This online seminar takes place on Tuesdays at UTC 13-14, which is equivalent to 9-10pm (China Standard Time); 3-4pm (Central European Summer Time); 9-10am (Eastern Daylight Time); 6-7am (Pacific Daylight Time).

Current organisers are Jan Dereziński (Warsaw) and Daniel Ueltschi (Warwick).

Scientific committee: Nalini Anantharaman (Strassbourg), Mihalis Dafermos (Cambridge), Stephan De Bièvre (Lille), Krzysztof Gawedzki (ENS Lyon), Bernard Helffer (Nantes), Vojkan Jaksic (McGill), Flora Koukiou (Cergy), Antti Kupiainen (Helsinki), Mathieu Lewin (Paris Dauphine), Bruno Nachtergaele (UC Davis), Claude-Alain Pillet (Toulon), Robert Seiringer (IST Austria), Jan Philip Solovej (Copenhagen), Hal Tasaki (Gakushuin).

If you would like to receive seminar announcements, please send an email to IAMPseminars@gmail.com with “subscribe” in the subject line; or “unsubscribe” to have your email address removed. You can also email comments or suggestions.

Other *One World seminars* are listed on the website of the probability seminar, which initiated the series.
The researchseminars.org website lists further mathematical-physics seminars.

July 21, 2020 |
Hugo Duminil-Copin (IHES / University of Geneva) Marginal triviality of the scaling limits of critical 4D Ising and φ_4^4 models In this talk, we will discuss the scaling limits of spin fluctuations in four-dimensional Ising-type models with nearest-neighbor ferromagnetic interaction at or near the critical point are Gaussian and its implications from the point of view of Euclidean Field Theory. Similar statements will be proven for the λφ4 fields over R^4 with a lattice ultraviolet cutoff, in the limit of infinite volume and vanishing lattice spacing. The proofs are enabled by the models' random current representation, in which the correlation functions' deviation from Wick's law is expressed in terms of intersection probabilities of random currents with sources at distances which are large on the model's lattice scale. Guided by the analogy with random walk intersection amplitudes, the analysis focuses on the improvement of the so-called tree diagram bound by a logarithmic correction term, which is derived here through multi-scale analysis. Video link: https://zoom.us/j/91201391937?pwd=Q2dCRXF0eklxeE55Mkd5Yk5ESE4vdz09 |

July 28, 2020 |
Nicolas Rougerie (University of Grenoble Alpes) Title: TBA Abstract: TBA Video link: TBA |

July 14, 2020 |
Hal Tasaki (Gakushuin University) 'Topological' index and general Lieb-Schultz-Mattis theorems for quantum spin chains A Lieb-Schultz-Mattis (LSM) type theorem states that a quantum many-body system with certain symmetry cannot have a unique ground state accompanied by a nonzero energy gap. While the original theorem treats models with continuous U(1) symmetry, new LSM-type statements that only assume discrete symmetry have been proposed recently in close connection with topological condensed matter physics. Here we shall prove such general LSM-type theorems by using the "topological" index intensively studied in the context of symmetry protected topological phase. Operator algebraic formulation of quantum spin chains plays an essential role in our approach. Here I do not assume any advanced knowledge in quantum spin systems or operator algebra, and illustrate the ideas of the proof (which I believe to be interesting). The talk is based on a joint work with Yoshiko Ogata and Yuji Tachikawa in arXiv:2004.06458. Video link: youtu.be/q0k1sch56Dk |

July 7, 2020 |
Bruno Després (Sorbonne University) Spectral-scattering theory and fusion plasmas Motivated by fusion plasmas and Tokamaks (ITER project), I will describe recent efforts on adapting the mathematical theory of linear unbounded self-adjoint operators (Kato, Lax, Reed-Simon, ....) to problems governed by kinetic equations coupled with Maxwell equations. Firstly it will be shown that Vlasov-Poisson-Ampere equations, linearized around non homogeneous Maxwellians, can be written in the framework of abstract scattering theory (linear Landau damping is a consequence). Secondly the absorption principle applied to the hybrid resonance will be discussed. All results come from long term discussions and collaborations with many colleagues (Campos-Pinto, Charles, Colas, Heuraux, Imbert-Gérard, Lafitte, Nicolopoulos, Rege, Weder, and many others). Video link: youtu.be/lmnm1D3NFp8 |

June 30, 2020 |
Laure Saint-Raymond (ENS Lyon) Fluctuation theory in the Boltzmann-Grad limit In this talk, I will discuss a long term project with T. Bodineau, I. Gallagher and S. Simonella on hard-sphere dynamics in the kinetic regime, away from thermal equilibrium. In the low density limit, the empirical density obeys a law of large numbers and the dynamics is governed by the Boltzmann equation. Deviations from this behavior are described by dynamical correlations, which can be fully characterized for short times. This provides both a fluctuating Boltzmann equation and large deviation asymptotics. Video link: youtu.be/fLDFA7ZCagA |

June 23, 2020 |
Nilanjana Datta (University of Cambridge) Discriminating between unitary quantum processes Discriminating between unknown objects in a given set is a fundamental task in experimental science. Suppose you are given a quantum system which is in one of two given states with equal probability. Determining the actual state of the system amounts to doing a measurement on it which would allow you to discriminate between the two possible states. It is known that unless the two states are mutually orthogonal, perfect discrimination is possible only if you are given arbitrarily many identical copies of the state. In this talk we consider the task of discriminating between quantum processes, instead of quantum states. In particular, we discriminate between a pair of unitary operators acting on a quantum system whose underlying Hilbert space is possibly infinite-dimensional. We prove that in contrast to state discrimination, one needs only a finite number of copies to discriminate perfectly between the two unitaries. Furthermore, no entanglement is needed in the discrimination task. The measure of discrimination is given in terms of the energy-constrained diamond norm and one of the key ingredients of the proof is a generalization of the Toeplitz-Hausdorff Theorem in convex analysis. Moreover, we employ our results to study a novel type of quantum speed limits which apply to pairs of quantum evolutions.This work was done jointly with Simon Becker (Cambridge), Ludovico Lami (Ulm) and Cambyse Rouze (Munich) Video link: youtu.be/gHEjszXSjMQ |

June 16, 2020 |
Nicola Pinamonti (University of Genova) Equilibrium states for interacting quantum field theories and their relative entropy During this talk we will review the construction of equilibrium states for interacting scalar quantum field theories, treated with perturbation theory, recently proposed by Fredenhagen and Lindner. We shall in particular see that this construction is a generalization of known results valid in the case of C*-dynamical systems. We shall furthermore discuss some properties of these states and we compare them with known results in the physical literature. In the last part of the talk, we shall show that notions like relative entropy or entropy production can be given for states which are of the form discussed in the first part of talk. We shall thus provide an extension to quantum field theory of similar concepts available in the case of C*-dynamical systems. Video link: youtu.be/excgcO7loj0 |

June 9, 2020 |
Andreas Winter (Universitat Autònoma de Barcelona) Energy-constrained diamond norms and the continuity of channel capacities and of open-system dynamics The channels, and more generally superoperators acting on the trace class operators of a quantum system naturally form a Banach space under the completely bounded trace norm (aka diamond norm). However, it is well-known that in infinite dimension, the norm topology is often "too strong" for reasonable applications. Here, we explore a recently introduced energy-constrained diamond norm on superoperators (subject to an energy bound on the input states). Our main motivation is the continuity of capacities and other entropic quantities of quantum channels, but we also present an application to the continuity of one-parameter unitary groups and certain one-parameter semigroups of quantum channels. Video link: youtu.be/05ZQPFB0aAc |

June 2, 2020 |
Mihalis Dafermos (Cambridge University) The nonlinear stability of the Schwarzschild metric without symmetry I will discuss an upcoming result proving the full finite-codimension non-linear asymptotic stability of the Schwarzschild family as solutions to the Einstein vacuum equations in the exterior of the black hole region. No symmetry is assumed. The work is based on our previous understanding of linear stability of Schwarzschild in double null gauge. Joint work with G. Holzegel, I. Rodnianski and M. Taylor. Video link: youtu.be/6Vh62H0rPiA |

May 26, 2020 |
Sven Bachmann (University of British Columbia) Adiabatic quantum transport In the presence of a spectral gap above the ground state energy, slowly driven condensed matter systems may exhibit quantized transport of charge. One of the earliest instances of this fact is the Laughlin argument explaining the integrality of the Hall conductance. In this talk, I will discuss transport by adiabatic processes in the presence of interactions between the charge carriers. I will explain the central role played by the locality of the quantum dynamics in two instances: the adiabatic theorem and an index theorem for quantized charge transport. I will also relate fractional transport to the anyonic nature of elementary excitations. Video link: youtu.be/ErgMuxMR_1A |

May 19, 2020 |
Pierre Clavier (University of Potsdam) Borel-Ecalle resummation for a Quantum Field Theory Borel-Ecalle resummation of resurgent functions is a vast generalisation of the well-known Borel-Laplace resummation method. It can be decomposed into three steps: Borel transform, averaging and Laplace transform. I will start by a pedagogical introduction of each of these steps. To illustrate the feasability of the Borel-Ecalle resummation method I then use it to resum the solution of a (truncated) Schwinger-Dyson equation of a Wess-Zumino model. This will be done using known results about this Wess-Zumino model as well as Sauzin's analytical bounds on convolution of resurgent functions. Video link: youtu.be/EzRoLEZhono |

May 12, 2020 |
Jan Philip Solovej (University of Copenhagen) Universality in the structure of Atoms and Molecules Abstract: The simplest approximate model of atoms and molecules is the celebrated Thomas-Fermi model. It is known to give a good approximation to the ground state energy of heavy atoms. The understanding of this approximation relies on a beautiful and very accurate application of semi-classical analysis. Although the energy approximation is good, it is, unfortunately, far from being accurate enough to predict quantities relevant to chemistry. Thomas-Fermi theory may nevertheless tell us something surprisingly accurate about the structure of atoms and molecules. I will discuss how a certain universality in the Thomas-Fermi model, indeed, holds approximately in much more complicated models, such as the Hartree-Fock model. I will also show numerical and experimental evidence that the approximate universality may hold even for real atoms and molecules. Video link: youtu.be/FCxkP7CqtQQ |

May 5, 2020 |
Martin Hairer (Imperial College London) The Brownian Castle Video link: youtu.be/Ve_EFZDbXTU |