compact Cauchy surfaces. I will start by explaining the classical theory and then point out some differences in the more general relativistic setting.\n (joint work with Steve Zelditch)\ n LOCATION:https://researchseminars.org/talk/IML-SMR/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Fumio Hiroshima (Kyushu University) DTSTART:20200611T090000Z DTEND:20200611T095000Z DTSTAMP:20260416T030430Z UID:IML-SMR/11 DESCRIPTION:Title: Localizations of bound states of a renormalized Hamiltonian\nby Fumio Hiroshima (Kyushu University) as part of Scattering\, microlocal analysis and renormalisation\n\n\nAbstract\nWe study the ground state of the renor malized and non-renormalized Nelson model in quantum field theory. Localiz ations of the ground state are discussed. The ground state can be seen as a function of the position variable $x$ and the field variable $\\phi$. We show the spatial exponential decay in $x$ in terms of the Agmon metric an d Gaussian domination in $\\phi$ for the ground state. The super exponenti al decay of the number of bosons in the ground state is also shown. To sho w the localizations we apply the Gibbs measure associated with the ground state.\n LOCATION:https://researchseminars.org/talk/IML-SMR/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Nguyen Viet Dang (Université de Lyon 1) DTSTART:20200611T100000Z DTEND:20200611T103000Z DTSTAMP:20260416T030430Z UID:IML-SMR/12 DESCRIPTION:Title: Renormalization of determinant lines in Quantum Field Theory\nby Nguy en Viet Dang (Université de Lyon 1) as part of Scattering\, microlocal an alysis and renormalisation\n\n\nAbstract\nIn the present talk\, we will di scuss how we understand a three page note from Quillen's notebook where he tries to make sense of the technique of "adding counterterms to the Lagra ngian to remove the infinities" used in renormalized perturbation theory. Then we explain what the counterterms are in the situation of a quantized fermion field\, interacting with a\ngauge field treated as an external fie ld. Our discussion will also be very much inspired by I.M Singer's lecture on families of Dirac operators with application to physics.\n LOCATION:https://researchseminars.org/talk/IML-SMR/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Peter Hintz (MIT) DTSTART:20200615T140000Z DTEND:20200615T145000Z DTSTAMP:20260416T030430Z UID:IML-SMR/13 DESCRIPTION:Title: Wave decay on asymptotically flat spacetimes\nby Peter Hintz (MIT) as part of Scattering\, microlocal analysis and renormalisation\n\n\nAbstrac t\nThe focus of this talk is the study of asymptotic expansions of linear waves propagating on stationary and asymptotically flat spacetimes. On the spectral side\, I will describe a hands-on approach to resolvent expansio ns near zero energy based on recent work by Vasy. I will discuss two main applications: first\, sharp decay for scattering by short range potentials on $\\mathbb{R}^3$\; second\, a strengthening of Price's Law on Kerr spac etimes.\n LOCATION:https://researchseminars.org/talk/IML-SMR/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Annalisa Panati (Université de Toulon / CPT Marseille) DTSTART:20200618T090000Z DTEND:20200618T095000Z DTSTAMP:20260416T030430Z UID:IML-SMR/14 DESCRIPTION:Title: Heat fluctuations in the two-time measurement framework and ultraviolet r egularity\nby Annalisa Panati (Université de Toulon / CPT Marseille) as part of Scattering\, microlocal analysis and renormalisation\n\n\nAbstr act\nIn this talk I will present some recent results about the connection between heat fluctuation in the two-time measurement framework and ultr aviolet regularity\, and I will sketch what we expect to happen for (toy)- models that can be renormalized through self-energy extraction.\n\nTo put the result in context\, in the first part of the talk I will review the ce lebrated fluctuation theorem in statistical mechanics and the two-time mea surement framework. Since Kurchan’s seminal work (2000)\, two-time meas urement statistics (also known as full counting statistics) has been sho wn to have an important theoretical role in the context of quantum statist ical mechanics\, as they allow for an extension of the celebrated fluctuat ion relation to the quantum setting. \n\nIn the second part of the talk\, I will present our recent results. We show that the description of heat fl uctuation differs considerably from its classical counterpart\, in particu lar a crucial role is played by ultraviolet regularity conditions. On a se t of canonical examples\, with bounded and unbounded perturbations\, we sh ow that\n\nour ultraviolet conditions are essentially necessary. If the fo rm factor of the perturbation does\n\nnot meet our assumptions\, the heat variation distribution exhibits heavy tails. The tails can be\n\nas heavy as preventing the existence of a fourth moment of the heat variation. This phenomenon has no classical analogue.\n\nI will conclude with some conjec tures for models that can be renormalized through self-energy extraction.\ n\n(Joint work with T. Benoist\, R. Raquépas)\n\nLink to the published pa per:\nhttps://link.springer.com/article/10.1007/s00023-018-0743-x\n LOCATION:https://researchseminars.org/talk/IML-SMR/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Nicolò Drago (Universität Würzburg) DTSTART:20200615T150000Z DTEND:20200615T153000Z DTSTAMP:20260416T030430Z UID:IML-SMR/15 DESCRIPTION:Title: On Maxwell's equations on globally hyperbolic spacetimes with timelike bo undary\nby Nicolò Drago (Universität Würzburg) as part of Scatterin g\, microlocal analysis and renormalisation\n\n\nAbstract\nWe study Maxwel l's equations as a theory for smooth $k$-forms on globally hyperbolic spac etimes with a timelike boundary. For that\, we investigate the wave operat or $\\Box_k$ with appropriate boundary conditions and characterize the spa ce of solutions of the associated initial and boundary value problem under reasonable assumptions. Subsequently we focus on the Maxwell operator $\\ delta d$. First we introduce two distinguished boundary conditions\, dubbe d $\\delta d$-tangential and $\\delta d$-normal boundary conditions. Asso ciated to these we introduce two different notions of gauge equivalence fo r the solutions of the Maxwell's operator and we prove that in both cases \, every equivalence class admits a representative abiding to the Lorentz gauge. We then construct a unital $*$-algebras $\\mathcal{A}$ of observabl es for the system described by the Maxwell's operator. Finally we prove th at\, as in the case of the Maxwell operator on globally hyperbolic spaceti mes with empty boundary\, $\\mathcal{A}$ possesses a non-trivial center.\n LOCATION:https://researchseminars.org/talk/IML-SMR/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Oliver Matte (Aalborg University) DTSTART:20200618T100000Z DTEND:20200618T105000Z DTSTAMP:20260416T030430Z UID:IML-SMR/16 DESCRIPTION:Title: Differentiability properties of stochastic flows and semigroup kernels in nonrelativistic QED\nby Oliver Matte (Aalborg University) as part of Scattering\, microlocal analysis and renormalisation\n\n\nAbstract\nIn thi s talk we consider the Pauli-Fierz model for a finite number of nonrelativ istic electrons in an external electrostatic potential interacting with th e quantized\, ultraviolet cutoff electromagnetic field. The semigroup gene rated by the corresponding Hamiltonian has a Fock space operator-valued in tegral kernel. We study the differentiability properties of this kernel\, with respect to time and electron positions\, away from the singularities of the electrostatic potential. We further obtain new decay and regularity results on possible ground state eigenvectors and more general elements o f spectral subspaces. The proofs of our results are based on Feynman-Kac f ormulas and an analysis of the differentiability properties of solutions t o certain stochastic differential equations associated with the Pauli-Fier z model. These equations have been introduced by Batu Güneysu\, Jacob Sch ach Møller and the present author in an earlier work.\n LOCATION:https://researchseminars.org/talk/IML-SMR/16/ END:VEVENT END:VCALENDAR