\nThe talk is based on a joint work with Yoshiko Ogata and Yuji Tachikawa in arXiv:2 004.06458.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Nicolas Rougerie (University of Grenoble Alpes) DTSTART;VALUE=DATE-TIME:20200728T130000Z DTEND;VALUE=DATE-TIME:20200728T140000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/12 DESCRIPTION:Title: Two modes approximation for bosons in a double well potential\n by Nicolas Rougerie (University of Grenoble Alpes) as part of One world IA MP mathematical physics seminar\n\n\nAbstract\nWe study the mean-field lim it for the ground state of bosonic particles in a double-well potential\, jointly with the limit of large inter-well separation/large potential ener gy barrier. Two one-body wave-functions are then macroscopially occupied\, one for each well. The physics in this two-modes subspace is usually desc ribed by a Bose-Hubbard Hamiltonian\, yielding in particular the transitio n from an uncorrelated "superfluid" state (each particle lives in both pot ential wells) to a correlated "insulating" state (half of the particles li ve in each potential well). \n\nThrough precise energy expansions we pro ve that the variance of the number of particles within each well is suppre ssed (violation of the central limit theorem)\, a signature of a correlate d ground state. \n\nQuantum fluctuations around the two-modes description are particularly relevant\, for they give energy contributions of the same order as the energy difference due to suppressed variances in the two-mod es subspace. We describe them in terms of two independent Bogoliubov Hamil tonians\, one for each potential well.\n\nJoint work with Alessandro Olgia ti and Dominique Spehner\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Hugo Duminil-Copin (IHES / University of Geneva) DTSTART;VALUE=DATE-TIME:20200721T130000Z DTEND;VALUE=DATE-TIME:20200721T140000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/13 DESCRIPTION:Title: Marginal triviality of the scaling limits of critical 4D Ising and &phi\;_4^4 models\nby Hugo Duminil-Copin (IHES / University of Geneva) as part of One world IAMP mathematical physics seminar\n\n\nAbstract\nIn this talk\, we will discuss the scaling limits of spin fluctuations in fou r-dimensional Ising-type models with nearest-neighbor ferromagnetic intera ction at or near the critical point are Gaussian and its implications from the point of view of Euclidean Field Theory. Similar statements will be p roven for the &lambda\;&phi\;4 fields over R^4 with a lattice ultraviolet cutoff\, in the limit of infinite volume and vanishing lattice spacing. Th e proofs are enabled by the models' random current representation\, in whi ch the correlation functions' deviation from Wick's law is expressed in te rms of intersection probabilities of random currents with sources at dista nces which are large on the model's lattice scale. Guided by the analogy w ith random walk intersection amplitudes\, the analysis focuses on the impr ovement of the so-called tree diagram bound by a logarithmic correction te rm\, which is derived here through multi-scale analysis.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Antti Kupiainen (University of Helsinki) DTSTART;VALUE=DATE-TIME:20200908T140000Z DTEND;VALUE=DATE-TIME:20200908T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/14 DESCRIPTION:Title: Integrability of Liouville Conformal Field Theory\nby Antti Kup iainen (University of Helsinki) as part of One world IAMP mathematical phy sics seminar\n\n\nAbstract\nA. Polyakov introduced Liouville Conformal Fie ld theory (LCFT) in 1981 as a way to put a natural measure on the set of R iemannian metrics over a two dimensional manifold. Ever since\, the work o f Polyakov has echoed in various branches of physics and mathematics\, ran ging from string theory to probability theory and geometry. In the context of 2D quantum gravity models\, Polyakovâ€™s approach is conjecturall y equivalent to the scaling limit of Random Planar Maps and through the Al day-Gaiotto- Tachikava correspondence LCFT is conjecturally related to cer tain 4D Yang-Mills theories. Through the work of Dorn\,Otto\, Zamolodchiko v and Zamolodchikov and Teschner LCFT is believed to be to a certain exten t integrable. \n\nI will review a probabilistic construction of LCFT devel oped together with David\, Rhodes and Vargas and recent proofs concerning the integrability of LCFT: \n-The proof in a joint work with Rhodes and Va rgas of the DOZZ formula (Annals of Mathematics\, 81-166\,191 (2020) \n-Th e proof in a joint work with Guillarmou\, Rhodes and Vargas of the bootstr ap conjecture for LCFT (arXiv:2005.11530).\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Victor Ivrii (University of Toronto) DTSTART;VALUE=DATE-TIME:20200915T140000Z DTEND;VALUE=DATE-TIME:20200915T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/15 DESCRIPTION:Title: Scott and Thomas-Fermi approximations to electronic density\nby Victor Ivrii (University of Toronto) as part of One world IAMP mathematic al physics seminar\n\n\nAbstract\nIn heavy atoms and molecules\, on the di stances $ a \\ll Z^{-1/2}$ from one of the nuclei (with a charge $Z_m$)\, we prove that the ground state electronic density $\\rho_\\Psi (x)$ is app roximated in $L^p$-norm by the ground state electronic density for a singl e atom in the model with no interactions between electrons.\n\nFurther\, o n the distances $a \\gg Z^{-1}$ from all of the nuclei (with a charge $Z_1 \,\\ldots\, Z_m$) we prove that $\\rho_\\Psi (x)$ is approximated in $L^p$ -norm\, by the Thomas-Fermi density. We cover both non-relativistic and re lativistic cases.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Alessandro Giuliani (University Roma Tre) DTSTART;VALUE=DATE-TIME:20200929T140000Z DTEND;VALUE=DATE-TIME:20200929T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/16 DESCRIPTION:Title: Non-renormalization of the `chiral anomaly' in interacting lattice Weyl semimetals\nby Alessandro Giuliani (University Roma Tre) as part of One world IAMP mathematical physics seminar\n\n\nAbstract\nWeyl semimet als are 3D condensed matter systems characterized by a degenerate Fermi su rface\, consisting of a pair of `Weyl nodes'. Correspondingly\, in the inf rared limit\, these systems behave effectively as Weyl fermions in 3+1 dim ensions. We consider a class of interacting 3D lattice models for Weyl sem imetals and prove that the quadratic response of the quasi-particle flow b etween the Weyl nodes\, which is the condensed matter analogue of the chir al anomaly in QED4\, is universal\, that is\, independent of the interacti on strength and form. Universality\, which is the counterpart of the Adler -Bardeen non-renormalization property of the chiral anomaly for the infrar ed emergent description\, is proved to hold at a non-perturbative level\, notwithstanding the presence of a lattice\n(in contrast with the original Adler-Bardeen theorem\, which is perturbative and requires relativistic in variance to hold). The proof relies on constructive bounds for the Euclide an ground state correlations combined with lattice Ward Identities\, and i t is valid arbitrarily close to the critical point where the Weyl points m erge and the relativistic description breaks down. Joint work with V. Mast ropietro and M. Porta.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Nalini Anantharaman (Strasbourg) DTSTART;VALUE=DATE-TIME:20201103T140000Z DTEND;VALUE=DATE-TIME:20201103T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/17 DESCRIPTION:Title: The bottom of the spectrum of a random hyperbolic surface\nby N alini Anantharaman (Strasbourg) as part of One world IAMP mathematical phy sics seminar\n\n\nAbstract\nI will report on work in progress with Laura M onk\, where we study the bottom of the spectrum of the laplacian\, on a co mpact hyperbolic surface chosen at random\, in the limit of growing genus. We pick combinatorial ideas from the study of random regular graphs\, to propose a strategy to prove that\, with high probability\, there are no ei genvalues below $1/4-\\epsilon$.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Peter Hintz (MIT) DTSTART;VALUE=DATE-TIME:20201110T140000Z DTEND;VALUE=DATE-TIME:20201110T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/18 DESCRIPTION:Title: Linear stability of slowly rotating Kerr spacetimes\nby Peter H intz (MIT) as part of One world IAMP mathematical physics seminar\n\n\nAbs tract\nI will describe joint work with Dietrich Häfner and András Vasy i n which we study the asymptotic behavior of linearized gravitational pertu rbations of Schwarzschild or slowly rotating Kerr black hole spacetimes. W e show that solutions of the linearized Einstein equation decay at an inve rse polynomial rate to a stationary solution (given by an infinitesimal va riation of the mass and angular momentum of the black hole)\, plus a pure gauge term. The proof uses a detailed description of the resolvent of an a ssociated wave equation on symmetric 2-tensors near zero energy.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Bruno Nachtergaele (UC Davis) DTSTART;VALUE=DATE-TIME:20201027T140000Z DTEND;VALUE=DATE-TIME:20201027T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/19 DESCRIPTION:Title: Gapped ground state phases of lattice systems - Stability of the bu lk gap\nby Bruno Nachtergaele (UC Davis) as part of One world IAMP mat hematical physics seminar\n\n\nAbstract\nI will give an overview of stabil ity results for the spectral gap above the ground states of quantum lattic e systems obtained in the past decade and explain the overall strategy int roduced by Bravyi\, Hastings\, and Michalakis. A new result I will present proves the stability of the bulk gap for infinite systems with an approac h that bypasses possible gapless boundary modes (joint work with Bob Sims and Amanda Young).\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Yoshiko Ogata (University of Tokyo) DTSTART;VALUE=DATE-TIME:20201215T140000Z DTEND;VALUE=DATE-TIME:20201215T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/20 DESCRIPTION:Title: Classification of symmetry protected topological phases in quantum spin systems\nby Yoshiko Ogata (University of Tokyo) as part of One wo rld IAMP mathematical physics seminar\n\n\nAbstract\nA Hamiltonian is in a SPT phase with a given symmetry if it cannot be \nsmoothly deformed into a trivial Hamiltonian without a phase transition\, \nif the deformation p reserves the symmetry\,\nwhile it can be smoothly deformed into a trivial Hamiltonian without a \nphase transition\, if the symmetry is broken durin g the deformation.\nWe consider this problem for one- and two-dimensional quantum spin systems with on-site finite \ngroup symmetries.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Jeremy Quastel (University of Toronto) DTSTART;VALUE=DATE-TIME:20201020T140000Z DTEND;VALUE=DATE-TIME:20201020T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/21 DESCRIPTION:Title: Towards KPZ Universality\nby Jeremy Quastel (University of Toro nto) as part of One world IAMP mathematical physics seminar\n\n\nAbstract\ nThe 1-d KPZ universality class contains random interface growth models\na s well as random polymer free energies and driven diffusive systems. \nTh e KPZ fixed point has now been determined\, through the exact solution of a special model\nin the class\, TASEP\, and is expected to describe the as ymptotic fluctuations for all models in the class.\nIt is an integrable Ma rkov process\, with transition probabilities described by a system of inte grable PDE's.\n

\nVery recently\, new techniques have become available to prove \nthe convergence of the KPZ equation itself\, as well as some no n-integrable extensions\nof TASEP\, to the KPZ fixed point. This talk wil l be a gentle introduction to these developments\nwith no prior knowledge assumed. The results are\, variously\, joint works with \nDaniel Remenik\ , Konstantin Matetski\, and Sourav Sarkar.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Roland Bauerschmidt (University of Cambridge) DTSTART;VALUE=DATE-TIME:20201124T140000Z DTEND;VALUE=DATE-TIME:20201124T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/22 DESCRIPTION:Title: The Coleman correspondence at the free fermion point\nby Roland Bauerschmidt (University of Cambridge) as part of One world IAMP mathemat ical physics seminar\n\n\nAbstract\nTwo-dimensional statistical and quantu m field theories are\nspecial in many ways. One striking instance of this is the equivalence\nof certain bosonic and fermionic fields\, known as bos onization. I will\nfirst review this correspondence in the explicit instan ce of the\nmassless Gaussian free field and massless Euclidean Dirac fermi ons. I\nwill then present a result that extends this correspondence to the \nnon-Gaussian `massless' sine-Gordon field on $\\R^2$ at $\\beta=4\\pi$ a nd\nmassive Dirac fermions. This is an instance of Coleman's prediction th at\nthe `massless' sine-Gordon model and the massive Thirring model are\ne quivalent. We use this correspondence to show that correlations of the\n`m assless' sine-Gordon model decay exponentially for $\\beta=4\\pi$.\nThis i s joint work with C. Webb (arXiv:2010.07096).\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Svitlana Mayboroda (University of Minnesota) DTSTART;VALUE=DATE-TIME:20201013T140000Z DTEND;VALUE=DATE-TIME:20201013T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/23 DESCRIPTION:Title: The landscape law for the integrated density of states\nby Svit lana Mayboroda (University of Minnesota) as part of One world IAMP mathema tical physics seminar\n\n\nAbstract\nComplexity of the geometry\, randomne ss of the potential\, and many other irregularities of the system can caus e powerful\, albeit quite different\, manifestations of localization\, a p henomenon of sudden confinement of waves\, or eigenfunctions\, to a small portion of the original domain. In the present talk we show that behind a possibly disordered system there exists a structure\, referred to as a lan dscape function\, which can predict the location and shape of the localize d eigenfunctions\, a pattern of their exponential decay\, and deliver accu rate bounds for the corresponding eigenvalues. In particular\, we establis h the "landscape law"\, the first non-asymptotic estimates from above and below on the integrated density of states of the Schroedinger operator usi ng a counting function for the minima of the localization landscape. The r esults are deterministic\, and rely on a new uncertainty principle. Narrow ing down to the context of disordered potentials\, we derive the best curr ently available bounds on the integrated density of states for the Anderso n model.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Stefan Hollands (University of Leipzig) DTSTART;VALUE=DATE-TIME:20201117T140000Z DTEND;VALUE=DATE-TIME:20201117T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/24 DESCRIPTION:Title: (In)determinism Inside Black Holes\nby Stefan Hollands (Univers ity of Leipzig) as part of One world IAMP mathematical physics seminar\n\n \nAbstract\nIn classical General Relativity\, the values of fields on spac etime are\nuniquely determined by their initial values within its "domain of\ndependence". However\, it may occur that the\nspacetime under consider ation extends beyond this domain\, and\nfields\, therefore\, are not entir ely determined by their initial data. In fact\, such a naive\nfailure of d eterminism occurs inside all physically relevant black holes.\n\nThe bound ary of the region determined by the initial data is\ncalled the "Cauchy ho rizon". Penrose has proposed ("strong cosmic censorship conjecture")\nthat the Cauchy horizon is actually unstable in the sense that the slightest p erturbation caused\nby remnant fields convert it to a final singularity. W hether or not this is the case --\nand thus whether there is a real proble m with determinism -- has been put into question recently.\n\nIn this coll oquium I ask wheter quantum effects will come to the rescue of strong cosm ic censorship.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Ian Jauslin (Princeton University) DTSTART;VALUE=DATE-TIME:20200922T140000Z DTEND;VALUE=DATE-TIME:20200922T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/25 DESCRIPTION:Title: An effective equation to study Bose gasses at both low and high den sities\nby Ian Jauslin (Princeton University) as part of One world IAM P mathematical physics seminar\n\n\nAbstract\nI will discuss an effective equation\, which is used to study the ground state\n of the interacting Bo se gas. The interactions induce many-body correlations\n in the system\, w hich makes it very difficult to study\, be it analytically or\n numericall y. A very successful approach to solving this problem is Bogolubov\n theor y\, in which a series of approximations are made\, after which the\n analy sis reduces to a one-particle problem\, which incorporates the many-body\n correlations. The effective equation I will discuss is arrived at by maki ng a\n very different set of approximations\, and\, like Bogolubov theory\ , ultimately\n reduces to a one-particle problem. But\, whereas Bogolubov theory is accurate\n only for very small densities\, the effective equatio n coincides with the\n many-body Bose gas at both low and at high densitie s.\n\n I will show some\n theorems which make this statement more precise\ , and present numerical\n evidence that this effective equation is remarka bly accurate for all\n densities\, small\, intermediate\, and large. That is\, the analytical and\n numerical evidence suggest that this effective e quation can capture many-body\n correlations in a one-particle picture bey ond what Bogolubov can accomplish.\n Thus\, this effective equation gives an alternative approach to study the low\n density behavior of the Bose ga s (about which there still are many important\n open questions). In additi on\, it opens an avenue to understand the physics of\n the Bose gas at int ermediate densities\, which\, until now\, were only\n accessible to Monte Carlo simulations.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Alessandro Pizzo (University of Rome Tor Vergata) DTSTART;VALUE=DATE-TIME:20201201T140000Z DTEND;VALUE=DATE-TIME:20201201T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/26 DESCRIPTION:Title: Stability of gapped quantum chains under small perturbations\nb y Alessandro Pizzo (University of Rome Tor Vergata) as part of One world I AMP mathematical physics seminar\n\n\nAbstract\nWe consider a family of qu antum chains that has attracted much interest amongst people studying topo logical phases of matter. Their Hamiltonians are perturbations\, by intera ctions of short range\, of a Hamiltonian consisting of on-site terms and w ith a strictly positive energy gap above its ground-state energy. For inte ractions that are form-bounded w.r.t. the on-site Hamiltonian terms\, we prove that the spectral gap of the perturbed Hamiltonian above its ground- state energy is bounded from below by a positive constant uniformly in th e length of the chain\, for small values of a coupling constant.\n\nIn our proof we use a novel method based on local Lie-Schwinger conjugations of the Hamiltonians associated with connected subsets of the chain\, that ca n be also applied to complex Hamiltonians obtained by considering complex values of the coupling constant.\n\nWe can treat fermions and bosons on th e same footing\, and our technique does not face a large field problem\, e ven though bosons are involved\, in contrast to most approaches. Furthermo re the method can be extended to higher spatial dimensions.\n\n(Joint work with S. Del Vecchio\, J. Fröhlich\, and S. Rossi.)\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Katrin Wendland (Albert-Ludwigs-Universität Freiburg) DTSTART;VALUE=DATE-TIME:20201208T140000Z DTEND;VALUE=DATE-TIME:20201208T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/27 DESCRIPTION:Title: On invariants shared by geometry and conformal field theory\nby Katrin Wendland (Albert-Ludwigs-Universität Freiburg) as part of One wor ld IAMP mathematical physics seminar\n\n\nAbstract\nI will recall how some conformal field theories can be given geometric interpretations. This can be useful from a practical point of view\, when geometric methods are tra nsferred from geometry to conformal field theory. I will in particular foc us on certain invariants that are shared by geometry and conformal field t heory\, including the complex elliptic genus. As we shall see\, this invar iant is also useful from a theoretical viewpoint\, since it captures infor mation about generic properties of certain theories.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Clotilde Fermanian-Kammerer (Université\; Paris Est - Cr&eac ute\;teil Val de Marne) DTSTART;VALUE=DATE-TIME:20201006T140000Z DTEND;VALUE=DATE-TIME:20201006T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/28 DESCRIPTION:Title: Nonlinear quantum adiabatic approximation\nby Clotilde Fermania n-Kammerer (Université\; Paris Est - Cré\;teil Val de Marne) a s part of One world IAMP mathematical physics seminar\n\n\nAbstract\nWe wi ll discuss generalization of the quantum adiabatic theorem to a nonlinear setting. We will consider evolution equations where the Hamiltonian operat or depends on the time variable and on a finite number of parameters that are fixed on some coordinates of the unknown\, making the equation non-lin ear. Under natural spectral hypotheses\, there exist special functions tha t we call « Instantaneous nonlinear eigenvectors » such that\, in the ad iabatic limit\, the solutions of the nonlinear equations with those initia l data remain close to them\, up to a rapidly oscillating phase. We will e xplain why this question arises\, discuss the proof of this result and sho w how it can fail (works in collaboration with Alain Joye and Rémi Carles ).\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Fabio Toninelli (Technical University Vienna) DTSTART;VALUE=DATE-TIME:20210112T140000Z DTEND;VALUE=DATE-TIME:20210112T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/29 DESCRIPTION:Title: The anisotropic KPZ equation and logarithmic super-diffusivity\ nby Fabio Toninelli (Technical University Vienna) as part of One world IAM P mathematical physics seminar\n\n\nAbstract\nThe AKPZ equation is an anis otropic variant of the celebrated (two-dimensional) KPZ stochastic PDE\, w hich is expected to describe the large-scale behavior of (2+1)-dimensional growth models whose average speed of growth is a non-convex function of the average slope (AKPZ universality class). Several interacting particle systems belonging to the AKPZ class are known\, notably a class of two-dim ensional interlaced particle systems introduced by A. Borodin and P. Ferra ri. In this talk\, I will show that the non-linearity of the AKPZ equation is marginally relevant in the Renormalization Group sense: in fact\, whil e the 2d-SHE is invariant under diffusive rescaling\, for AKPZ the diffusi on coefficient diverges (logarithmically) for large times\, implying margi nal super-diffusivity. [Based on joint work with G. Cannizzaro and D. Erha rd]\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Robert Seiringer (IST Austria) DTSTART;VALUE=DATE-TIME:20210119T140000Z DTEND;VALUE=DATE-TIME:20210119T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/30 DESCRIPTION:Title: Quantum fluctuations and dynamics of a strongly coupled polaron \nby Robert Seiringer (IST Austria) as part of One world IAMP mathematical physics seminar\n\n\nAbstract\nWe review old and new results on the Fröh lich polaron model. The discussion includes the validity of the (classical ) Landau--Pekar equations for the dynamics in the strong coupling limit\, quantum corrections to this limit\, as well as the divergence of the effec tive polaron mass.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Margherita Disertori (University of Bonn) DTSTART;VALUE=DATE-TIME:20210302T140000Z DTEND;VALUE=DATE-TIME:20210302T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/31 DESCRIPTION:Title: Supersymmetric transfer operators\nby Margherita Disertori (Uni versity of Bonn) as part of One world IAMP mathematical physics seminar\n\ n\nAbstract\nTransfer matrix approach is a powerful tool to study one dime nsional or quasi 1d statistical mechanical models. Transfer operator kerne ls arising in the context of quantum diffusion and the supersymmetric ap proach display bosonic and fermionic components. For such kernels\, the pr esence of fermion-boson symmetries allows to drastically simplify the prob lem. I will review the method and give some results for the case of random band matrices.\n\nThis is joint work with Sasha Sodin and Martin Lohmann. \n LOCATION:https://researchseminars.org/talk/IAMP_seminars/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Jan Wehr (University of Arizona) DTSTART;VALUE=DATE-TIME:20210330T140000Z DTEND;VALUE=DATE-TIME:20210330T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/32 DESCRIPTION:Title: Aggregation and deaggregation of interacting micro swimmers\nby Jan Wehr (University of Arizona) as part of One world IAMP mathematical p hysics seminar\n\n\nAbstract\nA swarm of light-sensitive robots is moving in a planar region\, changing the direction of motion randomly. Each robo t emits light\; in turn\, it adapts the speed of its motion to the total i ntensity of the light shed on it by the other robots. The adaptation take s time---the sensorial delay. Using a natural approximation of the equati ons of motion\, the robots may be programmed to make the sensorial delay n egative. In this case they are\, in some sense\, predicting the future. In a series of experiments by the Giovanni Volpe group and the University of Gothenburg (Sweden) it was shown that at a certain negative value of th e delay\, the collective behavior of the robots changes qualitatively from aggregation to deaggregation. I am going to explain this phenomenon by a n asymptotic analysis of the system of stochastic differential equations\, describing the motion of a single robot in an inhomogeneous landscape. \n \nThe results were obtained in a joint work with Giovanni Volpe\, Mite Mij alkov and Austin McDaniel. They display an interesting feature: while th e original system is driven by a single noise source\, the limiting one co ntains two independent ones. I will explain this by showing how one can g enerate two independent Wiener processes from a single one. Using this fa ct to rigorously justify the asymptotic results is a work in progress with Jeremiah Birrell.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Jürg Fröhlich (ETH Zürich) DTSTART;VALUE=DATE-TIME:20210126T140000Z DTEND;VALUE=DATE-TIME:20210126T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/33 DESCRIPTION:Title: The Evolution of States as the Fourth Pillar of Quantum Mechanics\nby Jürg Fröhlich (ETH Zürich) as part of One world IAMP mathematica l physics seminar\n\n\nAbstract\nI present ideas about how to extend the s tandard formalism of Quantum\nMechanics in such a way that the theory actu ally makes sense. My\ntentative extension is called\n\n "ET H-Approach to Quantum Mechanics"\n\n(for "Events\, Trees and Histories").\ n\nThis approach supplies the last of four pillars QM can be constructed u pon\,\nwhich are:

\n(i) Physical quantities characteristic of a phys ical system are represented\n by self-adjoint operators\;

\n(ii) t he time evolution of these operators is given by the Heisenberg equation\;

\n(iii) meaningful notions of states and of "potential" and "actual ev ents" have\n to be introduced\; and

\n(iv) a general law for the t ime evolution of states (superseding Schroedinger\n evolution\, which is inadequate) must be formulated.\n\nBesides briefly sketching the ETH-Ap proach in the setting of non-relativistic\nQM\, I present a family of very simple models of a very heavy atom coupled to\nthe radiation field in a l imit where the speed of light tends to infinity\,\nAn analysis of these mo dels\, which illustrate the ETH Approach\, is the main\nsubject of the tal k.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Tyler Helmuth (University of Durham) DTSTART;VALUE=DATE-TIME:20210223T140000Z DTEND;VALUE=DATE-TIME:20210223T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/34 DESCRIPTION:Title: Efficient algorithms for low-temperature spin systems\nby Tyler Helmuth (University of Durham) as part of One world IAMP mathematical phy sics seminar\n\n\nAbstract\nTwo fundamental algorithmic tasks associated t o discrete statistical mechanics models are approximate counting and appro ximate sampling. At high temperatures Markov chains give efficient algorit hms\, but at low temperatures mixing times can become impractically large\ , and Markov chain methods may fail to be efficient. Recently\, expansion methods (cluster expansions\, Pirogov--Sinai theory) have been put to use to develop provably efficient low-temperature algorithms for some discrete statistical mechanics models. I’ll introduce these algorithmic tasks\, outline how expansion algorithms work\, and indicate some open directions. \n LOCATION:https://researchseminars.org/talk/IAMP_seminars/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Sylvia Serfaty (Courant Institute) DTSTART;VALUE=DATE-TIME:20210323T140000Z DTEND;VALUE=DATE-TIME:20210323T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/35 DESCRIPTION:Title: Ginzburg-Landau vortices\, old and new\nby Sylvia Serfaty (Cour ant Institute) as part of One world IAMP mathematical physics seminar\n\n\ nAbstract\nWe present a review of results on vortices in the 2D Ginzburg-L andau model of superconductivity (also relevant for superfluidity and Bose -Einstein condensates)\, their onset at critical fields\, interaction and patterns. We also report on recent joint work with Carlos Roman and Etie nne Sandier in which we study the onset of vortex lines in the 3D model an d derive an interaction energy for them.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/35/ END:VEVENT BEGIN:VEVENT SUMMARY:Søren Fournais (Aarhus University) DTSTART;VALUE=DATE-TIME:20210105T140000Z DTEND;VALUE=DATE-TIME:20210105T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/36 DESCRIPTION:Title: The ground state energy of dilute Bose gases\nby Søren Fournai s (Aarhus University) as part of One world IAMP mathematical physics semin ar\n\n\nAbstract\nThe rigorous calculation of the ground state energy of d ilute Bose gases has been a challenging problem since the 1950s. In partic ular\, it is of interest to understand the extent to which the Bogoliubov pairing theory correctly describes the ground state of this physical syste m.\nIn this talk I will report on a recent proof of the second term in the energy expansion for dilute gases\, the so-called Lee-Huang-Yang term\, a nd its relation to Bogoliubov theory.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/36/ END:VEVENT BEGIN:VEVENT SUMMARY:Wei Wu (NYU Shanghai) DTSTART;VALUE=DATE-TIME:20210202T140000Z DTEND;VALUE=DATE-TIME:20210202T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/37 DESCRIPTION:Title: Massless phases for the Villain model in $d \\geq 3$\nby Wei Wu (NYU Shanghai) as part of One world IAMP mathematical physics seminar\n\n \nAbstract\nThe XY and the Villain models are mathematical idealization of real world models of liquid crystal\, liquid helium\, and superconductors . Their phase transition has important applications in condensed matter ph ysics and led to the Nobel\nPrize in Physics in 2016. However we are still far from a complete mathematical\nunderstanding of the transition. The sp in wave conjecture\, originally proposed by Dyson and by Mermin and Wagner \, predicts that at low temperature\, large scale behaviors of these model s are closely related to Gaussian free fields. I will review the historica l background and discuss some recent progress on this conjecture in $d \\g eq 3$.\nBased on the joint work with Paul Dario (Tel Aviv).\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/37/ END:VEVENT BEGIN:VEVENT SUMMARY:Gianluca Panati (University of Rome Sapienza) DTSTART;VALUE=DATE-TIME:20210316T140000Z DTEND;VALUE=DATE-TIME:20210316T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/38 DESCRIPTION:Title: The Localization Dichotomy in Solid State Physics\nby Gianluca Panati (University of Rome Sapienza) as part of One world IAMP mathematica l physics seminar\n\n\nAbstract\nSolid state systems exhibit a subtle inte rtwining between the topology of the\n"manifold" of occupied states and th e localization of electrons\, if the latter is appropriately defined. \n

\ni) either there exists an exponentially localized CWB\ , and correspondingly the Chern \nclass of $P_F$ vanishes (ordinary insula tor)\;

\nii) or

\nMore recently\, the previous dichotomy has been reformulated in such a way that it applies\nalso to non-periodic systems\, and a corres ponding "Localization Dichotomy conjecture" for\nnon-periodic systems has been stated. \n

\nIn my talk\, I will gently introduce the subject\, st arting from the periodic case\, and summarize the \nrecent attempts\, by s everal groups\, to prove the Localization Dichotomy for non-periodic syste ms. \n

\nThe talk is based on work in collaboration with D. Monaco\, M. Marcelli\, M. Moscolari\, \nA. Pisante\, and S. Teufel\, and on discussio ns with several colleagues.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/38/ END:VEVENT BEGIN:VEVENT SUMMARY:Gerald Dunne (University of Connecticut) DTSTART;VALUE=DATE-TIME:20210216T140000Z DTEND;VALUE=DATE-TIME:20210216T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/39 DESCRIPTION:Title: Resurgent Asymptotics and Non-perturbative Physics\nby Gerald D unne (University of Connecticut) as part of One world IAMP mathematical ph ysics seminar\n\n\nAbstract\nThere are several important conceptual and co mputational questions concerning path integrals\, which have recently been approached from new perspectives motivated by Ecalle's theory of resurgen t functions\, a mathematical formalism that unifies perturbative and non-p erturbative physics. I will review the basic ideas behind the connections between resurgent asymptotics and physics\, with examples from quantum mec hanics and matrix models.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/39/ END:VEVENT BEGIN:VEVENT SUMMARY:Herbert Spohn (TU Munich) DTSTART;VALUE=DATE-TIME:20210209T140000Z DTEND;VALUE=DATE-TIME:20210209T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/40 DESCRIPTION:Title: Generalised hydrodynamics of the Toda lattice\nby Herbert Spohn (TU Munich) as part of One world IAMP mathematical physics seminar\n\nAbs tract: TBA\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/40/ END:VEVENT BEGIN:VEVENT SUMMARY:Simone Warzel (TU Munich) DTSTART;VALUE=DATE-TIME:20210309T140000Z DTEND;VALUE=DATE-TIME:20210309T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/41 DESCRIPTION:Title: An invitation to quantum spin glasses\nby Simone Warzel (TU Mun ich) as part of One world IAMP mathematical physics seminar\n\n\nAbstract\ nQuantum spin glass models of mean-field type are prototypes of quantum sy stems exhibiting phase transitions related to the spead of the eigenstates in configuration space. \nOriginally motivated by spin glass physics\, t hey are discussed in relation to many-body localisation phenomena\, quantu m adiabatic algorithms as well as in the context of models in mathematical biology. \nQuantum effects transform the rich phase diagram of classical spin glasses as described by Parisi’s theory into an even more colourful landscape of phases which range from purely quantum paramagnetic to inter mediate behavior in which eigenstates occupy only a fraction of configurat ion space.\n\nIn this talk\, I will give an introduction to the multifacet ed motivations and challenges behind the study of these quantum glasses an d explain existing and expected results.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/41/ END:VEVENT BEGIN:VEVENT SUMMARY:Wojciech De Roeck (KU Leuven) DTSTART;VALUE=DATE-TIME:20210413T140000Z DTEND;VALUE=DATE-TIME:20210413T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/42 DESCRIPTION:Title: Impurities and boundaries for a class of gapped ground states\n by Wojciech De Roeck (KU Leuven) as part of One world IAMP mathematical ph ysics seminar\n\n\nAbstract\nIn the last two decades\, a lot of rigorous r esults have been proven for quantum ground states protected by a spectral gap in their Hamiltonian. Think for example of decay of correlations\, the topological classification of states\, and area laws of entanglement.\nFo r all of those results\, the spectral gap is a necessary input\, both on t he conceptual and on the technical level. \nImagine now that we consider s uch a gapped Hamiltonian that is perturbed locally by a term that is not s mall\, such that we certainly cannot hope to preserve the global gap. Comm on sense dictates that\, far away from the perturbation\, the ground state should not be seriously affected by this perturbation. \nWhile we cannot prove this in the generality in which it should be true\, I will describe some results that go in this direction.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/42/ END:VEVENT BEGIN:VEVENT SUMMARY:Eric Carlen (Rutgers University) DTSTART;VALUE=DATE-TIME:20210420T140000Z DTEND;VALUE=DATE-TIME:20210420T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/43 DESCRIPTION:Title: Kac Master Equations\, Classical and Quantum\nby Eric Carlen (R utgers University) as part of One world IAMP mathematical physics seminar\ n\n\nAbstract\nThis lecture will review recent progress and open problems concerning Kac Master Equations in both the classical and quantum setting. It will be based largely on recent papers written in collaboration with M aria Carvalho\, Michael Loss and Bernt Wennberg.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/43/ END:VEVENT BEGIN:VEVENT SUMMARY:Bernard Helffer (Paris-Sud / Nantes) DTSTART;VALUE=DATE-TIME:20210406T140000Z DTEND;VALUE=DATE-TIME:20210406T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/44 DESCRIPTION:Title: Semiclassical methods and tunneling effects: old and new\nby Be rnard Helffer (Paris-Sud / Nantes) as part of One world IAMP mathematical physics seminar\n\n\nAbstract\nIn 1982-1983 the so-called symmetric doubl e well problem was rigorously analyzed in any dimension in the semi-classi cal context by B. Simon and Helffer-Sjöstrand.\nThis involves semi-clas sical Agmon estimates\, Harmonic approximation\, WKB constructions and a v ery fine analysis of the so-called tunneling effect in order to establish the splitting between the lowest eigenvalues.\n\nThe strategy followed by Helffer-Sjöstrand appears to be quite efficient in many other contexts. After recalling how it works on the initial double well problem\,\nwe will discuss in a rather impressionist way the main successes of the approach along the years.\nFinally we will focus on a quite recent result by Bonna illie-Hérau-Raymond devoted to the measure of a magnetic tunneling in Sur face Superconductivity and discuss open problems.\n\nThe presented results correspond to contributions by various subsets of the following set of au thors : Bonnaillie\, Fournais\, Helffer\, Hérau\, Kachmar\, Morame\, Nier \,\nRaymond\, Simon\, Sjöstrand and many others...\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/44/ END:VEVENT BEGIN:VEVENT SUMMARY:Sabine Jansen (LMU Munich) DTSTART;VALUE=DATE-TIME:20210427T140000Z DTEND;VALUE=DATE-TIME:20210427T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/45 DESCRIPTION:Title: Virial expansion for mixtures: some examples & recent results\n by Sabine Jansen (LMU Munich) as part of One world IAMP mathematical physi cs seminar\n\n\nAbstract\nMayer's expansion is an expansion of the pressur e in powers of the activity (fugacity) in equilibrium statistical mechanic s\; the virial expansion is an expansion in powers of the density. Rigorou s convergence results have been available for decades\, nevertheless for m ixtures the theory of density expansions is less advanced than the theory of activity expansions. I will review the setting\, and discuss some recen t results for the virial expansion for mixtures (multi-species systems) an d illustrate them with three concrete models: mixtures of hard spheres of different sizes\, non-overlapping rods of different lengths\, and a hierar chical mixture of cubes in $Z^d$. The last two examples are helpful toy mo dels for which concrete formulas are available and phase transitions can b e studied. Based in part on joint works with Tobias Kuna\, Stephen Tate\, Dimitrios Tsagkarogiannis and Daniel Ueltschi.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/45/ END:VEVENT BEGIN:VEVENT SUMMARY:David Brydges (University of British Columbia) DTSTART;VALUE=DATE-TIME:20210511T140000Z DTEND;VALUE=DATE-TIME:20210511T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/46 DESCRIPTION:Title: Lace expansions and spin models\nby David Brydges (University o f British Columbia) as part of One world IAMP mathematical physics seminar \n\n\nAbstract\nI will review lace expansions starting with their\nrelatio n to the other expansions in statistical mechanics and then\ndiscussing th eir application to spin models. Akira Sakai opened\nthis avenue in 2007 wi th his proof that in sufficiently high dimension\n$d$ the two point functi on for the critical Ising model is asymptotic\nto $c_d |x-y|^{-(d-2)}$. I n arxiv.org/abs/1905.09605 Tyler\nHelmuth\, Mark Holmes and I have introduced a different way to deri ve\nlace expansions based on the Symanzik random walk representation.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/46/ END:VEVENT BEGIN:VEVENT SUMMARY:Marcel Griesemer (University of Stuttgart) DTSTART;VALUE=DATE-TIME:20210518T140000Z DTEND;VALUE=DATE-TIME:20210518T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/47 DESCRIPTION:Title: From Short-Range to Contact Interactions in Many-Body Quantum Syste ms\nby Marcel Griesemer (University of Stuttgart) as part of One world IAMP mathematical physics seminar\n\n\nAbstract\nMany-body quantum system s with short-ranged two-body interactions\, such as ultracold quantum gase s are often described by simplified models with contact interactions (some times called delta-potentials). The merit of such models is their simplici ty\, solvability (to some extent) and lack of irrelevant or unknown detail . They are also toy models of renormalization. On the other hand\, in dime nsions $d\\geq 2$ contact interactions are not small perturbations of the free energy\, which makes their self adjoint implementation in the case of $N>2$ particles a subtle business. This talk gives an introduction to the mathematics of many-particle quantum systems with two-body contact intera ctions and their approximation by Schrödinger operators.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/47/ END:VEVENT BEGIN:VEVENT SUMMARY:Constanza Rojas-Molina (Cergy Paris University) DTSTART;VALUE=DATE-TIME:20210525T140000Z DTEND;VALUE=DATE-TIME:20210525T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/48 DESCRIPTION:Title: Fractional random Schrödinger operators\, integrated density of st ates and localization\nby Constanza Rojas-Molina (Cergy Paris Universi ty) as part of One world IAMP mathematical physics seminar\n\n\nAbstract\n We will review some recent results on the fractional Anderson model\, a ra ndom Schrödinger operator driven by a fractional laplacian. The interest of the latter lies in its association to stable Levy processes\, random wa lks with long jumps and anomalous diffusion. We discuss the interplay betw een the non-locality of the fractional laplacian and the localization prop erties of the random potential in the fractional Anderson model\, in both the continuous and discrete settings. In the discrete setting we study the integrated density of states and show a fractional version of Lifshitz ta ils. This coincides with results obtained in the continuous setting by the probability community. This talk is based on joint work with M. Gebert (L MU Munich).\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/48/ END:VEVENT BEGIN:VEVENT SUMMARY:Chris Fewster (University of York) DTSTART;VALUE=DATE-TIME:20210504T140000Z DTEND;VALUE=DATE-TIME:20210504T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/49 DESCRIPTION:Title: Measurement of quantum fields in curved spacetimes\nby Chris Fe wster (University of York) as part of One world IAMP mathematical physics seminar\n\n\nAbstract\nA standard account of the measurement chain in quan tum mechanics involves a probe (itself a quantum system) coupled temporari ly to the system of interest. Once the coupling is removed\, the probe is measured and the results are interpreted as the measurement of a system ob servable. Measurement schemes of this type have been studied extensively i n Quantum Measurement Theory\, but they are rarely discussed in the contex t of quantum fields and still less on curved spacetimes. \n\nIn this talk I will describe how measurement schemes may be formulated for quantum fiel ds on curved spacetime within the general setting of algebraic QFT. In par ticular\, I will show how measurements of probe observables correspond to measurements of "induced" local system observables and describe the role o f state update rules. The framework is local and fully covariant\, allowin g the consistent description of measurements made in spacelike separated r egions. Furthermore\, specific models can be given in which the framework may be exemplified by concrete calculations. I will also explain how this framework can shed light on an old problem due to Sorkin concerning "impos sible measurements" in which measurement apparently conflicts with causali ty. Finally\, I will discuss new results indicating that the system observ ables that can be induced by measurement schemes form a large subspace of the algebra of all local observables.\n\nThe talk is based on work with Ra iner Verch [Leipzig]\, (Comm. Math. Phys. 378\, 851–889(2020)\, arXiv:18 10.06512\; see also arXiv:1904.06944 for a summary)\, with Henning Bostelm ann and Maximilian Ruep [York] ( Phys. Rev. D 103 (2021) 025017\; arXiv:20 03.04660) and work in progress with Ian Jubb [Dublin] and Maximilian Ruep. \n LOCATION:https://researchseminars.org/talk/IAMP_seminars/49/ END:VEVENT BEGIN:VEVENT SUMMARY:Benjamin Schlein (University of Zürich) DTSTART;VALUE=DATE-TIME:20210601T140000Z DTEND;VALUE=DATE-TIME:20210601T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/50 DESCRIPTION:Title: Correlation energy of weakly interacting Fermi gases\nby Benjam in Schlein (University of Zürich) as part of One world IAMP mathematical physics seminar\n\n\nAbstract\nWe consider Fermi gases in a mean-field reg ime. To leading order\, the ground state energy is given by Hartree-Fock t heory. The correction to the Hartree-Fock energy\, produced by the many-bo dy interaction\, is known as correlation energy. In this talk\, we obtain a formula for the correlation energy\, based on the observation that\, ene rgetically\, the main excitations of the Fermi sea are particle-hole pairs that behave\, approximately\, as bosons and can therefore be dealt with t hrough (bosonic) Bogoliubov theory. The talk is based on joint works with N. Benedikter\, P.T. Nam\, M. Porta and R. Seiringer.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/50/ END:VEVENT BEGIN:VEVENT SUMMARY:Laszlo Erdös (IST Austria) DTSTART;VALUE=DATE-TIME:20210608T140000Z DTEND;VALUE=DATE-TIME:20210608T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/51 DESCRIPTION:Title: Eigenstate thermalisation hypothesis and Gaussian fluctuations for Wigner matrices\nby Laszlo Erdös (IST Austria) as part of One world I AMP mathematical physics seminar\n\n\nAbstract\nWe prove that any determi nistic matrix is approximately\nthe identity in the eigenbasis of a large random Wigner matrix W\nwith an optimal error inversely proportional to th e square root of the dimension.\nThis verifies a strong form of Quantum U nique Ergodicity \nwith an optimal convergence rate and we also prove Gaus sian fluctuations\naround this convergence.\nThe key technical tool is a n ew multi-resolvent local law for Wigner\nensemble and the Dyson Brownian m otion for eigenvector overlaps.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/51/ END:VEVENT BEGIN:VEVENT SUMMARY:Gordon Slade (UBC Vancouver) DTSTART;VALUE=DATE-TIME:20210615T140000Z DTEND;VALUE=DATE-TIME:20210615T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/52 DESCRIPTION:Title: Mean-field tricritical polymers\nby Gordon Slade (UBC Vancouver ) as part of One world IAMP mathematical physics seminar\n\n\nAbstract\nWe provide a full description of a tricritical phase diagram in the setting of a mean-field random walk model of a polymer density transition. The mod el involves a continuous-time random walk on the complete graph in the lim it as the number of vertices N in the graph grows to infinity. The walk ha s a repulsive self-interaction\, as well as a competing attractive self-in teraction whose strength is controlled by a parameter g. A chemical potent ial ν controls the walk length. We determine the phase diagram in the (g\ ,ν) plane\, as a model of a density transition for a single linear polyme r chain. The proof uses a supersymmetric representation for the random wal k model\, followed by a single block-spin renormalisation group step to re duce the problem to a 1-dimensional integral\, followed by application of the Laplace method for an integral with a large parameter. The talk is bas ed on joint work with Roland Bauerschmidt\, Probability and Mathematical P hysics 1\, 167-204 (2020)\; arXiv:1911.00395 .\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/52/ END:VEVENT BEGIN:VEVENT SUMMARY:Clément Tauber (University of Strasbourg) DTSTART;VALUE=DATE-TIME:20210622T140000Z DTEND;VALUE=DATE-TIME:20210622T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/53 DESCRIPTION:Title: Topological indices for shallow-water waves\nby Clément Tauber (University of Strasbourg) as part of One world IAMP mathematical physics seminar\n\n\nAbstract\nIn this talk\, I will apply tools from topological insulators to a fluid dynamics problem: the rotating shallow-water wave m odel with odd viscosity. The bulk-edge correspondence explains the presenc e of remarkably stable waves propagating towards the east along the equato r and observed in some Earth oceanic layers. The odd viscous term is a sma ll-scale regularization that provides a well defined Chern number for this continuous model where momentum space is unbounded. Equatorial waves then appear as interface modes between two hemispheres with a different topolo gy. However\, in presence of a sharp boundary there is a surprising mismat ch in the bulk-edge correspondence: the number of edge modes depends on th e boundary condition. I will explain the origin of such a mismatch using s cattering theory and Levinson’s theorem. This talk is based on a series of joint works with Pierre Delplace\, Antoine Venaille\, Gian Michele Graf and Hansueli Jud.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/53/ END:VEVENT BEGIN:VEVENT SUMMARY:Mathieu Lewin (Paris Dauphine University) DTSTART;VALUE=DATE-TIME:20210629T140000Z DTEND;VALUE=DATE-TIME:20210629T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/54 DESCRIPTION:Title: Density Functional Theory: some recent results\nby Mathieu Lewi n (Paris Dauphine University) as part of One world IAMP mathematical physi cs seminar\n\n\nAbstract\nThe quantum electrons in an atom or a molecule a re in principle described by the Schrödinger multi-particle linear equati on. Unfortunately\, in most cases it is essentially impossible to find a s ufficiently precise numerical approximation of the solution\, due to the v ery high dimensionality of the problem. It is absolutely necessary to reso rt to approximate models\, most of which being nonlinear. Density Function al Theory (DFT) is probably the most successful and widely used method in Chemistry and Physics. In this talk I will explain what DFT is and outline its mathematical formulation. I will then describe some recent results ob tained in collaboration with Elliott H. Lieb (Princeton) and Robert Seirin ger (IST Austria).\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/54/ END:VEVENT BEGIN:VEVENT SUMMARY:Nikolaos Zygouras (University of Warwick) DTSTART;VALUE=DATE-TIME:20210706T140000Z DTEND;VALUE=DATE-TIME:20210706T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/55 DESCRIPTION:Title: On the 2d-KPZ\nby Nikolaos Zygouras (University of Warwick) as part of One world IAMP mathematical physics seminar\n\n\nAbstract\nThe Kar dar-Parisi-Zhang (KPZ) equation in dimension 1 is by now fairly well under stood\, both in terms of its solution theory and its phenomenology. But in the critical dimension 2\, the first steps of progress have only recentl y been made\, which shows signs of a rich structure. In particular\, a pha se transition is observed when the noise is suitably scaled. Below the cri tical scaling\, the 2d KPZ coincides with the Edwards-Wilkinson universali ty\, while at the critical scaling and beyond\, its behaviour is still mys terious. We will review joint works with F. Caravenna and R. Sun as well a s contributions by other groups\, and expose some of the tools used\, incl uding (discrete) stochastic analysis\, renewal theory\, and mathematical p hysics ideas from the study of disorder relevance and Schrodinger operator s with point interactions.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/55/ END:VEVENT BEGIN:VEVENT SUMMARY:Mark Malamud (Peoples Friendship University of Russia\, Moscow) DTSTART;VALUE=DATE-TIME:20210713T140000Z DTEND;VALUE=DATE-TIME:20210713T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/56 DESCRIPTION:Title: On the spectral theory of Schrodinger and Dirac operators with poin t interactions and quantum graphs\nby Mark Malamud (Peoples Friendship University of Russia\, Moscow) as part of One world IAMP mathematical phy sics seminar\n\n\nAbstract\nModern concepts of extension theory of symmetr ic operators\, including concepts of boundary triples\, corresponding Weyl functions\, and boundary operators will be discussed. Applications to Sch rodinger and Dirac operators with point interactions\, as well as to quant um graphs\, will be demonstrated. It turns out that certain spectral prope rties of each of these operators (deficiency indices\, selfadjointness\, d iscreteness\, lower semiboundedness\, etc) strictly correlate to that of a special difference operator. In the first two cases the corresponding dif ference operator is generated by a special Jacobi matrix. This matrix appe ars as a boundary operator of the corresponding Schrodinger and Dirac real ization in an appropriate boundary triple. In the case of quantum graphs a similar role is played by a certain weighted discrete Laplacian on the un derlying discrete graph\, which also appears as a boundary operator.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/56/ END:VEVENT BEGIN:VEVENT SUMMARY:Phan Thành Nam (LMU Munich) DTSTART;VALUE=DATE-TIME:20210720T140000Z DTEND;VALUE=DATE-TIME:20210720T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/57 DESCRIPTION:Title: Bogoliubov excitation spectrum of dilute trapped Bose gases\nby Phan Thành Nam (LMU Munich) as part of One world IAMP mathematical physi cs seminar\n\n\nAbstract\nIn 1947\, Bogoliubov proposed an approximation f or the low-lying eigenvalues of weakly interacting Bose gases and used tha t to explain Landau’s criterion for superfluidity. We will discuss a rig orous derivation of Bogoliubov’s approximation for a general trapped Bos e gas in the Gross-Pitaevskii regime\, where the two-body scattering proce ss of particles leads to an interesting nonlinear effect. The talk is base d on joint work with Arnaud Triay.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/57/ END:VEVENT BEGIN:VEVENT SUMMARY:Eveliina Peltola (University of Bonn) DTSTART;VALUE=DATE-TIME:20210727T140000Z DTEND;VALUE=DATE-TIME:20210727T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/58 DESCRIPTION:Title: On large deviations of SLEs\, real rational functions\, and zeta-re gularized determinants of Laplacians\nby Eveliina Peltola (University of Bonn) as part of One world IAMP mathematical physics seminar\n\n\nAbstr act\nWhen studying large deviations (LDP) of Schramm-Loewner evolution (SL E) curves\,\nwe recently introduced a ''Loewner potential'' that describes the rate function for the LDP.\nThis object turned out to have several in trinsic\, and perhaps surprising\, connections to various fields.\nFor ins tance\, it has a simple expression in terms of zeta-regularized determinan ts of Laplace-Beltrami operators.\nOn the other hand\, minima of the Loewn er potential solve a nonlinear first order PDE that arises\nin a semiclass ical limit of certain correlation functions in conformal field theory\,\na rguably also related to isomonodromic systems.\nFinally\, and perhaps most interestingly\, the Loewner potential minimizers classify\nrational funct ions with real critical points\, thereby providing a novel proof for\na ve rsion of the now well-known Shapiro-Shapiro conjecture in real enumerative geometry.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/58/ END:VEVENT BEGIN:VEVENT SUMMARY:Antti Knowles (University of Geneva) DTSTART;VALUE=DATE-TIME:20210831T140000Z DTEND;VALUE=DATE-TIME:20210831T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/59 DESCRIPTION:Title: The Euclidean phi^4_2 theory as a limit of an interacting Bose gas< /a>\nby Antti Knowles (University of Geneva) as part of One world IAMP mat hematical physics seminar\n\n\nAbstract\nLocal Euclidean field theories ov er d-dimensional space have been extensively studied in the mathematical l iterature since the sixties\, motivated by high-energy physics and statist ical mechanics. For d=2\, I explain how the complex scalar field theory wi th quartic interaction arises as a limit of an interacting Bose gas at pos itive temperature\, when the density of the gas becomes large and the rang e of the interaction becomes small. The proof is based on a quantitative a nalysis of a new functional integral representation of the interacting Bos e gas combined with a Nelson-type argument for a general nonlocal field th eory. Joint work with Jürg Fröhlich\, Benjamin Schlein\, and Vedran Sohi nger.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/59/ END:VEVENT BEGIN:VEVENT SUMMARY:Pierre Germain (New York University) DTSTART;VALUE=DATE-TIME:20210907T140000Z DTEND;VALUE=DATE-TIME:20210907T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/60 DESCRIPTION:Title: Derivation of the kinetic wave equation\nby Pierre Germain (New York University) as part of One world IAMP mathematical physics seminar\n \n\nAbstract\nThe kinetic wave equation (KWE) is to nonlinear waves what t he Boltzmann equation is to classical particles. The KWE is also very clos ely related to quantum versions of the Boltzmann equation. Finally\, the K WE provides an entrypoint into turbulent phenomena\, since it is aimed at describing weakly turbulent flows. For all these reasons\, the KWE is an i nteresting object\, and the question of its validity a fundamental one. I will review recent progress on this question.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/60/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniela Cadamuro (University of Leipzig) DTSTART;VALUE=DATE-TIME:20210810T140000Z DTEND;VALUE=DATE-TIME:20210810T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/61 DESCRIPTION:Title: Operator-algebraic construction of quantum integrable models with b ound states\nby Daniela Cadamuro (University of Leipzig) as part of On e world IAMP mathematical physics seminar\n\n\nAbstract\nThe rigorous cons truction of quantum field theories with self-interaction is one of the lon gstanding problems of Mathematical Physics. Progress in this respect has b een made in integrable field theories in 1+1 spacetime dimensions. These a re characterized by a factorizing scattering matrix\, where two-particle i nteraction determines scattering completely.\n\nSpecifically\, some of the se theories (so-called scalar models without bound states) have been succe ssfully treated in the operator-algebraic approach\, which is based on qua ntum fields localized in infinitely extended wedge regions. The existence of strictly localized observables is then obtained by abstract W*-algebrai c arguments. This avoids dealing with the functional analytic properties o f pointlike interacting fields\, which are difficult to control due to the convergence problem of the infinite series of their form factors.\n\nIn e xtension of these results\, we consider S-matrices with poles in the physi cal strip (corresponding to the notion of `bound states’ in the quantum mechanical sense). We exhibit wedge-local fields in these models\, which arise as a deformation of those in the non-boundstate models by an additiv e term\, the so called ``bound state operator''. This technique applies to a variety of theories\, e.g.\, the Bullough-Dodd model\, the Z(N)-Ising m odel\, the affine Toda field theories and the Sine-Gordon model. The link between these wedge-local fields and strictly local operator algebras is s ubject to ongoing research.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/61/ END:VEVENT BEGIN:VEVENT SUMMARY:Ron Peled (Tel Aviv University) DTSTART;VALUE=DATE-TIME:20210824T140000Z DTEND;VALUE=DATE-TIME:20210824T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/62 DESCRIPTION:Title: Quantitative estimates for the effect of disorder on low-dimensiona l lattice systems\nby Ron Peled (Tel Aviv University) as part of One w orld IAMP mathematical physics seminar\n\n\nAbstract\nThe addition of an a rbitrarily weak random field to low-dimensional classical statistical phys ics models leads to the "rounding" of first-order phase transitions at all temperatures\, as predicted in 1975 by Imry and Ma and proved rigorously in 1989 by Aizenman and Wehr. This phenomenon was recently quantified for the two-dimensional random-field Ising model (RFIM)\, proving that it exhi bits exponential decay of correlations at all temperatures and all positiv e random-field strengths. The talk will present new results on the quantit ative aspects of the phenomenon for general systems with discrete and cont inuous symmetries\, including Potts\, spin $O(n)$ and spin glass models. T he discussion is further extended to real- and integer-valued height funct ion models driven by a random field\, for which we study the fluctuations of the gradient and height variables. Among the challenges presented by th e latter setup is a conjectured roughening transition in the random-field strength for the three-dimensional integer-valued random-field Gaussian fr ee field.\nJoint work with Paul Dario and Matan Harel.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/62/ END:VEVENT BEGIN:VEVENT SUMMARY:Sasha Sodin (Queen Mary University London) DTSTART;VALUE=DATE-TIME:20210817T140000Z DTEND;VALUE=DATE-TIME:20210817T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/63 DESCRIPTION:Title: Lower bounds on the eigenfunctions of random Schroedinger operators in a strip\nby Sasha Sodin (Queen Mary University London) as part of One world IAMP mathematical physics seminar\n\n\nAbstract\nIt is known tha t the eigenfunctions of a random Schroedinger\noperator in a strip decay e xponentially. In some regimes\, the same is\ntrue in higher dimensions. It is however not clear whether the\neigenfunctions have an exact rate of ex ponential decay. In the strip\,\nit is natural to expect that the rate sho uld be given by the slowest\nLyapunov exponent\, however\, only the upper bound has been previously\nestablished.\n\nWe shall discuss some recent pr ogress on this problem\, and its\nconnection to a question\, perhaps inter esting in its own right\, in the\ntheory of random matrix products. Based on joint work with Ilya\nGoldsheid.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/63/ END:VEVENT BEGIN:VEVENT SUMMARY:Yvan Velenik (Université\; de Genè\;ve) DTSTART;VALUE=DATE-TIME:20210914T140000Z DTEND;VALUE=DATE-TIME:20210914T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/64 DESCRIPTION:Title: Fluctuations of a layer of unstable phase in the planar Ising model \nby Yvan Velenik (Université\; de Genè\;ve) as part of On e world IAMP mathematical physics seminar\n\n\nAbstract\nI'll first review some of the known results about phase separation\, fluctuations of interf aces and (equilibrium) aspects of metastability in the planar Ising model. This will naturally lead us to consider a setup in which an interface sep arates a layer of unstable phase along the boundary of the system from the stable phase occupying the bulk. I'll then describe a recent work\, in wh ich we prove that\, after a 1/3:2/3 scaling\, the distribution of this int erface weakly converges to the distribution of the stationary trajectories of an explicit Ferrari-Spohn diffusion. The proof relies on a rigorous re duction to an effective interface model\, which I'll briefly sketch.\n\nTh is is based on a joint work with Dima Ioffe\, Sébastien Ott and Senya Shl osman\; arXiv:2011.11997 .\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/64/ END:VEVENT BEGIN:VEVENT SUMMARY:Rostyslav Hryniv (Ukrainian Catholic University) DTSTART;VALUE=DATE-TIME:20210928T140000Z DTEND;VALUE=DATE-TIME:20210928T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/65 DESCRIPTION:Title: Generalized soliton solutions of the Korteweg-de Vries equation \nby Rostyslav Hryniv (Ukrainian Catholic University) as part of One world IAMP mathematical physics seminar\n\n\nAbstract\nThe Korteweg--de Vries ( KdV) equation is a non-linear dispersive equation describing shallow-water waves and possessing many intriguing properties. One of them is existence of the so-called soliton solutions representing solitary waves travelling with constant speed and shape\, as well as a special way in which several such solitons interact. Another interesting fact is that solutions of the KdV equation can be obtained as solutions of the inverse scattering probl em for the family of associated Schroedinger operators\, as discovered by S.Gardner\, J.Green\, M.Kruskal and R.Miura in 1967\, and the classical so liton solutions of the KdV correspond precisely to the so-called reflectio nless potentials (I.Kay and H.Moses\, 1956).\n\nThe aim of this talk is tw o-fold. Firstly\, we characterise the family of all Schroedinger operators with integrable reflectionless potentials and give an explicit formula pr oducing all such potentials. Secondly\, we use the inverse scattering tran sform approach to describe all solutions of the KdV equation whose initial (t=0) profile is an integrable reflectionless potential. Such solutions w ill stay integrable and reflectionless for all positive times and can be c alled generalized soliton solutions of KdV. \n\nThis research extends and specifies in several ways the previous work on reflectionless potentials by V.Marchenko\, C.Remling et al. and generalized soliton solutions of the KdV equation introduced by V.Marchenko in 1991 and F.Gesztesy\, W.Karwows ki\, and Z.Zhao in 1992. The talk is based on a joint project with B.Melny k and Ya.Mykytyuk (Lviv Franko National University).\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/65/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Loss (Georgia Institute of Technology) DTSTART;VALUE=DATE-TIME:20211005T140000Z DTEND;VALUE=DATE-TIME:20211005T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/66 DESCRIPTION:Title: Which magnetic fields support a zero mode?\nby Michael Loss (Ge orgia Institute of Technology) as part of One world IAMP mathematical phys ics seminar\n\n\nAbstract\nI present some results concerning the size of m agnetic fields that support zero modes for the three dimensional Dirac equ ation and related problems for spinor equations. The critical quantity\, i s the $3/2$ norm of the magnetic field $B$. The point is that the spinor s tructure enters the analysis in a crucial way. This is joint work with Rup ert Frank at LMU Munich.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/66/ END:VEVENT BEGIN:VEVENT SUMMARY:Rupert L. Frank (California Institute of Technology and LMU Munich ) DTSTART;VALUE=DATE-TIME:20211019T140000Z DTEND;VALUE=DATE-TIME:20211019T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/67 DESCRIPTION:Title: Eigenvalue bounds for Schrodinger operators with complex potentials \nby Rupert L. Frank (California Institute of Technology and LMU Munic h) as part of One world IAMP mathematical physics seminar\n\n\nAbstract\nW e discuss open problems and recent progress concerning eigenvalues of Schr odinger operators with complex potentials. We seek bounds for individual e igenvalues or sums of them which depend on the potential only through some L^p norm. While the analogues of these questions are (almost) completely understood for real potentials\, the complex case leads to completely new phenomena\, which are related to interesting questions in harmonic and com plex analysis.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/67/ END:VEVENT BEGIN:VEVENT SUMMARY:Klaus Fredenhagen (Universität Hamburg) DTSTART;VALUE=DATE-TIME:20210921T140000Z DTEND;VALUE=DATE-TIME:20210921T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/68 DESCRIPTION:Title: Towards an algebraic construction of Quantum Field Theory\nby K laus Fredenhagen (Universität Hamburg) as part of One world IAMP mathemat ical physics seminar\n\n\nAbstract\nAlgebraic quantum field theory provide s a conceptual and mathematically precise framework for the analysis of st ructural features of quantum field theory.\nDuring the last decades\, it h as in addition provided a generalization of quantum field theory to generi c Lorentzian spacetimes\, and\, moreover\, an elegant reformulation of ren ormalized perturbative quantum field theory. The principles used there act ually determine also a C*-algebraic formulation which is surprisingly rich and leads to some nonperturbative results.\nIn particular\, the time slic e axiom can be derived\, a version of Noether's theorem is obtained\, and the renormalization group flow caused by anomalies becomes visible in the algebraic structure. The talk is based on joint work with Detlev Buchholz (2020) and on joint work with Romeo Brunetti\, Michael Dütsch and Kasia R ejzner (2021).\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/68/ END:VEVENT BEGIN:VEVENT SUMMARY:Paweł Nurowski (Polish Academy of Sciences\, Warsaw) DTSTART;VALUE=DATE-TIME:20211116T140000Z DTEND;VALUE=DATE-TIME:20211116T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/69 DESCRIPTION:Title: Split real form of Lie group G2: simple\, exceptional and naturally appearing in physics\nby Paweł Nurowski (Polish Academy of Sciences\ , Warsaw) as part of One world IAMP mathematical physics seminar\n\n\nAbst ract\nA simple exceptional Lie group G2 was predicted to exist by Wilhelm Killing in 1887. Its geometric realization appeared later\, in 1893\; it i s due to Friedrich Engel and Elie Cartan. They realized this group as a sy mmetry group of two quite different geometric structures on five manifolds . \nIn my talk I will try to explain how the idea of these G2 symmetric ge ometric structures could came to minds of Cartan and Engel. My explanation will be based on properties of the root diagram of G2. I will keep my lec ture self contained\, so I will define the G2 root diagram and will explai n how to use it. After nailing down the two 5-dimensional G2 -symmetric ge ometries of Cartan and Engel\, I will show how they appear naturally in co nstrained classical mechanics.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/69/ END:VEVENT BEGIN:VEVENT SUMMARY:Christophe Garban (Université Lyon 1) DTSTART;VALUE=DATE-TIME:20211012T140000Z DTEND;VALUE=DATE-TIME:20211012T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/70 DESCRIPTION:Title: Continuous symmetry breaking along the Nishimori line\nby Chris tophe Garban (Université Lyon 1) as part of One world IAMP mathematical p hysics seminar\n\n\nAbstract\nI will discuss a new way to prove continuous symmetry breaking for (classical) spin systems on Z^d\, d\\geq 3 which do es not rely on "reflection positivity". \nOur method applies to models wh ose spins take values in S^1\, SU(n) or SO(n) in the presence of a certain quenched disorder called the Nishimori line. The proof of continuous symm etry breaking is based on two ingredients

\n1) the notion of "group sy nchronization" in Bayesian statistics. In particular a recent result by Ab be\, Massoulié\, Montanari\, Sly and Srivastava (2018) which proves group synchronization when d\\geq 3.

\n2) a gauge transformation on both th e disorder and the spin configurations due to Nishimori (1981).

\nI wi ll end the talk with an application of these techniques to a deconfining t ransition for U(1) lattice gauge theory on the Nishimori line. \nThis is a joint work with Tom Spencer (https://arxiv.org/abs/2109.01617).\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/70/ END:VEVENT BEGIN:VEVENT SUMMARY:Tomaž Prosen (University of Ljubljana) DTSTART;VALUE=DATE-TIME:20211026T140000Z DTEND;VALUE=DATE-TIME:20211026T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/71 DESCRIPTION:Title: Random Matrix Spectral Fluctuations in Quantum Lattice Systems\ nby Tomaž Prosen (University of Ljubljana) as part of One world IAMP math ematical physics seminar\n\n\nAbstract\nI will discuss the problem of unre asonable effectiveness of random matrix theory for description of spectral fluctuations in extended quantum lattice systems. A class of interacting spin systems has been recently identified - specifically\, the so-called d ual unitary circuits - where the spectral form factor is proven to match w ith circular ensembles of random matrix theory. The key ideas of novel met hodology needed in the proofs will be discussed which are very different t han the standard periodic-orbit based methods in quantum chaos of few body semiclassical systems.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/71/ END:VEVENT BEGIN:VEVENT SUMMARY:Lea Bossmann (IST Austria) DTSTART;VALUE=DATE-TIME:20211102T140000Z DTEND;VALUE=DATE-TIME:20211102T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/72 DESCRIPTION:Title: Asymptotic expansion of low-energy excitations for weakly interacti ng bosons\nby Lea Bossmann (IST Austria) as part of One world IAMP mat hematical physics seminar\n\n\nAbstract\nWe consider a system of N bosons in the mean-field scaling regime in an external trapping potential. We der ive an asymptotic expansion of the low-energy eigenstates and the correspo nding energies\, which provides corrections to Bogoliubov theory to any or der in 1/N. We show that the structure of the ground state and of the non- degenerate low-energy eigenstates is preserved by the dynamics if the exte rnal trap is switched off. This talk is based on joint works with Sören P etrat\, Peter Pickl\, Robert Seiringer and Avy Soffer.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/72/ END:VEVENT BEGIN:VEVENT SUMMARY:Gaultier Lambert (University of Zurich) DTSTART;VALUE=DATE-TIME:20211109T140000Z DTEND;VALUE=DATE-TIME:20211109T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/73 DESCRIPTION:Title: Universality for free fermions point processes\nby Gaultier Lam bert (University of Zurich) as part of One world IAMP mathematical physics seminar\n\n\nAbstract\nI report on recent results obtained with A. Delepo rte on universality of local statistics for the ground state of a free Fer mi gas confined in a generic potential on ℝ^n. This model was introduced by Macchi in 1975 and it forms a determinantal point process whose kernel is the spectral projector associated to a Schrödinger operator −ℏ^2 Δ+V. I will explain how to obtain the asymptotics of the kernel of this p rojector as ℏ→0 using methods from semiclassical analysis and discuss some probabilistic consequences. In particular\, this implies universality of microscopic fluctuations\, both in the bulk and around regular boundar y points.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/73/ END:VEVENT BEGIN:VEVENT SUMMARY:Julian Sonner (University of Geneva) DTSTART;VALUE=DATE-TIME:20211123T140000Z DTEND;VALUE=DATE-TIME:20211123T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/74 DESCRIPTION:Title: Random matrices and black holes: new connections from holographic d uality\nby Julian Sonner (University of Geneva) as part of One world I AMP mathematical physics seminar\n\n\nAbstract\nQuantum chaotic systems ar e often defined via the assertion that their spectral statistics coincides with\, or is well approximated by\, random matrix theory (RMT). In turn\, the late-time ergodic behaviour of chaotic quantum systems is expected to fall into a small number of universality classes of RMT dynamics. Recent developments in holographic duality have made it possible to characterise the ergodic late-time behaviour of black holes in asymptotically anti de S itter space in similar terms. In this talk I will start by introducing the basic ideas and notions of holographic duality (also known as AdS/CFT)\, before moving on to these more recent developments\, mostly focussing on l ow-dimensional examples.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/74/ END:VEVENT BEGIN:VEVENT SUMMARY:Niklas Beisert (ETH Zurich) DTSTART;VALUE=DATE-TIME:20211130T140000Z DTEND;VALUE=DATE-TIME:20211130T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/75 DESCRIPTION:Title: Planar Integrability and Yangian Symmetry in N=4 Supersymmetric Yan g–Mills\nby Niklas Beisert (ETH Zurich) as part of One world IAMP ma thematical physics seminar\n\n\nAbstract\nThe discovery and utilisation of integrability in the planar limit of certain gauge and string theory mode ls has made available many exciting non-perturbative results and insights for the AdS/CFT correspondence. In this talk I will introduce the prototyp ical AdS/CFT duality between string theory on AdS₅×S⁵ and N=4 supersy mmetric Yang–Mills theory\, and highlight the usefulness of planar integ rability through some achievements. I will then present a formal notion of integrability as a hidden Yangian symmetry of the action. Importantly\, t his symmetry is realised on field theory objects in a non-standard fashion for which a rigorous framework to deal with its implications is lacking. I will demonstrate that this symmetry indeed leads to non-trivial relation s for quantum correlations functions of this model. In order to make them work out\, I also show in what sense the symmetry is compatible with BRST gauge fixing.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/75/ END:VEVENT BEGIN:VEVENT SUMMARY:Nina Holden (ETH Zurich) DTSTART;VALUE=DATE-TIME:20211207T140000Z DTEND;VALUE=DATE-TIME:20211207T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/76 DESCRIPTION:Title: Conformal welding in Liouville quantum gravity: recent results and applications\nby Nina Holden (ETH Zurich) as part of One world IAMP ma thematical physics seminar\n\n\nAbstract\nLiouville quantum gravity (LQG) is a natural model for a random fractal surface with origins in conformal field theory and string theory. A powerful tool in the study of LQG is con formal welding\, where multiple LQG surfaces are combined into a single LQ G surface. The interfaces between the original LQG surfaces are typically described by variants of the random fractal curves known as Schramm-Loewne r evolutions (SLE). We will present a few recent conformal welding results for LQG surfaces and applications to the integrability of SLE and LQG par tition functions. Based on joint work with Ang and Sun and with Lehmkuehle r.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/76/ END:VEVENT BEGIN:VEVENT SUMMARY:Nicolai Reshetikhin (University of California\, Berkeley) DTSTART;VALUE=DATE-TIME:20211214T140000Z DTEND;VALUE=DATE-TIME:20211214T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/77 DESCRIPTION:Title: On the asymptotic behavior of character measures in large tensor po wers of finite dimensional representations of simple Lie algebras\nby Nicolai Reshetikhin (University of California\, Berkeley) as part of One w orld IAMP mathematical physics seminar\n\n\nAbstract\nLet $V$ be a finite dimensional representation of a simple Lie algebra and $H$ be an positive element of its Cartan subalgebra ("magnetic field"). On the space $V^{\\ot imes N}$ we have a natural density matrix $N\\exp(-H)$ where $H$ acts diag onally: $H(x\\otimes y\\otimes z\\dots)=Hx\\otimes y\\otimes z\\dots+x\\ot imes Hy\\otimes z\\dots+x\\otimes y\\otimes Hz\\dots+\\dots$. The space $V ^{\\otimes N}$ decomposes into a direct\nsum of irreducible subrepresentat ions:\n\\[\nV^{\\otimes N}\\simeq \\oplus_{\\lambda} V_\\lambda^{\\oplus m (\\lambda\, N)}\n\\]\nwhere $\\lambda$ is the highest weight of the repres entation $V_\\lambda$ and $m(\\lambda\, N)$\nis its multiplicity in the te nsor product. The character distribution assigns the probability \n\\[\np_ {\\lambda}(N\,H)=\\frac{m(\\lambda\, N)Tr_{V_\\lambda}(e^{-H)})}{(Tr_V(e^{ -H}))^N}\n\\]\nto each $\\lambda$ in the decomposition of the tensor produ ct.\n\nOne of the natural problems for this distribution is to find its as ymptotic \nin the limit $N\\to \\infty$ and $\\lambda\\to \\infty$ in the appropriate way.\nWhen $H=0$ the character distribution becomes a uniform distribution.\nIn this case\, in such generality the asymptotic was studi ed by Ph. Biane\, 1993 by T. Tate and S. Zelditch\, 2004. For tensor power s of vector representations the asymptotic was derived by S. Kerov in 1986 . When $H$ is generic\, i.e. when $H$ is strictly inside of the principal Weyl chamber\nit was computed by O.Postnova and N.R. in 2018. This talk is based on a joint work with O. Postnova and V. Serganova (to appear on the arxiv).\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/77/ END:VEVENT BEGIN:VEVENT SUMMARY:Claudio Dappiaggi (Università\; di Pavia) DTSTART;VALUE=DATE-TIME:20220111T140000Z DTEND;VALUE=DATE-TIME:20220111T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/78 DESCRIPTION:Title: Stochastic Partial Differential Equations and Renormalization à la Epstein-Glaser\nby Claudio Dappiaggi (Università\; di Pavia) as part of One world IAMP mathematical physics seminar\n\n\nAbstract\nWe pre sent a novel framework for the study of a large class of nonlinear stochas tic partial differential equations\, which is inspired by the algebraic ap proach to quantum\nfield theory. The main merit is that\, by realizing ran dom fields within a suitable algebra of functional-valued distributions\, we are able to use specific techniques proper of microlocal\nanalysis. The se allow us to deal with renormalization using an Epstein-Glaser perspecti ve\, hence without resorting to any specific regularization scheme. As a concrete example we shall use this method to discuss the stochastic $\\Phi ^3_d$ model and we shall comment on its applicability to the stochastic no nlinear Schrödinger equation -- Joint work with Nicolò Drago\, Paolo Rin aldi and Lorenzo Zambotti.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/78/ END:VEVENT BEGIN:VEVENT SUMMARY:Marcin Lis (University of Vienna) DTSTART;VALUE=DATE-TIME:20220118T140000Z DTEND;VALUE=DATE-TIME:20220118T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/79 DESCRIPTION:Title: An elementary proof of phase transition in the planar XY model\ nby Marcin Lis (University of Vienna) as part of One world IAMP mathematic al physics seminar\n\n\nAbstract\nUsing elementary methods we obtain a pow er-law lower bound on the two-point function of the planar XY spin model a t low temperatures. This was famously first rigorously obtained by Fröhli ch and Spencer and establishes a Berezinskii-Kosterlitz-Thouless phase tra nsition in the model. Our argument relies on a new loop representation of spin correlations\, a recent result of Lammers on delocalisation of intege r-valued height functions\, and classical correlation inequalities. This i s joint work with Diederik van Engelenburg.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/79/ END:VEVENT BEGIN:VEVENT SUMMARY:Christoph Schweigert (Universität Hamburg) DTSTART;VALUE=DATE-TIME:20211221T140000Z DTEND;VALUE=DATE-TIME:20211221T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/80 DESCRIPTION:Title: More about CFT correlators\nby Christoph Schweigert (Universit ät Hamburg) as part of One world IAMP mathematical physics seminar\n\n\nA bstract\nI will explain two recent developments concerning bulk fields in\ ntwo-dimensional rational conformal field theories: the importance of\nthe relative Serre functor to study bulk fields for logarithmic\nconformal fi eld theories and the use of stringnet techniques to\nsimplify the construc tion of correlators for semisimple modular\ntensor categories.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/80/ END:VEVENT BEGIN:VEVENT SUMMARY:Vojkan Jaksic (McGill University) DTSTART;VALUE=DATE-TIME:20220322T140000Z DTEND;VALUE=DATE-TIME:20220322T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/81 DESCRIPTION:Title: Approach to equilibrium in translation-invariant quantum systems: s ome structural results\nby Vojkan Jaksic (McGill University) as part o f One world IAMP mathematical physics seminar\n\n\nAbstract\nWe formulate the problem of approach to equilibrium in algebraic quantum statistical me chanics and study some of its structural aspects\, focusing on the relatio n between the zeroth law of thermodynamics (approach to equilibrium) and t he second law (increase of entropy). Our main result is that approach to e quilibrium is necessarily accompanied by a strict increase of the specific (mean) entropy. In the course of our analysis\, we introduce the concept of quantum weak Gibbs state which is of independent interest.\n\nThis is a joint work with C. Tauber and C.-A. Pillet\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/81/ END:VEVENT BEGIN:VEVENT SUMMARY:Michele Schiavina (ETH Zürich) DTSTART;VALUE=DATE-TIME:20220125T140000Z DTEND;VALUE=DATE-TIME:20220125T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/83 DESCRIPTION:Title: Ruelle Zeta Function from Field Theory\nby Michele Schiavina (E TH Zürich) as part of One world IAMP mathematical physics seminar\n\n\nAb stract\nI will discuss a field-theoretic interpretation of Ruelle's zeta f unction\, which "counts" prime geodesics on hyperbolic manifolds\, as the partition function for a topological field theory (BF) with an unusual gau ge fixing condition available on contact manifolds. This suggests a rephra sing of a conjecture due to Fried\, on the equivalence between Ruelle's ze ta function (at zero) and the analytic torsion\, as gauge-fixing independe nce in the Batalin--Vilkovisky formalism.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/83/ END:VEVENT BEGIN:VEVENT SUMMARY:Daisuke Shiraishi (Kyoto University) DTSTART;VALUE=DATE-TIME:20220201T140000Z DTEND;VALUE=DATE-TIME:20220201T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/84 DESCRIPTION:Title: Recent progress on loop-erased random walk in three dimensions\ nby Daisuke Shiraishi (Kyoto University) as part of One world IAMP mathema tical physics seminar\n\n\nAbstract\nLoop-erased random walk (LERW) is a m odel for a random simple path\, which is created by running a simple rando m walk and\, whenever the random walk hits its path\, removing the resulti ng loop and continuing. LERW was originally introduced by Greg Lawler in 1 980. Since then\, it has been studied extensively both in mathematics and physics literature. Indeed\,\nLERW has a strong connection with other mode ls in statistical physics\, especially the uniform spanning tree which ari ses in statistical physics in conjunction with the Potts model. In this ta lk\, I will talk about some recent progress on LERW while focusing on the three-dimensional case. This is joint work with Xinyi Li.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/84/ END:VEVENT BEGIN:VEVENT SUMMARY:Makiko Sasada (University of Tokyo) DTSTART;VALUE=DATE-TIME:20220308T140000Z DTEND;VALUE=DATE-TIME:20220308T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/85 DESCRIPTION:Title: Topological structures and the role of symmetry in the hydrodynamic limit of nongradient models\nby Makiko Sasada (University of Tokyo) a s part of One world IAMP mathematical physics seminar\n\n\nAbstract\nRecen tly\, we introduce a general framework in order to systematically investig ate hydrodynamics limits of various microscopic stochastic large scale int eracting systems in a unified fashion. In particular\, we introduced a new cohomology theory called the uniformly cohomology to investigate the unde rlying topological structure of the interacting system. Our theory gives a new interpretation of the macroscopic parameters\, the role played by the group action on the microscopic system\, and the origin of the diffusion matrix associated to the macroscopic hydrodynamic equation. Furthermore\, we rigorously formulate and prove for a relatively general class of models Varadhan’s decomposition of closed forms\, which plays a key role in th e proof of hydrodynamic limits of nongradient models. Our result is applic able for many important models including generalized exclusion processes\, multi-species exclusion processes\, exclusion processes on crystal lattic es and so on. Based on joint papers with Kenichi Bannai and Yukio Kametani \n(https://arxiv.org/abs/2009.04699\, https://arxiv.org/abs/2111.0893 4).\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/85/ END:VEVENT BEGIN:VEVENT SUMMARY:Serena Cenatiempo (GSSI L'Aquila) DTSTART;VALUE=DATE-TIME:20220329T140000Z DTEND;VALUE=DATE-TIME:20220329T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/86 DESCRIPTION:Title: Trial states for the zero temperature dilute Bose gas\nby Seren a Cenatiempo (GSSI L'Aquila) as part of One world IAMP mathematical physic s seminar\n\n\nAbstract\nNon-relativistic interacting bosons at zero tempe rature\, in two and three dimensions\, are expected to exhibit a fascinati ng critical phase\, famously known as condensate phase. Even though a proo f of Bose-Einstein condensation in the thermodynamic limit is still beyond reach of the current available methods\, the mathematical physics communi ty has recently gained an enhanced comprehension of other aspects of the m acroscopic behavior of low temperature Bose gases\, in several interesting regimes. In this talk we review part of these advances\, by describing tr ial states for the dilute three dimensional Bose gas\, capturing the celeb rated Lee-Huang-Yang sub-leading correction to the ground state energy. We conclude with some open questions and perspectives.\n\nBased on joint wor ks with G. Basti\, C. Boccato\, C. Brennecke\, C. Caraci\, A. Olgiati\, G. Pasqualetti and B. Schlein.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/86/ END:VEVENT BEGIN:VEVENT SUMMARY:Jerzy Lewandowski (University of Warsaw) DTSTART;VALUE=DATE-TIME:20220315T140000Z DTEND;VALUE=DATE-TIME:20220315T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/87 DESCRIPTION:Title: Horizon equations\nby Jerzy Lewandowski (University of Warsaw) as part of One world IAMP mathematical physics seminar\n\n\nAbstract\nThe extremity assumptions imposes a set of non-trivial equations on the\nintri nsic and extrinsic geometry of the horizon. Some of them already\ngot more attention since they are applied in the near horizon geometries\n(NHG)\, some other are less know. All of them are very important for the\nexistenc e and uniqueness of extremal black hole solutions to Einstein's\nequations . In 4d spacetime\, an integrability condition for the NHG\nequation is av ailable that is satisfied by the family of non-extremal\nhorizon geometrie s\, namely by those that are of the Petrov type D. What\nis special about that equation\, is that its solutions exhibit similar\nproperties to those proved in the global black hole spacetime theory:\nspherical topology of horizon cross sections\, rigidity\, no-hair.\n\nExtension of the research to the horizons that had a Hopf bundle\nstructure led to interesting resul ts about the global structure of the\nKerr-NUT-(A)dS spaces. Misner's co nstruction was generalised to the\ncase when none of the three parameters (NUT\, Kerr\, and the cosmological\nconstant) vanishes. The resulting fami ly contains also exact solutions\nto Einstein's equations that admit no ho rizon or nowhere time like\nKilling vector and describe a topologically s pherical universe evolving\nfrom the past scry to the future scry in a non -singular manner.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/87/ END:VEVENT BEGIN:VEVENT SUMMARY:Martin Zirnbauer (University of Cologne) DTSTART;VALUE=DATE-TIME:20220215T140000Z DTEND;VALUE=DATE-TIME:20220215T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/88 DESCRIPTION:Title: Field theory of Anderson transitions reviewed: Color-Flavor Transfo rmation\nby Martin Zirnbauer (University of Cologne) as part of One wo rld IAMP mathematical physics seminar\n\n\nAbstract\nThis talk is in two p arts. First\, the field-theoretic approach to (de-)localization in Anderso n-type models for disordered electrons is reviewed\, with emphasis placed on the presence of a hyperbolic target-space sector and the expected patte rn of spontaneous symmetry breaking. The second part is a review of the "C olor-Flavor (CF) Transformation" (MZ\, 1996). Conceived as a variant of th e Efetov-Wegner supersymmetry method\, the CF Transformation is tailored t o quantum systems with disorder distributed according to Haar measure for any compact Lie group of classical type (A\, B\, C\, or D). It has been ap plied to Dyson's Circular Ensembles\, random-link network models\, quantum chaotic graphs\, disordered Floquet dynamics\, and more. It is reviewed h ere as a rigorous tool to derive the effective field theory for systems in the metallic regime.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/88/ END:VEVENT BEGIN:VEVENT SUMMARY:Erik Skibsted (Aarhus University) DTSTART;VALUE=DATE-TIME:20220208T140000Z DTEND;VALUE=DATE-TIME:20220208T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/89 DESCRIPTION:Title: Stationary scattering theory\, the N-body long-range case\nby E rik Skibsted (Aarhus University) as part of One world IAMP mathematical ph ysics seminar\n\n\nAbstract\nWithin the class of Dereziński-Enss pair-pot entials which includes Coulomb potentials and for which asymptotic complet eness is known\, we show that all entries of the N-body quantum scattering matrix have a well-defined meaning at any given non-threshold energy. As a function of the energy parameter the scattering matrix is weakly continu ous. This result generalizes a similar one obtained previously by Yafaev f or systems of particles interacting by short-range potentials. As for Yafa ev’s works we do not make any assumption on the decay of channel eigenst ates. The main part of the proof consists in establishing a number of Kato -smoothness bounds needed for justifying a new formula for the scattering matrix. Similarly we construct and show strong continuity of channel wave matrices for all non-threshold energies. The set of so-called stationary c omplete energies has full measure. We show that the scattering and channel wave matrices constitute a well-defined ‘scattering theory’ at such e nergies\, in particular at any stationary complete energy the scattering m atrix is unitary\, strongly continuous and characterized by asymptotics of minimum generalized eigenfunctions.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/89/ END:VEVENT BEGIN:VEVENT SUMMARY:Marek Biskup (UCLA) DTSTART;VALUE=DATE-TIME:20220301T140000Z DTEND;VALUE=DATE-TIME:20220301T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/90 DESCRIPTION:Title: Extremal points of random walks on planar and tree graphs\nby M arek Biskup (UCLA) as part of One world IAMP mathematical physics seminar\ n\n\nAbstract\nI will review recent progress on the description of points heavily visited by paths of random walks. The focus will be on the situati ons where the random walk has an approximate scale-invariant structure and the associated local time process is thus logarithmically correlated in s pace. Two geometric settings will be considered: the simple random walk on finite subsets of the square lattice and the random walk on homogeneous t rees of finite depth. In the former case\, a full description will be give n of the scaling limit of thick\, thin and avoided points for the walk run up to the times proportional to the cover time. For the latter setting\, the law of the most frequently visited leaf-vertex\, and the time spent th ere\, will be given in the limit of the tree depth tending to infinity. In both cases\, the spatial laws will be determined by a corresponding multi plicative chaos measure. Based on joint papers with Y. Abe\, S. Lee and O. Louidor.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/90/ END:VEVENT BEGIN:VEVENT SUMMARY:Lorenzo Taggi (Sapienza Università di Roma) DTSTART;VALUE=DATE-TIME:20220222T140000Z DTEND;VALUE=DATE-TIME:20220222T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/91 DESCRIPTION:Title: Macroscopic loops in the interacting Bose gas\, Spin O(N) and relat ed models\nby Lorenzo Taggi (Sapienza Università di Roma) as part of One world IAMP mathematical physics seminar\n\n\nAbstract\nWe consider a g eneral system of interacting random loops which includes several models of interest\, such as the spin O(N) model\, the double dimer model\, random lattice permutations\, and is related to the loop O(N) model and to the in teracting Bose gas in discrete space. We present an overview on these mode ls\, introduce some of the main open questions about the size and the geom etry of the loops\, and present some recent results about the occurrence o f macroscopic loops in dimensions d > 2 as the inverse temperature is larg e enough.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/91/ END:VEVENT BEGIN:VEVENT SUMMARY:Edward Witten (IAS) DTSTART;VALUE=DATE-TIME:20220412T140000Z DTEND;VALUE=DATE-TIME:20220412T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/92 DESCRIPTION:Title: Black Hole Entropies and Algebras\nby Edward Witten (IAS) as pa rt of One world IAMP mathematical physics seminar\n\n\nAbstract\nI will re view the idea of black hole entropy\, as originally discovered by Bekenste in and Hawking roughly half a century ago\, and then explain how to interp ret black hole entropy in terms of an appropriate algebra of observables.\ n LOCATION:https://researchseminars.org/talk/IAMP_seminars/92/ END:VEVENT BEGIN:VEVENT SUMMARY:Deepak Dhar (IISER Pune) DTSTART;VALUE=DATE-TIME:20220426T140000Z DTEND;VALUE=DATE-TIME:20220426T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/93 DESCRIPTION:Title: Hard rigid rods on hypercubical lattices\nby Deepak Dhar (IISER Pune) as part of One world IAMP mathematical physics seminar\n\n\nAbstrac t\nI consider a system of hard rigid rods of length $k$ and width $1$\, o n $d$-dimensional hypercubic lattices. \nI will show that in the limit of large $k$\, the entropy per site at full packing $ s(d\,k)$ for $d=2$ s atisfies \n$$ \\lim_{k \\rightarrow \\infty} \\frac { s(d\,k) k^2}{\\log k} =1\, $$\nand give heuristic arguments that this result would be true also for all dimensions $d>2.$\n\nIf $k$ is large enough ($ k> 6 $ in $2 $-d\, and $k>4$ in $3$-d)\, this model is known to undergo two phase tra nsitions when chemical potential is increased: from a low density isotropi c phase to an intermediate density nematic phase\, and on further increas e to a high-density phase with no orientational order. I will present ev idence to suport the conjecture that\, for large $k$\, the second phase t ransition is a first order transition with a discontinuity in density as a function of the chemical potential\, in all dimensions greater than 1\, and if the chemical potential per rod at the transition is $\\mu^*(k\,d)$\ , and the density of holes jumps from a value $\\epsilon_1(k\,d)$ to $\\e psilon_2(k\,d)$\, we have for all $d \\geq 2$\n$$\\lim_{ k \\rightarrow \ \infty} \\frac{ \\epsilon_1(d\, k) k^2}{\\log k} =1\,$$\n$$\\lim_{k \\righ tarrow \\infty} \\frac{ \\exp\\left[ \\frac{\\mu^*(d\, k)}{k} \\right] \\l og k}{k} =1\,$$\n$$\\lim_{k \\rightarrow \\infty} \\frac{\\epsilon_2(d\, k) k ^m}{\\epsilon_1(d\,k)} =0\, ~{\\rm for~ all}~m>0.$$\n\nReferences: D eepak Dhar and R. Rajesh\, Phys. Rev. E 103\, 042130 (2021)\;\n Aagam Shah \, D. Dhar and R. Rajesh\, Phys. Rev. E. 105\, 034103 (2022).\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/93/ END:VEVENT BEGIN:VEVENT SUMMARY:Wojciech Dybalski (Adam Mickiewicz University) DTSTART;VALUE=DATE-TIME:20220517T140000Z DTEND;VALUE=DATE-TIME:20220517T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/94 DESCRIPTION:Title: Interacting massless excitations in 1+1 dimensional QFT\nby Woj ciech Dybalski (Adam Mickiewicz University) as part of One world IAMP math ematical physics seminar\n\n\nAbstract\nMassless 1+1 dimensional quantum f ield theories have a peculiar\nscattering theory. Since the motion of the excitations is dispersionless\, \nonly the distinction between left-movers and right-movers is meaningful. \nThus complete particle interpretation ( asymptotic completeness) can be expected already at the level of two-body scattering. This effect will be illustrated by certain wedge-local models of interacting Wigner particles. In the second part of the talk I will mov e to the more exotic case of infraparticles\, i.e.\, excitations which are not of Wigner type. It is known that infraparticles abound in 1+1 massles s QFT\, even in the familiar case of free field theory. A natural definiti on of a scattering amplitude for infraparticles will be proposed and teste d in this latter model. Paradoxically\, infraparticles in free field theor y exhibit non-trivial scattering. \n\nThe talk is based on joint works wit h Yoh Tanimoto (CMP 305\, 427-440 (2011)) and Jens Mund (arXiv:2109.02128) .\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/94/ END:VEVENT BEGIN:VEVENT SUMMARY:Vieri Mastropietro (University of Milan) DTSTART;VALUE=DATE-TIME:20220510T140000Z DTEND;VALUE=DATE-TIME:20220510T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/95 DESCRIPTION:Title: Anomalies and non-perturbative QFT\nby Vieri Mastropietro (Univ ersity of Milan) as part of One world IAMP mathematical physics seminar\n\ n\nAbstract\nAdler and Bardeen in 1969 established the non-renormalization of the chiral anomaly\, writing it as a perturbative expansion which is o rder by order vanishing\; since then\, this property has found uncountable applications\, including the Standard Model consistence via the anomaly c ancellation condition (Bouchiat\, Iliopoulos\, Meyer 1972). After reviewi ng briefly this notion\, we prove the anomaly non renormalization at a non -perturbative level in the case of lattice vector boson-fermion models in d=1+1 (uniformly in the lattice) and in d=3+1 (up to a cut-off of the orde r of the inverse coupling). The proof relies on bounds on the large distan ce decay of correlations and Ward Identities\, both exact and emerging. In the case of chiral models\, like the effective electroweak theory with qu artic Fermi interaction in d=3+1\, some Ward Identites are violated and th e anomaly can be proved to vanish up to subdominant corrections which are rigorously bounded\, under the cancellation condition on charges and with a cut-off of the order of the inverse coupling. Open problems and conjectu res will be finally discussed.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/95/ END:VEVENT BEGIN:VEVENT SUMMARY:Chiara Saffirio (University of Basel) DTSTART;VALUE=DATE-TIME:20220621T140000Z DTEND;VALUE=DATE-TIME:20220621T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/96 DESCRIPTION:Title: Mean-field evolution and semiclassical limit of many interacting fe rmions\nby Chiara Saffirio (University of Basel) as part of One world IAMP mathematical physics seminar\n\n\nAbstract\nWe will review recent pro gresses in the derivation of effective evolution equations for the dynamic s of many weakly interacting fermions. We will focus on the mean-field reg ime and couple it with a semiclassical limit to obtain\, as the number of particles goes to infinity\, the Hartree-Fock and the Vlasov equations. We will comment on the class of singular interactions and quantum states tha t we are able to treat\, drawing a comparison with the PDE theory of the l imiting equations.\nBased on joint works with J. Chong and L. Laflèche.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/96/ END:VEVENT BEGIN:VEVENT SUMMARY:Benjamin Doyon (King's College London) DTSTART;VALUE=DATE-TIME:20220531T140000Z DTEND;VALUE=DATE-TIME:20220531T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/98 DESCRIPTION:Title: Ergodicity\, large-scale correlations and hydrodynamics in many-bod y systems\nby Benjamin Doyon (King's College London) as part of One wo rld IAMP mathematical physics seminar\n\n\nAbstract\nLong-time behaviours in statistical ensembles of many-body systems are notoriously difficult to access. Hydrodynamics\, which is the theory for the emergent large-scale dynamics\, gives a lot of information\, such as exact asymptotics of corre lation functions. It turns out that at the Euler scale\, the emergent theo ry for extended systems is largely universal. I will discuss a number of s uch universal results in one dimension of space. Some can be shown rigorou sly: a notion of ergodicity at all frequencies hold for correlation functi ons in stationary states of all short-range quantum spin chains. The Boltz mann-Gibbs principle\, where local observables project onto hydrodynamic m odes in two-point functions\, and the linearised Euler equations\, are als o established. The complete space of hydrodynamic modes is the space of `` extensive conserved quantities”\, which is defined unambiguously. I will illustrate these concepts in integrable systems\, using generalised hydro dynamics. For correlations in non-stationary states\, much less is establi shed. I will describe a macroscopic fluctuation theory for the Euler scale which provides a framework for these. In particular\, I will explain how a new type of long-range correlations\, hitherto not observed\, appear whe n the system is subject to fluid motion\, which breaks the paradigm that s eparate fluid cells are not correlated.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/98/ END:VEVENT BEGIN:VEVENT SUMMARY:Owen Gwilliam (University of Massachusetts Amherst) DTSTART;VALUE=DATE-TIME:20220628T140000Z DTEND;VALUE=DATE-TIME:20220628T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/99 DESCRIPTION:Title: Observables in the Batalin-Vilkovisky formalism: from Feynman diagr ams to commutative diagrams\nby Owen Gwilliam (University of Massachus etts Amherst) as part of One world IAMP mathematical physics seminar\n\n\n Abstract\nThis talk will discuss a convergence between perturbative QFT an d higher algebra\, in the sense of homological algebra\, operads\, and hig her categories\, although we do not expect the listener to have any expert ise in those topics. A key notion here is a factorization algebra\, which captures the local-to-global nature of the observables of a field theory a nd which is due to Beilinson and Drinfeld. With a focus on the example of Chern-Simons theory\, we will discuss how the BV/factorization package off ers a new view on the emergence of algebraic structures\, like braided mon oidal categories\, from physics.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/99/ END:VEVENT BEGIN:VEVENT SUMMARY:Michele Correggi (Politecnico di Milano) DTSTART;VALUE=DATE-TIME:20220705T140000Z DTEND;VALUE=DATE-TIME:20220705T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/100 DESCRIPTION:Title: Ground State Properties in the Quasi-Classical Regime\nby Mich ele Correggi (Politecnico di Milano) as part of One world IAMP mathematica l physics seminar\n\n\nAbstract\nWe study the ground state energy and grou nd states of systems coupling non-relativistic quantum particles and force -carrying Bose fields\, such as radiation\, in the quasi-classical approxi mation. The latter is very useful whenever the force-carrying field has a very large number of excitations\, and thus behaves in a semiclassical way \, while the non-relativistic particles\, on the other hand\, retain their microscopic features. We prove that the ground state energy of the fully microscopic model converges to the one of a nonlinear quasi classical func tional depending on both the particles' wave function and the classical co nfiguration of the field. Equivalently\, this energy can be interpreted as the lowest energy of a Pekar-like functional with an effective nonlinear interaction for the particles only. If the particles are confined\, the gr ound state of the microscopic system converges as well\, to a probability measure concentrated on the set of minimizers of the quasi classical energ y.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/100/ END:VEVENT BEGIN:VEVENT SUMMARY:Kevin Costello (Perimeter Institute) DTSTART;VALUE=DATE-TIME:20220524T140000Z DTEND;VALUE=DATE-TIME:20220524T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/101 DESCRIPTION:Title: Form factors of gauge theory as correlators of a vertex algebra\nby Kevin Costello (Perimeter Institute) as part of One world IAMP mathe matical physics seminar\n\n\nAbstract\nForm factors are scattering amplitu des in the presence of a local operator. I will explain that\, for certain gauge groups\, form factors of self-dual Yang-Mills theory (with some add itional fields) are the correlators of a vertex algebra. This is joint wor k with Natalie Paquette\, and is closely related to the celestial holograp hy program.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/101/ END:VEVENT BEGIN:VEVENT SUMMARY:Hirosi Ooguri (Caltech & Kavli IPMU) DTSTART;VALUE=DATE-TIME:20220419T140000Z DTEND;VALUE=DATE-TIME:20220419T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/102 DESCRIPTION:Title: Symmetry in QFT and Gravity\nby Hirosi Ooguri (Caltech & Kavli IPMU) as part of One world IAMP mathematical physics seminar\n\n\nAbstrac t\nI will review aspects of symmetry in quantum field theory and combine t hem with the AdS/CFT correspondence to derive constraints on symmetry in q uantum gravity. The quantum gravity constraints to be discussed include th e no-go theorem on global symmetry\, the completeness of gauge charges\, a nd the decomposition of high energy states into gauge group representation s.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/102/ END:VEVENT BEGIN:VEVENT SUMMARY:Jacob Shapiro (Princeton) DTSTART;VALUE=DATE-TIME:20220405T140000Z DTEND;VALUE=DATE-TIME:20220405T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/103 DESCRIPTION:Title: Continuum and strongly disordered topological insulators\nby J acob Shapiro (Princeton) as part of One world IAMP mathematical physics se minar\n\n\nAbstract\nA natural question to ask in the field of topological insulators is whether continuum descriptions on L^2(R^d) and effective di screte descriptions on l^2(Z^d) agree\, at the level of the long time dyna mics and at the level of the topological indices. This is shown to be the case at least for a class of models of the integer quantum Hall effect. Th e basic tool to approach the problem is homotopies of Fredholm operators. This same tool is also shown to apply to other problems in topological ins ulators\, such as the bulk-edge correspondence for Z_2 time-reversal invar iant strongly disordered discrete systems. This talk is based on joint wor ks with Michael I. Weinstein and with Jeff Schenker and Alex Bols.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/103/ END:VEVENT BEGIN:VEVENT SUMMARY:Stefan Teufel (University of Tübingen) DTSTART;VALUE=DATE-TIME:20220712T140000Z DTEND;VALUE=DATE-TIME:20220712T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/104 DESCRIPTION:Title: A slightly different look at the bulk-edge correspondence in quant um Hall systems\nby Stefan Teufel (University of Tübingen) as part of One world IAMP mathematical physics seminar\n\n\nAbstract\nThe bulk-edge correspondence of transport coefficients in quantum Hall systems is usuall y shown for systems with a (mobility) gap in the bulk and at zero temperat ure. I will present recent results showing equality of magnetization in th e bulk and edge current in microscopic models without and with interaction between electrons. This equality holds at positive temperature and withou t assuming a (mobility) gap in the bulk\, and is robust to perturbations n ear the edges. I then discuss how the equality of transport coefficients c an be recovered from this form of bulk-edge correspondence\, at least in s ome cases. My talk is based on joint work with Horia Cornean\, Jonas Lampa rt\, Massimo Moscolari\, and Tom Wessel.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/104/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Ueltschi (University of Warwick) DTSTART;VALUE=DATE-TIME:20220503T140000Z DTEND;VALUE=DATE-TIME:20220503T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/105 DESCRIPTION:Title: Random loop models and their universal behaviour in dimension 3+\nby Daniel Ueltschi (University of Warwick) as part of One world IAMP m athematical physics seminar\n\n\nAbstract\nI will discuss several loop sou p models that represent classical or quantum systems\nof statistical physi cs. These systems undergo phase transitions that are characterised\nby the occurrence of macroscopic loops. \n\nAs it turns out\, the joint distribu tion of the loop lengths exhibits a universal behaviour:\nIn 3+ dimension it is always given by a Poisson-Dirichlet distribution. The heuristics\nis based on the fact that the loops are so intertwined that they behave effe ctively in\nmean-field fashion. Hence the connection to the split-merge pr ocess\, whose invariant\nmeasure is Poisson-Dirichlet.\n\nI will also disc uss consequences about symmetry breaking in certain quantum spin\nsystems. \n\nThis talk is based on collaborations over the years with D. Gandolfo\, J. Ruiz\, C. Goldschmidt\,\nP. Windridge\, V. Betz\, S. Grosskinsky\, A. Lovisolo\, C. Benassi\, J. Bjö\;rnberg\,\nJ. Frö\;hlich.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/105/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Aizenman (Princeton) DTSTART;VALUE=DATE-TIME:20220607T140000Z DTEND;VALUE=DATE-TIME:20220607T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/106 DESCRIPTION:Title: A new perspective on a pair of two dimensional phenomena: delocali zation in random height functions and the Berezinskii-Kosterlitz-Thouless phase of O(2) symmetric spin models\nby Michael Aizenman (Princeton) a s part of One world IAMP mathematical physics seminar\n\n\nAbstract\nDeloc alization in integer-restricted Gaussian field\, and other random height f unctions formulated over planar doubly-periodic lattices\, is shown to imp ly slow (power law) decay of correlations in the corresponding dual O(2) s ymmetric two-component spin model. The link proceeds through a lower bound on the spin-spin correlation in terms of the probability of their sites b eing on a common level loop of the dual random height function. Motivated by this observation\, we have extended the recent proof by P. Lammers of delocalization transition in two dimensional graphs of degree three\, to a ll doubly periodic graphs\, in particular to Z^2. The extension is establi shed through a monotonicity argument based on lattice inequalities of O. R egev and N. Stephens-Davidowitz. Taken together the results yield a new p erspective on the BKT phase transition in O(2)-invariant models and comple te a new proof of delocalization in two-dimensional integer-valued height functions. (Both phenomena are unique to two dimension\, and have been pre viously proven and studied by other means). \nThat talk is based on a joi nt work by M. Aizenman\, M. Harel J. Shapiro and R. Peled.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/106/ END:VEVENT BEGIN:VEVENT SUMMARY:Camillo De Lellis (IAS) DTSTART;VALUE=DATE-TIME:20221129T140000Z DTEND;VALUE=DATE-TIME:20221129T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/107 DESCRIPTION:Title: Anomalous dissipation for the forced Navier-Stokes equations\n by Camillo De Lellis (IAS) as part of One world IAMP mathematical physics seminar\n\n\nAbstract\nConsider smooth (or at least Leray) solutions to 3d Navier-Stokes\n\\[\n\\left\\{\n\\begin{array}{ll}\n\\partial_t u^\\vareps ilon + {\\rm div}\\\, (u^\\varepsilon \\otimes u^\\varepsilon ) + \\nabla p^\\varepsilon = \\varepsilon \\Delta u^\\varepsilon\\\\ \\\\\nu^\\varepsi lon (0\, \\cdot) = u^\\varepsilon_0\\\, .\n\\end{array}\\right.\n\\]\nWhil e the balance of the energy is\n\\[\n\\frac{d}{dt} \\frac{1}{2} \\int |u|^ 2 (x\,t)\\\, dx = - \\varepsilon \\int |Du|^2 (x\,t)\\\, dx\\\, \,\n\\]\ni t is a tenet of the theory of fully developed turbulence that in a variety of situations the left hand side should typically be independent of $\\va repsilon$: the mechanism is not supposed to be ignited by high oscillation s in the initial data\, which would trigger an ``immediate'' dissipation t hrough the viscosity\, but it is rather thought to be an effect of the qua dratic nonlinearity. It is on the other hand very challenging to produce r igorous examples. If the bounds on $u_0^\\varepsilon$ are too strong\, the well-posedness theory for Euler obstructs the anomalous dissipation up un til the first blow-up time of Euler. With sufficiently coarse bounds Euler can be shown to have a variety of dissipative solutions\, but it is very difficult to prove the convergence of Navier-Stokes to any of them. \nIn a recent joint work with Elia Bruè we study the forced version of the equ ation and we can prove rigorously that\, as soon as the regularity of the force drops below the known thresholds for the well-posedness of classical Euler\, it is in fact possible to show anomalous dissipation.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/107/ END:VEVENT BEGIN:VEVENT SUMMARY:Karol Kozlowski (ENS Lyon) DTSTART;VALUE=DATE-TIME:20221018T140000Z DTEND;VALUE=DATE-TIME:20221018T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/109 DESCRIPTION:Title: Towards an exact rigorous construction of the Sinh-Gordon quantum field theory in 1+1 dimensions\nby Karol Kozlowski (ENS Lyon) as part of One world IAMP mathematical physics seminar\n\n\nAbstract\nThe bootstra p program was devised in the late 70s/early 80s as a possible path for a f ully explicit construction of numerous massive integrable quantum field th eories in 1+1 dimensions. Ultimately\, it allows one to express the physic ally pertinent observables in these models --- the multi-point correlation functions also called Wightman functions --- in terms of form factor seri es expansion. On technical grounds\, the latter correspond to fully explic it series of multiple integrals in which the $n^{\\rm th}$ summand is give n by a $n$-fold integral. The well definiteness of such a construction amo unts to proving the convergence of these series expansions and this was a basically an open problem.\n\nIn this talk\, I will review the boostrap ap proach to the construction of the Sinh-Gordon quantum field theory. In par ticular\, I will discuss the type of representations one gets for the mult i-point correlation functions in this model. Then\, I will discuss the rec ent progress I achieved on the convergence problem for the form factor ser ies arising in the description of space-like separated two-point functions . The proof of the convergence of amounts to obtaining a sufficiently shar p estimate on the leading large-$n$ behaviour of the $n$-fold integral ari sing in those series. This appeared possible by refining some of the techn iques that were fruitful in the analysis of the large-$n$ behaviour of int egrals over the spectrum of $n\\times n$ random Hermitian matrices.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/109/ END:VEVENT BEGIN:VEVENT SUMMARY:Dorothea Bahns (Georg-August-Universität Göttingen) DTSTART;VALUE=DATE-TIME:20220927T140000Z DTEND;VALUE=DATE-TIME:20220927T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/110 DESCRIPTION:Title: The Sine Gordon Model in hyperbolic signature\nby Dorothea Bah ns (Georg-August-Universität Göttingen) as part of One world IAMP mathem atical physics seminar\n\n\nAbstract\nI will review some recent results in the construction of the Sine Gordon\nmodel in hyperbolic signature in the setting of perturbative algebraic\nquantum field theory. One focus is on the construction of a Haag Kastler\nnet of observables (of operators on a Hilbert space)\, the other will be\nto explain how the adiabatic switching function can be removed in\nexpectation values in thermal states. The met hods presented are a\nmixture of "old and new" in constructive and algebra ic quantum field theory.\n\nThis is joint work with Kasia Rejzner\, Klaus Fredenhagen\, and Nicola\nPinamonti.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/110/ END:VEVENT BEGIN:VEVENT SUMMARY:Slava Rychkov (IHES) DTSTART;VALUE=DATE-TIME:20220920T140000Z DTEND;VALUE=DATE-TIME:20220920T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/111 DESCRIPTION:Title: Tensor Renormalization Group at Low Temperatures\nby Slava Ryc hkov (IHES) as part of One world IAMP mathematical physics seminar\n\n\nAb stract\nTensor RG is a real-space approach to renormalization in lattice m odels. It shows impressive numerical results\, but its rigorous theory is still in its infancy. I will start by reminding the basics of Tensor RG\, and what makes it potentially more powerful than Wilson-Kadanoff approach. I will then explain how Tensor RG can be used to understand the Ising mod el in nonzero magnetic field at low temperatures. This gives an alternativ e to the Pirogov-Sinai theory and to the renormalization group methods in the contour representation from the 1980’s. Joint work with Tom Kennedy\ , to appear soon.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/111/ END:VEVENT BEGIN:VEVENT SUMMARY:Tomohiro Sasamoto (Tokyo Institute of Technology) DTSTART;VALUE=DATE-TIME:20220719T140000Z DTEND;VALUE=DATE-TIME:20220719T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/112 DESCRIPTION:Title: Mapping macroscopic fluctuation theory for the symmetric simple ex clusion process to a classically integrable system\nby Tomohiro Sasamo to (Tokyo Institute of Technology) as part of One world IAMP mathematical physics seminar\n\n\nAbstract\nThe large deviation principle for symmetric simple exclusion process(SEP) had been established by \nKipnis\, Olla\, V aradhan in 1989 [1]. A somewhat different formulation\, known as the macro scopic \nfluctuation theory (MFT)\, was initiated and developed by Jona-La sinio et al in 2000’s [2]. The basic \nequations of the theory\, MFT equ ations\, are coupled nonlinear partial differential equations and \nhave r esisted exact analysis except for stationary situation. In this talk we in troduce a novel \ngeneralization of the Cole-Hopf transformation and show that it maps the MFT equations for SEP \nto the classically integrable Abl owitz-Kaup-Newell-Segur(AKNS) system. This allows us to solve \nthe equati ons exactly in time dependent regime by adapting standard ideas of inverse scattering method. \n\nThe talk is based on a joint work with Kirone Mall ick and Hiroki Moriya [3]. \n\nReferences\n\n[1] C. Kipnis\, S. Olla\, S. R. S. Varadhan\, \nHydrodynamics and large deviations for simple exclusion processes\, Comm. Pure Appl. Math.\, 42:115–137\, 1989.\n\n[2] L. Berti ni\, A. De Sole\, D. Gabrielli\, G. Jona-Lasinio\, and C. Landim\,\nMacros copic fluctuation theory\, Rev. Mod. Phys.\, 87:593–636\, 2015.\n\n[3] K irone Mallick\, Hiroki Moriya\, Tomohiro Sasamoto\,\nExact solution of the macroscopic fluctuation theory for the symmetric exclusion process\,\narX iv: 2202.05213\, to appear in Phys. Rev. Lett.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/112/ END:VEVENT BEGIN:VEVENT SUMMARY:Sohei Ashida (Gakushuin University) DTSTART;VALUE=DATE-TIME:20221025T140000Z DTEND;VALUE=DATE-TIME:20221025T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/113 DESCRIPTION:Title: Mathematics of molecular structures and dynamics\nby Sohei Ash ida (Gakushuin University) as part of One world IAMP mathematical physics seminar\n\n\nAbstract\nI will talk about mathematically rigorous results c oncerned with studies\nof molecules. The subject corresponds to N-body pro blems of the\nSchrödinger equation from the standpoint of mathematics. Fi rst\, we will\nconsider the spectrum and long-time asymptotic behaviors\, focusing on\nscattering matrices of N-body Schrödinger equation. Next we will\nconsider quantitative studies based on the Born-Oppenheimer\napproxi mation. Results related to estimates of electronic energy levels\nsuch as the upper bound of electronic density and results concerned with\nthe Hart ree-Fock equation will be presented.\n\nReferences: [1] Kyushu J.\nMath. 7 5\, 277-294 (2021) (arXiv:2002.07426) [2] Hiroshima Math. J.\, 52\,\n177-2 16 (2022) (arXiv:1811.07527) [3] arXiv:2012.09397 to appear in\nTohoku Mat h. J. [4] arXiv:2112.09521 to appear in Hokkaido Math. J. [5]\narXiv:2205. 10300\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/113/ END:VEVENT BEGIN:VEVENT SUMMARY:Paweł Duch (Adam Mickiewicz University) DTSTART;VALUE=DATE-TIME:20221004T140000Z DTEND;VALUE=DATE-TIME:20221004T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/114 DESCRIPTION:Title: Flow equation approach to singular stochastic PDEs\nby Paweł Duch (Adam Mickiewicz University) as part of One world IAMP mathematical p hysics seminar\n\n\nAbstract\nMost stochastic PDEs arising in physics\, su ch as the KPZ equation describing the motion of a growing interface or the stochastic quantization equation of the $\\Phi^4$ Euclidean QFT\, are ill -posed in the classical analytic sense due to irregular nature of random t erms. Equations of this type are called singular. Regularization and renor malization are usually necessary to give mathematical meaning to such equa tions. In the talk\, I will present a novel technique of solving singular stochastic PDEs. The technique is based on the renormalization group flow equation. It is applicable to a large class of parabolic or elliptic SPDEs with fractional Laplacian\, additive noise and polynomial non-linearity. It covers equations in the whole super-renormalizable regime. A nice featu re of the method is that it avoids the algebraic and combinatorial problem s arising in different approaches. Based on arXiv:2109.11380 and arXiv:220 1.05031.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/114/ END:VEVENT BEGIN:VEVENT SUMMARY:Christoph Kopper (Ecole Polytechnique) DTSTART;VALUE=DATE-TIME:20221011T140000Z DTEND;VALUE=DATE-TIME:20221011T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/115 DESCRIPTION:Title: On asymptotically free scalar fields\nby Christoph Kopper (Eco le Polytechnique) as part of One world IAMP mathematical physics seminar\n \n\nAbstract\nI present recent work (Annales Henri Poincaré 2022) analysi ng the flow equations of the renormalisation group in the mean field appro ximation. There it is shown that these equations for scalar fields in four dimensional euclidean space\, have solutions which are UV asymptotically free. I comment on this result\, also in view of the literature\, in parti cular with regard to the triviality of \\varphi^4_4-theory. We close with an outlook on future perspectives.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/115/ END:VEVENT BEGIN:VEVENT SUMMARY:Jian Ding (Peking University) DTSTART;VALUE=DATE-TIME:20220830T140000Z DTEND;VALUE=DATE-TIME:20220830T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/116 DESCRIPTION:Title: Repeated emergence of 4/3-exponent\nby Jian Ding (Peking Unive rsity) as part of One world IAMP mathematical physics seminar\n\n\nAbstrac t\nIn this talk\, I will describe the emergence of the 4/3-exponent in two seemingly unrelated\nmodels: random distance of Liouville quantum gravity and correlation length for the two-dimensional random field Ising model. I will then explain that such 4/3-exponent\, while being unexpected among respective communities even from a physics perspective\, has in fact been hinted in Leighton-Shor (1989) and Talagrand (2014) where the 4/3-exponent emerges in a random matching problem. Finally\, I will present the heuris tic computation which leads to the emergence of the 4/3-exponent.\n\nWhile I will review related progress on these topics\, the two papers featuring 4/3-exponent are with Subhajit Goswami and with Mateo Wirth.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/116/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Strohmaier (University of Leeds) DTSTART;VALUE=DATE-TIME:20220726T140000Z DTEND;VALUE=DATE-TIME:20220726T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/117 DESCRIPTION:Title: A mathematical analysis of Casimir interactions and determinant fo rmulae\nby Alexander Strohmaier (University of Leeds) as part of One w orld IAMP mathematical physics seminar\n\n\nAbstract\nI will explain a mat hematical treatment of Casimir interactions of perfect conductors in which the Casimir energy is written as the trace of an operator without the nee d for regularisations. I will also show some consequences of this approach \, relations to microlocal analysis\, and will prove a trace formula that allows to compute the Casimir energy in terms of determinants of single la yer operators. Such formulae have been derived by other methods in the phy sics literature and we will show that all these approaches give the same w ell defined Casimir energy.\n\n(Based on joint work with F. Hanisch and A. Waters\, as well as numerical work with T. Betcke and X. Sun).\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/117/ END:VEVENT BEGIN:VEVENT SUMMARY:Giovanni Felder (ETH Zürich) DTSTART;VALUE=DATE-TIME:20221101T140000Z DTEND;VALUE=DATE-TIME:20221101T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/118 DESCRIPTION:Title: Boltzmann's billiard and table tennis\nby Giovanni Felder (ETH Zürich) as part of One world IAMP mathematical physics seminar\n\n\nAbst ract\nIn Boltzmann's billiard a particle moves in a half-plane subject to a central force and is reflected elastically when it hits the boundary. Bo ltzmann took the central force to be the sum of a gravitational inverse-sq uare-law force and a centrifugal term proportional to the\ninverse cube of the distance to the centre. He formulated the expectation that except for special values of the parameters the system would be chaotic and would ob ey his Ergodic Hypothesis. Recently Gallavotti and Jauslin showed that the system is integrable if the\ncentrifugal term is omitted: it has a second conserved quantity besides the energy. I will review this result and show that this integrable Boltzmann system has the Poncelet property: if in a level set of the conserved quantities a trajectory is periodic then all tr ajectories on the level set are periodic. As for the classical Poncelet th eorem on inscribed-circumscribed polygons in Jacobi's interpretation\, the result relies on the theory of elliptic curves. I will also present some work in progress with Misha Feigin on Boltzmann's table tennis\, the three dimensional version of Boltzmann's integrable system\, and the relation t o QRT maps on biquadratic plane curves.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/118/ END:VEVENT BEGIN:VEVENT SUMMARY:Jonathan Dimock (SUNY at Buffalo) DTSTART;VALUE=DATE-TIME:20220816T140000Z DTEND;VALUE=DATE-TIME:20220816T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/119 DESCRIPTION:Title: Ultraviolet Stability for Quantum Electrodynamics in d=3\nby J onathan Dimock (SUNY at Buffalo) as part of One world IAMP mathematical ph ysics seminar\n\n\nAbstract\nWe report on results for quantum electrodynam ics on a finite\nvolume Euclidean spacetime in dimension $d=3$. The theory is formulated as a\nfunctional integral on a fine toroidal lattice involv ing both fermion fields and\nabelian gauge fields. The main result is that \, after renormalization\, the partition\nfunction is bounded uniformly in the lattice spacing. This is a first step toward\nthe construction of the model. The result is obtained by renormalization group\nanalysis pioneere d by Balaban. A single renormalization group transformation\ninvolves bloc k averaging\, a split into large and small field regions\, and an identifi cation of effective actions in the small field regions via cluster expansi ons.\nThis leads to flow equations for the parameters of the theory. Renor malization\nis accomplished by fine-tuning the initial conditions for thes e equations. Large\nfield regions need no renormalization\, but are shown to give a tiny contribution.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/119/ END:VEVENT BEGIN:VEVENT SUMMARY:Martin Fraas (UC Davis) DTSTART;VALUE=DATE-TIME:20220802T140000Z DTEND;VALUE=DATE-TIME:20220802T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/120 DESCRIPTION:Title: Projections\, parallel transport and adiabatic theory\nby Mart in Fraas (UC Davis) as part of One world IAMP mathematical physics seminar \n\n\nAbstract\nI will give an overview of adiabatic theory with the focus on a geometric point of view. The talk will cover traditionally adiabatic theory\, adiabatic theory in many-body systems\, and a recent work with W . De Roeck and A. Elgart on the adiabatic theory for disordered systems.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/120/ END:VEVENT BEGIN:VEVENT SUMMARY:Anton Alekseev (University of Geneva) DTSTART;VALUE=DATE-TIME:20221115T140000Z DTEND;VALUE=DATE-TIME:20221115T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/121 DESCRIPTION:Title: Virasoro Hamiltonian spaces\nby Anton Alekseev (University of Geneva) as part of One world IAMP mathematical physics seminar\n\n\nAbstra ct\nIn this talk\, we consider Hamiltonian actions of the group of diffeom orphisms of the circle. This is a semiclassical countepart of Virasoro alg ebra actions in Conformal Field Theory. The main examples include Virasoro coadjoint orbits (previously studied by Segal\, Kirillov\, Witten and oth ers) and moduli spaces of hyperbolic metrics on surfaces with boundary. Ou r study is motivated by recent progress in Jackiw-Teitelboim quantum gravi ty. In particular\, we give mathematical interpretation of some 2D - 1D du ality phenomena.\n\nThe talk is based on work in progress with Eckhard Mei nrenken.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/121/ END:VEVENT BEGIN:VEVENT SUMMARY:Ivan Avramidi (New Mexico Tech) DTSTART;VALUE=DATE-TIME:20221122T140000Z DTEND;VALUE=DATE-TIME:20221122T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/122 DESCRIPTION:Title: Spectral Asymptotics of Elliptic Operators on Manifolds\nby Iv an Avramidi (New Mexico Tech) as part of One world IAMP mathematical physi cs seminar\n\n\nAbstract\nThe study of spectral properties of natural geom etric elliptic partial differential operators acting on smooth sections of vector bundles over Riemannian manifolds is a central theme in global ana lysis\, differential geometry and mathematical physics. Instead of studyin g the spectrum of a differential operator $L$ directly one usually studies its spectral functions\, that is\, spectral traces of some functions of t he operator\, such as the spectral zeta function $\\zeta(s)=\\Tr L^{-s}$ a nd the heat trace $\\Theta(t)=\\Tr\\exp(-tL)$. The kernel $U(t\;x\,x')$ of the heat semigroup $\\exp(-tL)$\, called the heat kernel\, plays a major role in quantum field theory and quantum gravity\, index theorems\, non-co mmutative geometry\, integrable systems and financial mathematics. We revi ew some recent progress in the study of spectral asymptotics. We study mor e general spectral functions\, such as $\\Tr f(tL)$\, that we call quantum heat traces. Also\, we define new invariants of differential operators th at depend not only on the their eigenvalues but also on the eigenfunctions \, and\, therefore\, contain much more information about the geometry of t he manifold. Furthermore\, we study some new invariants\, such as $\\Tr\\e xp(-tL_+)\\exp(-sL_-)$\, that contain relative spectral information of two differential operators. Finally we show how the convolution of the semigr oups of two different operators can be computed by using purely algebraic methods.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/122/ END:VEVENT BEGIN:VEVENT SUMMARY:Sinya Aoki (YITP\, Kyoto University) DTSTART;VALUE=DATE-TIME:20221213T140000Z DTEND;VALUE=DATE-TIME:20221213T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/123 DESCRIPTION:Title: Lattice QCD: Introduction\, results and challenges\nby Sinya A oki (YITP\, Kyoto University) as part of One world IAMP mathematical physi cs seminar\n\n\nAbstract\nLattice QCD is a non-perturbative definition of QCD (Quantum ChromoDynamics) on a discrete spacetime.\nI first give a comp rehensive review on lattice QCD from the continuum QCD to numerical simul ations.\nAs a representative of lattice QCD investigations\, I introduce h adron mass calculations including an extraction of a hadron mass from the hadron propagator\, its quark mass dependence and its extrapolation to a zero lattice spacing limit. I also present the latest results on hadron spectra including electromagnetic corrections.\nFinally I explain a recent challenge in lattice QCD\, an extraction of hadron interactions such as n uclear forces\, starting from a definition of potentials in QCD to numeric al results on scattering phase shifts.\nThroughout my talk\, I comment on degrees of rigorousness of the lattice QCD method from time to time.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/123/ END:VEVENT BEGIN:VEVENT SUMMARY:Razvan Gurau (Universität Heidelberg) DTSTART;VALUE=DATE-TIME:20221108T140000Z DTEND;VALUE=DATE-TIME:20221108T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/124 DESCRIPTION:Title: Melonic field theories\nby Razvan Gurau (Universität Heidelbe rg) as part of One world IAMP mathematical physics seminar\n\n\nAbstract\n Like random matrices\, random tensors exhibit a 1/N expansion\, but their large N limit is more amenable to analytic computations. In particular ten sor field theories provide a new class of large N theories\, the so called melonic theories. In this talk I will present an overview of recent resul ts on such theories and discuss their implications.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/124/ END:VEVENT BEGIN:VEVENT SUMMARY:John Imbrie (University of Virginia) DTSTART;VALUE=DATE-TIME:20221206T140000Z DTEND;VALUE=DATE-TIME:20221206T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/125 DESCRIPTION:Title: On the Many-Body Localization Transition\nby John Imbrie (Univ ersity of Virginia) as part of One world IAMP mathematical physics seminar \n\n\nAbstract\nA quantum system is said to be many-body localized (MBL) i f it fails\nto thermalize. This can be understood as a consequence of the\ nexistence of an extensive set of local integrals of motion (LIOMs). In\n2 016\, I showed that there is an MBL phase by constructing LIOMs at\nstrong disorder (the proof depended on a certain assumption on level\nstatistics ). The nature of the transition out of the MBL phase has\nbeen a subject o f study and conjecture. In recent work with\nMorningstar and Huse (PRB\, 2 020)\, we utilize a series of\napproximations to develop specific RG flow equations. These are\nsimilar to the Kosterlitz-Thouless (KT) flow equatio ns\, but there are\nimportant differences that place the MBL transition in a new\nuniversality class.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/125/ END:VEVENT BEGIN:VEVENT SUMMARY:Massimiliano Gubinelli (University of Oxford) DTSTART;VALUE=DATE-TIME:20221220T140000Z DTEND;VALUE=DATE-TIME:20221220T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/126 DESCRIPTION:Title: A stochastic analysis of EQFTs: the forward-backwards equation for Grassmann measures\nby Massimiliano Gubinelli (University of Oxford) as part of One world IAMP mathematical physics seminar\n\n\nAbstract\nI wi ll report on a research program to use ideas from stochastic analysis in t he context of constructive quantum field theories. Stochastic analysis can be summarized as the study of measures on path space via push-forward fro m Gaussian measures. The basic example is the Ito map which sends Brownian motion to a Markov diffusion process solution to a stochastic differentia l equation. Parisi-Wu stochastic quantisation can be understood as a stoch astic analysis of an Euclidean quantum field\, in the above sense. In this talk I will focus on another way to introduce such an “Ito map” which has connection to the continuous renormalization group a la Polchinski an d which uses a forward-backwards stochastic differential equation. In orde r to be able to give a full non-perturbative construction I will focus on the case of Grassmann measures seen as instances of non-commutative random fields.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/126/ END:VEVENT BEGIN:VEVENT SUMMARY:Jan Dereziński (University of Warsaw) DTSTART;VALUE=DATE-TIME:20230110T140000Z DTEND;VALUE=DATE-TIME:20230110T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/127 DESCRIPTION:Title: Dirac-Coulomb Hamiltonians\nby Jan Dereziński (University of Warsaw) as part of One world IAMP mathematical physics seminar\n\n\nAbstra ct\nI will discuss the theory of Dirac operators perturbed by the Coulomb potential in an arbitrary dimension. These operators are interesting for s everal reasons:\n\n– They have obvious applications to atomic physics.\n \n– If one neglects the mass term\, they are formally homogeneous.\n\n – Depending on the coupling constant and dimension\, they exhibit severa l distinct scaling behaviors (or if you prefer the high energy jargon\, va rious “renormalization group flows”).\n\n– Their definition involves subtle boundary conditions.\n\n– They are exactly solvable in terms of Whittaker functions.\n\nMy talk will be based on recent joint work with B łażej Ruba.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/127/ END:VEVENT BEGIN:VEVENT SUMMARY:Amanda Young (Technical University of Munich) DTSTART;VALUE=DATE-TIME:20230307T140000Z DTEND;VALUE=DATE-TIME:20230307T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/128 DESCRIPTION:Title: A bulk gap in the presence of edge states for a truncated Haldane pseudopotential\nby Amanda Young (Technical University of Munich) as p art of One world IAMP mathematical physics seminar\n\n\nAbstract\nIn this talk\, we discuss the bulk gap for a truncated\n1/3-filled Haldane pseudop otential for the fractional quantum Hall\neffect in the cylinder geometry. In the case of open boundary\nconditions\, a lower bound on the spectral gap (which is uniform in the\nvolume and particle number) accurately refle cts the presence of edge\nstates\, which do not persist into the bulk. A u niform lower bound for\nthe Hamiltonian with periodic boundary conditions is also obtain. Both\nof these bounds are proved by identifying invariant subspaces to which\nspectral gap and ground state energy estimating method s originally\ndeveloped for quantum spin Hamiltonians are applied. Customi zing the gap\ntechnique to the invariant subspace\, however\, we are able to avoid the\nedge states and establish a more precise estimate on the bul k gap in the\ncase of periodic boundary conditions. The same approach can also be\napplied to prove a bulk gap for the analogously truncated Haldane \npseudopotential with maximal half filling\, which describes a strongly\n correlated system of spinless bosons in a cylinder geometry. This is\nbase d off joint work with S. Warzel.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/128/ END:VEVENT BEGIN:VEVENT SUMMARY:Lingrui Ge (University of California\, Irvine) DTSTART;VALUE=DATE-TIME:20230404T140000Z DTEND;VALUE=DATE-TIME:20230404T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/129 DESCRIPTION:Title: Multiplicative Jensen’s formula and quantitative global theory f or ID quasiperiodic operators\nby Lingrui Ge (University of California \, Irvine) as part of One world IAMP mathematical physics seminar\n\n\nAbs tract\nWe prove multiplicative Jensen’s formula and establish quantitati ve global theory for analytic one-frequency Schrodinger operators. We will also discuss the motivations and further applications.\nThis is based on a joint work with Jiangong You\, Svetlana Jitomirskaya and Qi Zhou.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/129/ END:VEVENT BEGIN:VEVENT SUMMARY:Christian Maes (KU Leuven) DTSTART;VALUE=DATE-TIME:20230221T140000Z DTEND;VALUE=DATE-TIME:20230221T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/130 DESCRIPTION:Title: Nonequilibrium extension of Third Law\nby Christian Maes (KU L euven) as part of One world IAMP mathematical physics seminar\n\n\nAbstrac t\nThe Nernst-Planck Postulate (Third Law of Thermodynamics stating that t he entropy becomes zero at zero temperature) has a different status from t he other Laws: it is not a consequence of the general structure of statis tical thermodynamics\, it can fail\, and it does not carry a straightforwa rd dynamic or kinetic derivation when it does hold. In this talk we consi der the latter question\, by extending the Third Law to nonequilibrium jum p processes. We give sufficient conditions in a Nonequilibrium Nernst The orem\, that the operationally defined excess heat vanishes at absolute zer o\, and from counter examples\, we understand that those conditions are we ll on target. We give an example of a zero-temperature nonequilibrium tra nsition where the heat capacity abruptly diverges as a function of the che mical potential. The main ingredients in the proof are a formulation of t he quasistatic relaxation between nonequilibrium steady conditions\,d a co mbined application of the matrix tree and the matrix forest theorem.\n\nJo int work with Faezeh Khodabandehlou and Karel Netocny.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/130/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Elgart (Virginia Tech) DTSTART;VALUE=DATE-TIME:20230207T140000Z DTEND;VALUE=DATE-TIME:20230207T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/131 DESCRIPTION:Title: Localization of the random XXZ spin chain in fixed energy interval s\nby Alexander Elgart (Virginia Tech) as part of One world IAMP mathe matical physics seminar\n\n\nAbstract\nA Schrödinger operator $H$ is know n to exhibit quasi-locality: Matrix elements of analytic functions of $H$ decay exponentially away from the diagonal. Localization for a random Schr ödinger operator can be expressed as an extension of this feature to Bore l measurable functions with support in the region of localization.\n\n\nWe show that the spin-$\\frac12$ XXZ random chain Hamiltonian $H_{XXZ}$ mani fests a suitably defined notion of quasi-locality as well. We exploit this property to prove that $H_{XXZ}$ exhibits localization in any fixed energ y interval (expressed as quasi-locality for Borel measurable functions of $H_{XXZ}$ with support in the energy interval). Localization is proved in a nontrivial region of the parameter space\, which includes weak interact ion and strong disorder regimes\, and is independent of the size of the sy stem\, depending only on the energy interval.\n\n\nBased on a joint work w ith Abel Klein\, https://arxiv.org/abs/2210.14873\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/131/ END:VEVENT BEGIN:VEVENT SUMMARY:Christian Hainzl (Mathematisches Institut der Universität Münche n) DTSTART;VALUE=DATE-TIME:20230124T140000Z DTEND;VALUE=DATE-TIME:20230124T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/132 DESCRIPTION:Title: Correlation energy of an electron gas in the mean-field approximat ion\nby Christian Hainzl (Mathematisches Institut der Universität Mü nchen) as part of One world IAMP mathematical physics seminar\n\n\nAbstrac t\nThe correlation energy of a high density fermionic Coulomb gas\, called Jellium\, is expected to be given by the Gell-Mann Brueckner formula. I w ill discuss an analogue of this formula for the mean-field regime. I prese nt a rigorous upper bound established by variational methods in the case o f Coulomb interaction. I will further review similar results for more regu lar potentials\, which is meanwhile well understood for particles in a fix ed box. The talk is based on joint work with Martin Christiansen and P. T. Nam.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/132/ END:VEVENT BEGIN:VEVENT SUMMARY:Hermann Schulz-Baldes (Friedrich-Alexander-Universitaet Erlangen-N uernberg) DTSTART;VALUE=DATE-TIME:20230321T140000Z DTEND;VALUE=DATE-TIME:20230321T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/133 DESCRIPTION:Title: Pseudo-gaps for random hopping models\nby Hermann Schulz-Balde s (Friedrich-Alexander-Universitaet Erlangen-Nuernberg) as part of One wor ld IAMP mathematical physics seminar\n\n\nAbstract\nFor one-dimensional ra ndom Schrödinger operators\, the integrated density of states\nis known t o be given in terms of the (averaged) rotation number of the Pr¨ufer phas e\ndynamics. This paper develops a controlled perturbation theory for the rotation number\naround an energy at which all the transfer matrices commu te and are hyperbolic. Such\na hyperbolic critical energy appears in rando m hopping models. The main result is a\nHölder continuity of the rotation number at the critical energy that implies the existence\nof a pseudo-gap . The proof uses renewal theory. The result is illustrated by numerics.\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/133/ END:VEVENT BEGIN:VEVENT SUMMARY:Cristina Toninelli (Univ. Paris Dauphine) DTSTART;VALUE=DATE-TIME:20230516T140000Z DTEND;VALUE=DATE-TIME:20230516T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/134 DESCRIPTION:by Cristina Toninelli (Univ. Paris Dauphine) as part of One wo rld IAMP mathematical physics seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/134/ END:VEVENT BEGIN:VEVENT SUMMARY:Flora Koukiou (Cergy–Pontoise University) DTSTART;VALUE=DATE-TIME:20230530T140000Z DTEND;VALUE=DATE-TIME:20230530T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/135 DESCRIPTION:by Flora Koukiou (Cergy–Pontoise University) as part of One world IAMP mathematical physics seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/135/ END:VEVENT BEGIN:VEVENT SUMMARY:Scott Armstrong (New York University) DTSTART;VALUE=DATE-TIME:20230613T140000Z DTEND;VALUE=DATE-TIME:20230613T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/136 DESCRIPTION:by Scott Armstrong (New York University) as part of One world IAMP mathematical physics seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/136/ END:VEVENT BEGIN:VEVENT SUMMARY:Michał Wrochna (Cergy Paris University) DTSTART;VALUE=DATE-TIME:20230418T140000Z DTEND;VALUE=DATE-TIME:20230418T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/137 DESCRIPTION:by Michał Wrochna (Cergy Paris University) as part of One wor ld IAMP mathematical physics seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/137/ END:VEVENT BEGIN:VEVENT SUMMARY:Nikita Nekrasov (Simons Center for Geometry and Physics) DTSTART;VALUE=DATE-TIME:20230502T140000Z DTEND;VALUE=DATE-TIME:20230502T150000Z DTSTAMP;VALUE=DATE-TIME:20230330T211235Z UID:IAMP_seminars/138 DESCRIPTION:by Nikita Nekrasov (Simons Center for Geometry and Physics) as part of One world IAMP mathematical physics seminar\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/IAMP_seminars/138/ END:VEVENT END:VCALENDAR