BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jürg Fröhlich (ETH Zürich) DTSTART:20200709T150000Z DTEND:20200709T163000Z DTSTAMP:20260422T225726Z UID:AQFP/1 DESCRIPTION:Title: Res ults on interacting Bose Gases\nby Jürg Fröhlich (ETH Zürich) as pa rt of Analysis\, Quantum Fields\, and Probability\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/AQFP/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Thierry Bodineau (Ecole Polytechnique) DTSTART:20200917T150000Z DTEND:20200917T163000Z DTSTAMP:20260422T225726Z UID:AQFP/2 DESCRIPTION:Title: Log -Sobolev inequality for the continuum sine-Gordon model\nby Thierry Bo dineau (Ecole Polytechnique) as part of Analysis\, Quantum Fields\, and Pr obability\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/AQFP/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Aizenman (Princeton) DTSTART:20201210T160000Z DTEND:20201210T173000Z DTSTAMP:20260422T225726Z UID:AQFP/3 DESCRIPTION:Title: Mar ginal triviality of the scaling limits of 4D critical Ising and $\\Phi^4$ models\nby Michael Aizenman (Princeton) as part of Analysis\, Quantum Fields\, and Probability\n\n\nAbstract\nThe talk will present the recent p roof that in four\ndimensions the spin fluctuations of Ising-type models a t their critical\npoints are Gaussian in their scaling limits (infinite vo lume\, vanishing\nlattice spacing). Similar statement is proven for the s caling limits of\nmore general $\\Phi^4$ fields constructed through a latt ice cutoff. The\nproofs are facilitated by the systems’ random current r epresentation\, in\nwhich the deviation from Wick's law are expressed in t erms of\nintersection probabilities of random currents with prescribed sou rces.\nThis approach previously yielded such statements for D>4. Their rec ent\nextension to the marginal dimension was enabled by a multiscale analy sis\nof the critical clusters’ intersections. (Joint work with Hugo\nD uminil-Copin.)\n LOCATION:https://researchseminars.org/talk/AQFP/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Vincent Vargas (Ecole Normale Supérieure) DTSTART:20201112T160000Z DTEND:20201112T173000Z DTSTAMP:20260422T225726Z UID:AQFP/4 DESCRIPTION:Title: Lio uville conformal field theory: equivalence between the path integral and t he bootstrap construction\nby Vincent Vargas (Ecole Normale Supérieur e) as part of Analysis\, Quantum Fields\, and Probability\n\n\nAbstract\nL iouville conformal field theory (LCFT) is a family of Conformal field theo ries which arise in a wide variety of contexts in the physics and the prob abilistic literature: SUSY Yang-Mills\, the scaling limit of large planar maps\, etc... There are two main and seemingly unrelated approaches to LCF T in the physics literature: one in the Feynman path integral formulation and one in the conformal bootstrap approach. Recently\, we constructed rig orously LCFT in the Feynman path integral formulation via probability theo ry (and more specifically the Gaussian Free Field). In this talk\, I will present recent work which shows that both approaches (probabilistic constr uction of the Feynman path integral and conformal bootstrap) are in fact i dentical. A key ingredient in our work is the analysis of an infinite dime nsional semigroup\, the so-called Liouville semigroup. Based on a series o f joint works with C. Guillarmou\, F. David\, A. Kupiainen and R. Rhodes.\ n LOCATION:https://researchseminars.org/talk/AQFP/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Slava Rychkov (IHES) DTSTART:20201008T150000Z DTEND:20201008T163000Z DTSTAMP:20260422T225726Z UID:AQFP/5 DESCRIPTION:Title: CFT Osterwalder-Schrader Theorem\nby Slava Rychkov (IHES) as part of Anal ysis\, Quantum Fields\, and Probability\n\n\nAbstract\nMost QFT axioms are only good to prove theorems but not to compute anything measurable. One e xception are the Euclidean Conformal Field Theory (CFT) axioms in d>=3 dim ensions\, which do lead to surprisingly strong “bootstrap" constraints o n scaling dimensions of various conjecturally existing Euclidean CFTs (suc h as the critical point of the 3d Ising and O(2) models). In this talk I w ill not discuss the bootstrap as such\, but I will explain the Euclidean C FT axioms and will relate them to the Osterwalder-Schrader and Wightman ax ioms. The OS linear growth condition does not obviously follow from the Eu clidean CFT axioms\, but fortunately there is a route to Wightman axioms w hich does not rely on the Glaser-Osterwalder-Schrader construction. Based on work in progress with Petr Kravchuk and Jiaxin Qiao.\n LOCATION:https://researchseminars.org/talk/AQFP/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Marcello Porta (SISSA) DTSTART:20210114T160000Z DTEND:20210114T173000Z DTSTAMP:20260422T225726Z UID:AQFP/6 DESCRIPTION:Title: Ano maly non-renormalization in interacting Weyl semimetals\nby Marcello P orta (SISSA) as part of Analysis\, Quantum Fields\, and Probability\n\n\nA bstract\nWeyl semimetals are three-dimensional condensed matter systems ch aracterized by a degenerate Fermi surface\, consisting of a pair of `Weyl nodes'. Correspondingly\, in the infrared limit\, these systems behave eff ectively as Weyl fermions in 3+1 dimensions. As predicted by Nielsen and N inomiya in 1983\, when exposed to electromagnetic fields these materials a re expected to simulate the axial anomaly of QED\, by giving rise to a net quasi-particle flow between Weyl nodes.\n \n\nWe consider a class of inte racting lattice models for Weyl semimetals and prove that the quadratic re sponse of the quasi-particle flow is universal\, and equal to the chiral t riangle graph of QED. Universality is the counterpart of the Adler-Bardeen non-renormalization property of the axial anomaly for QED\, in a condense d matter setting. Our proof relies on the rigorous Wick rotation for real- time transport coefficients\, on constructive bounds for Euclidean ground state correlations\, and on lattice Ward Identities. Joint work with A. Gi uliani and V. Mastropietro.\n LOCATION:https://researchseminars.org/talk/AQFP/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Laszlo Erdös (IST Austria) DTSTART:20210211T160000Z DTEND:20210211T173000Z DTSTAMP:20260422T225726Z UID:AQFP/7 DESCRIPTION:Title: Eig enstate thermalisation hypothesis and functional CLT for Wigner matrices\nby Laszlo Erdös (IST Austria) as part of Analysis\, Quantum Fields\, and Probability\n\n\nAbstract\nWe prove that any deterministic matrix is approximately the identity in the eigenbasis of a large random Wigner matr ix W with an optimal error inversely proportional to the square root of th e dimension. This verifies a strong form of Quantum Unique Ergodicity wit h an optimal convergence rate and we also prove Gaussian fluctuations arou nd this convergence after a small spectral averaging. This requires to ext end the classical CLT for linear eigenvalue statistics\, Tr f(W)\, to incl ude a deterministic matrix A and we identify three different modes of fl uctuation for Tr f(W)A in the entire mesoscpic regime. The key technical t ool is a new multi-resolvent local law for Wigner ensemble.\n LOCATION:https://researchseminars.org/talk/AQFP/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Roberto Longo (Roma "Tor Vergata") DTSTART:20210311T160000Z DTEND:20210311T173000Z DTSTAMP:20260422T225726Z UID:AQFP/8 DESCRIPTION:Title: The massive modular Hamiltonian\nby Roberto Longo (Roma "Tor Vergata") as part of Analysis\, Quantum Fields\, and Probability\n\n\nAbstract\nA solu tion of the Klein-Gordon equation can be viewed as a signal carried by a c lassical wave packet\, or as the wave function of a quantum particle\, or as a coherent state in Quantum Field Theory. Our recent work concerns the definition\, computation and interpretation of the local entropy of this o bject and its relation to quantum energy inequalities. The Operator Algebr aic approach\, in particular the Tomita-Takesaki modular theory\, provides a natural framework and powerful methods for our analysis. In this talk\, I will discuss part of the general ground for our analysis and some key r esults\, in particular the solution of an old problem in QFT: the descript ion of the modular Hamiltonian associated with a space ball B in the free scalar massive QFT\; this sets up the formula for the entropy density of a real wave packet.\n LOCATION:https://researchseminars.org/talk/AQFP/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Hendrik Weber (Bath) DTSTART:20210610T150000Z DTEND:20210610T163000Z DTSTAMP:20260422T225726Z UID:AQFP/9 DESCRIPTION:Title: Gib bs measures in infinite dimensions - Some new results on a classical topic \nby Hendrik Weber (Bath) as part of Analysis\, Quantum Fields\, and P robability\n\n\nAbstract\nGibbs measures on spaces of functions or distrib utions play an important role in \nvarious contexts in mathematical physic s. They can\, for example\, be viewed as continuous \ncounterparts of cla ssical spin models such as the Ising model\, they are an important steppin g \nstone in the rigorous construction of Quantum Field Theories\, and the y are invariant under the \nflow of certain dispersive PDEs\, permitting t o develop a solution theory with random initial data\, \nwell below the de terministic regularity threshold. \n\nThese measures have been constructed and studied\, at least since the 60s\, but over the last few \nyears ther e has been renewed interest\, partially due to new methods in stochastic a nalysis\, including\nHairer’s theory of regularity structures and Gubine lli-Imkeller-Perkowski’s theory of \nparacontrolled distributions. \n\nI n this talk I will present two independent but complementary results that can be obtained with \nthese new techniques. I will first show how to obta in estimates on samples from of the Euclidean \n$\\phi^4_3$ measure\, base d on SPDE methods. I will then discuss a new method to show the \nemergenc e of phase transitions in the phi^4_3 theory. \n\nThis is based on joint w orks with \nA. Chandra\, A. Moinat https://arxiv.org/abs/1910.13854\n\n and \n\nA. Chandra\, T. Gunaratnam https://arxiv.org/abs/2006.15933\n LOCATION:https://researchseminars.org/talk/AQFP/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Faulkner DTSTART:20210408T150000Z DTEND:20210408T163000Z DTSTAMP:20260422T225726Z UID:AQFP/10 DESCRIPTION:Title: Al gebraic approach to quantum error correction and the AdS/CFT correspondenc e\nby Thomas Faulkner as part of Analysis\, Quantum Fields\, and Proba bility\n\n\nAbstract\nI will discuss the quantum error correction (QEC) ap proach to the AdS/CFT correspondence from an algebraic point of view. I w ill study exact QEC codes as models of AdS/CFT and connect these models to Longo-Rehren subnets. I do this by proving the existence of a consistent assignment of conditional expectations acting on the boundary theory algeb ras. I will also discuss shortcomings of these exact codes that will hopef ully be fixed by introducing small errors.\n LOCATION:https://researchseminars.org/talk/AQFP/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Andras Vasy (Stanford) DTSTART:20210701T150000Z DTEND:20210701T163000Z DTSTAMP:20260422T225726Z UID:AQFP/11 DESCRIPTION:Title: Th e Feynman propagator and its positivity properties\nby Andras Vasy (St anford) as part of Analysis\, Quantum Fields\, and Probability\n\n\nAbstra ct\nOne usually considers wave equations as evolution equations\, i.e. imp oses initial data and solves them. Equivalently\, one can consider the for ward and backward solution operators for the wave equation\; these solve a n equation $Lu=f$\, for say $f$ compactly supported\, by demanding that $u $ is supported at points which are reachable by forward\, respectively bac kward\, time-like or light-like curves. This property corresponds to causa lity. But it has been known for a long time that in certain settings\, suc h as Minkowski space\, there are other ways of solving wave equations\, na mely the Feynman and anti-Feynman solution operators (propagators). I will explain a general setup in which all of these propagators are inverses of the wave operator on appropriate function spaces\, and also mention posit ivity properties\, and the connection to spectral and scattering theory in Riemannian settings\, self-adjointness\, as well as to the classical para metrix construction of Duistermaat and Hormander.\n LOCATION:https://researchseminars.org/talk/AQFP/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Abdelmalek Abdesselam (U Virginia) DTSTART:20211014T150000Z DTEND:20211014T163000Z DTSTAMP:20260422T225726Z UID:AQFP/12 DESCRIPTION:Title: Ex ploring conformal invariance with hierarchical models\nby Abdelmalek A bdesselam (U Virginia) as part of Analysis\, Quantum Fields\, and Probabil ity\n\n\nAbstract\nIn the context of the AdS/CFT correspondence\, in Eucli dean signature\, an important basic fact is the bijection between conforma l transformations of the boundary and hyperbolic isometries of the bulk. A n infinite regular tree with the graph distance can be seen as a quintesse ntial bare-bones version of a hyperbolic space. It turns out there is a na tural way to define analogues of conformal maps on the boundary of such a tree and\, quite miraculously\, these are in bijection with tree isometrie s. Moreover\, a Euclidean QFT on this boundary is the same as a hierarchic al model as considered by Dyson in his study of the long-range Ising model and by Wilson when he introduced the approximate renormalization group re cursion. I will try to give a pedagogical introduction to this circle of i deas\, and I will discuss a particular model where there is hope to be abl e to prove conformal invariance from first principles via a rigorous nonpe rturbative renormalization group approach.\n LOCATION:https://researchseminars.org/talk/AQFP/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Sourav Chatterjee (Stanford) DTSTART:20211111T160000Z DTEND:20211111T173000Z DTSTAMP:20260422T225726Z UID:AQFP/13 DESCRIPTION:Title: So me progress on 3D Yang-Mills\nby Sourav Chatterjee (Stanford) as part of Analysis\, Quantum Fields\, and Probability\n\n\nAbstract\nI will talk about some recent progress on the problem of constructing 3D Euclidean Yan g-Mills theories. This is based on joint work with Sky Cao.\n LOCATION:https://researchseminars.org/talk/AQFP/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Yoshiko Ogata (Tokyo) DTSTART:20220113T120000Z DTEND:20220113T133000Z DTSTAMP:20260422T225726Z UID:AQFP/14 DESCRIPTION:Title: An invariant of symmetry protected topological phases with on-site finite gr oup symmetry for two-dimensional Fermion systems\nby Yoshiko Ogata (To kyo) as part of Analysis\, Quantum Fields\, and Probability\n\n\nAbstract\ nWe consider SPT-phases with on-site finite group G symmetry for two-dimen sional Fermion systems.We derive an invariant of the classification.\n LOCATION:https://researchseminars.org/talk/AQFP/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Tom Kennedy (Arizona) DTSTART:20211209T160000Z DTEND:20211209T173000Z DTSTAMP:20260422T225726Z UID:AQFP/15 DESCRIPTION:Title: Re normalization group maps for Ising models and tensor networks\nby Tom Kennedy (Arizona) as part of Analysis\, Quantum Fields\, and Probability\n \n\nAbstract\nWe will briefly review Wilson-Kadanoff type renormalization group (RG) maps for Ising spin systems and the lack of progress in provin g that there is a non-trivial fixed point for these maps. (These maps are also known as real-space RG transformations.) The Ising model can be writt en as a tensor network\, and RG maps can be defined in the tensor network formalism. Numerical studies of such RG maps have been quite successful at reproducing the known critical behavior in two dimensions. In joint work with Slava Rychkov we proved that in two dimensions for a particular tenso r network RG map the high temperature fixed point is locally stable\, i.e. \, there is a neighborhood of the high temperature fixed point such that f or an initial tensor in this neighborhood\, the iterations of the RG map c onverge to the high temperature fixed point. We hope that this is a modest first step towards proving the existence of a non-trivial fixed point for a tensor network RG map which would correspond to the critical point of t he Ising model.\n LOCATION:https://researchseminars.org/talk/AQFP/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Simone Warzel (TUM) DTSTART:20200210T160000Z DTEND:20200210T173000Z DTSTAMP:20260422T225726Z UID:AQFP/16 DESCRIPTION:by Simone Warzel (TUM) as part of Analysis\, Quantum Fields\, and Probability\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/AQFP/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Alessandro Giuliani (Roma Tre) DTSTART:20220324T160000Z DTEND:20220324T173000Z DTSTAMP:20260422T225726Z UID:AQFP/17 DESCRIPTION:Title: Re normalization at all orders for lattice infrared QED4 with massless electr on\nby Alessandro Giuliani (Roma Tre) as part of Analysis\, Quantum Fi elds\, and Probability\n\n\nAbstract\nOne of the goals of constructive Qua ntum Field Theory (QFT) is to provide a convergent algorithm for computing a consistent set of Euclidean correlation functions starting from a given bare action and\, next\, to reconstruct the corresponding real-time corre lations via analytic continuation in the time variable. This program prove d successful for constructing several low dimensional toy QFT models but r esults in 3 and 4 dimensions are still scarce. Until now\, not even a cons istent construction of infrared QED4 with small electron mass at all order s in renormalized perturbation theory was available\, unless a loop regula rization scheme was employed or a number of non-gauge-invariant counter-te rms were included in the bare action.\nIn this talk I will describe such a consistent construction\, at all orders in renormalized perturbation theo ry\, in a lattice gauge theory model of QED4 with massless electron and no other counter-term than the one for the electron mass. We also prove that \, in the presence of an infrared (IR) cutoff on the photon propagator\, t he model is non-perturbatively well-defined\, provided the electron charge is sufficiently small (a priori\, non-uniformly in the IR cutoff).\nThe p roof is based on a Wilsonian Renormalization Group (RG) scheme and uses id eas developed in the last decade in the context of lattice gauge theory mo dels of graphene and Weyl semimetals. In particular\, we use Ward Identiti es at each RG step to control the flow of the effective couplings\, includ ing the non-gauge-invariant ones produced at intermediate steps by the mul tiscale procedure\, and prove their infrared asymptotic freedom. Time perm itting\, I will comment on the perspectives opened by this and related wor ks on the full construction of infrared QED4\, on the non-perturbative com putation of the chiral anomaly and on the spontaneous emergence of Lorentz symmetry. Joint work with Marco Falconi and Vieri Mastropietro.\n LOCATION:https://researchseminars.org/talk/AQFP/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Stottmeister (U Hannover) DTSTART:20220407T150000Z DTEND:20220407T163000Z DTSTAMP:20260422T225726Z UID:AQFP/18 DESCRIPTION:Title: On the scaling limit of the Ising anyon chain\nby Alexander Stottmeister (U Hannover) as part of Analysis\, Quantum Fields\, and Probability\n\n\n Abstract\nIn this talk I will present a Hamiltonian approach to the scalin g limit of the Ising anyon chain\, a 1+1-dimensional instance of the class ical 2-dimensional Ising model. The scaling limit is constructed using an operator algebraic formulation of the Wilson-Kadanoff renormalization grou p. At criticality\, conformal symmetry is recovered by showing the converg ence of the Koo-Saleur formula\, approximating the Virasoro generators.\n\ nIf time permits\, I will comment on applications to the quantum simulatio n of conformal field theories.\n\nThis is joint work with Tobias J. Osborn e and Daniela Cadamuro\, and based on previous work with Vincenzo Morinell i\, Gerardo Morsella and Yoh Tanimoto.\n LOCATION:https://researchseminars.org/talk/AQFP/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Bjoern Bringmann (IAS Princeton) DTSTART:20220609T150000Z DTEND:20220609T160000Z DTSTAMP:20260422T225726Z UID:AQFP/19 DESCRIPTION:Title: In variant Gibbs measures for the three-dimensional cubic nonlinear wave equa tion\nby Bjoern Bringmann (IAS Princeton) as part of Analysis\, Quantu m Fields\, and Probability\n\n\nAbstract\nIn this talk\, we prove the inva riance of the Gibbs measure for the three-dimensional cubic nonlinear wave equation\, which is also known as the hyperbolic $\\Phi^4_3$-model. This result is the hyperbolic counterpart to seminal works on the parabolic $\\ Phi^4_3$-model by Hairer ’14 and Hairer- Matetski ’18.\nIn the first h alf of this talk\, we illustrate Gibbs measures in the context of Hamilton ian ODEs\, which serve as toy-models. We also connect our theorem with cla ssical and recent developments in constructive QFT\, dispersive PDEs\, and stochastic PDEs.\nIn the second half of this talk\, we give a non-technic al overview of the proof. As part of this overview\, we first introduce a caloric representation of the Gibbs measure\, which leads to an inter- pla y of both parabolic and hyperbolic theories. Then\, we briefly discuss the local dynamics of the cubic nonlinear wave equation\, focusing on a hidde n cancellation between sextic stochastic objects.\nThis is joint work with Y. Deng\, A. Nahmod\, and H. Yue.\n LOCATION:https://researchseminars.org/talk/AQFP/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Massimiliano Gubinelli (U Bonn) DTSTART:20220512T150000Z DTEND:20220512T160000Z DTSTAMP:20260422T225726Z UID:AQFP/20 DESCRIPTION:Title: Wh at is stochastic quantization?\nby Massimiliano Gubinelli (U Bonn) as part of Analysis\, Quantum Fields\, and Probability\n\n\nAbstract\nIn this talk I will introduce the idea of stochastic quantization from a mathemat ical perspective\, as a tool to analyze rigorously Euclidean quantum field s. I will show that there are several different "stochastic quantizations ” and I will attempt to exemplify common structures which take the form of a stochastic analysis of Euclidean quantum fields.\n LOCATION:https://researchseminars.org/talk/AQFP/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Kasia Rejzner (U York) DTSTART:20220714T150000Z DTEND:20220714T160000Z DTSTAMP:20260422T225726Z UID:AQFP/21 DESCRIPTION:Title: Sy mmetries in (perturbative) algebraic quantum field theory\nby Kasia Re jzner (U York) as part of Analysis\, Quantum Fields\, and Probability\n\n\ nAbstract\nIn this talk I will review recent progress on describing symmet ries and renormalisation using the C*-algebraic framework proposed by Buch holz and Fredenhagen in their paper from 2019. The recent progress involve s the formulation of renormalisation group and the anomalous unitary quant um Noether theorem. This is based on a join paper with Brunetti\, Duetsch and Fredenhagen.\n LOCATION:https://researchseminars.org/talk/AQFP/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Wei Wu (NYU Shanghai) DTSTART:20221013T150000Z DTEND:20221013T160000Z DTSTAMP:20260422T225726Z UID:AQFP/22 DESCRIPTION:Title: Ma ssless phases for the Villain model in d>=3\nby Wei Wu (NYU Shanghai) as part of Analysis\, Quantum Fields\, and Probability\n\n\nAbstract\nThe XY and the Villain models are models which exhibit the celebrated Kosterli tz-Thouless phase transitions in two dimensions. The spin wave conjecture\ , originally proposed by Dyson and by Mermin and Wagner\, predicts that at low temperature\, spin correlations of these models are closely related t o Gaussian free fields. I will review the historical background and discus s some recent progress on this conjecture in d>=3. Based on the joint work with Paul Dario (CNRS).\n LOCATION:https://researchseminars.org/talk/AQFP/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Paweł Duch (U Poznan) DTSTART:20221110T160000Z DTEND:20221110T170000Z DTSTAMP:20260422T225726Z UID:AQFP/23 DESCRIPTION:Title: We ak universality and singular stochastic PDEs\nby Paweł Duch (U Poznan ) as part of Analysis\, Quantum Fields\, and Probability\n\n\nAbstract\nTh e macroscopic or mesoscopic dynamics of many systems interacting with a ra ndom or chaotic environment can be described in terms of singular (i.e. cl assically ill-posed) stochastic partial differential equations. Typically\ , such stochastic PDEs depend only on a few parameters and govern the larg e-scale behavior of a huge number of different microscopic systems. This p roperty is called universality.\n\nIn the talk\, I will discuss the proof of the universality of the macroscopic scaling limit of solutions of a cla ss of parabolic stochastic PDEs with fractional Laplacian\, additive noise and polynomial non-linearity. I consider the so-called weakly non-linear regime and not necessarily Gaussian noises which are stationary\, centered \, sufficiently regular and satisfy some integrability and mixing conditio ns. The result applies to situations when the singular stochastic PDE obta ined in the scaling limit is close to critical and extends some of the exi sting universality results about the continuous interface growth models an d the phase coexistence models whose large scale behavior is governed by t he KPZ equation and the dynamical $\\Phi^4_3$ model\, respectively.\n\nThe proof uses a novel approach to singular stochastic PDEs based on the reno rmalization group flow equation. A nice feature of the method is that it c overs the full sub-critical (i.e. super-renormalizable) regime\, does not use any diagrammatic representation and avoids all combinatorial problems. Based on arXiv:2109.11380.\n LOCATION:https://researchseminars.org/talk/AQFP/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Wojciech de Roeck DTSTART:20230309T160000Z DTEND:20230309T170000Z DTSTAMP:20260422T225726Z UID:AQFP/24 DESCRIPTION:Title: Cl assification of short-range entangled quantum states and pumping processes \nby Wojciech de Roeck as part of Analysis\, Quantum Fields\, and Prob ability\n\n\nAbstract\nI will introduce the topic of classification of sho rt-range entangled quantum states. Physically speaking\, these states are ground states of gapped Hamiltonians without any intrinsic topological ord er (ie. no anyonic excitations\, for example)\, but one can define them in a neat abstract way that avoids such elaborate concepts. \nI will try to sketch some open problems\, and some results. In particular on the classi fication of pumping processes of such states\, which can be viewed as a ge neralization of Thouless pumps.\n LOCATION:https://researchseminars.org/talk/AQFP/24/ END:VEVENT END:VCALENDAR