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Quantum and classical fields interacting with geometry, Paris
from
Monday, March 18, 2024 (8:30 AM)
to
Friday, April 26, 2024 (9:30 PM)
Monday, March 18, 2024
9:30 AM
Minicourse: Geometry of Killing horizons and applications to black hole physics

Eric Gourgoulhon
(
LUTH, Observatoire de Paris
)
Minicourse: Geometry of Killing horizons and applications to black hole physics
Eric Gourgoulhon
(
LUTH, Observatoire de Paris
)
9:30 AM  10:30 AM
Room: amphithéâtre Yvonne ChoquetBruhat
I. Null hypersurfaces and nonexpanding horizons 1. Basic geometry of null hypersurfaces a) null geodesic generators b) crosssections c) expansion and shear d) null Raychaudhuri equation 2. Definition and main properties of nonexpanding horizons a) marginally trapped crosssections area invariance b) area invariance c) canonical affine connection d) total geodesicness (see https://relativite.obspm.fr/blackholes/ihp24/ for details and slides)
11:00 AM
Minicourse: Geometry of Killing horizons and applications to black hole physics

Eric Gourgoulhon
(
LUTH, Observatoire de Paris
)
Minicourse: Geometry of Killing horizons and applications to black hole physics
Eric Gourgoulhon
(
LUTH, Observatoire de Paris
)
11:00 AM  12:00 PM
Room: amphithéâtre Yvonne ChoquetBruhat
II. Killing horizons 1. Isometry groups and Killing vectors 2. Definition and examples of Killing horizons 3. Killing horizons as nonexpanding horizons 4. Vanishing of the shear 5. Surface gravity 6. Zeroth Law of black hole dynamics 7. Bifurcate Killing horizons
1:30 PM
Minicourse: Constructive Quantum Field Theory on manifolds

Nguyen Viet Dang
(
Sorbonne Université
)
Minicourse: Constructive Quantum Field Theory on manifolds
Nguyen Viet Dang
(
Sorbonne Université
)
1:30 PM  2:30 PM
Room: amphithéâtre Yvonne ChoquetBruhat
In this course, I will try to give an introduction to the nonperturbative construction of certain models of quantum field theories on manifolds. I will focus on the construction of the $P(\phi)_2$ theories on Riemann surfaces using both the Nelson bounds and the stochastic partial differential (SPDE) methods. Then I plan to discuss the KontsevichSegal axioms for this model following a recent construction of Jiasheng Lin. Finally, I will conclude the course by sketching the construction of the $\Phi^4_3$ measure on 3manifolds based on SPDE methods which is joint work with BailleulFerdinandTo. (part 1)
3:00 PM
Minicourse: Constructive Quantum Field Theory on manifolds

Nguyen Viet Dang
(
Sorbonne Université
)
Minicourse: Constructive Quantum Field Theory on manifolds
Nguyen Viet Dang
(
Sorbonne Université
)
3:00 PM  4:00 PM
Room: amphithéâtre Yvonne ChoquetBruhat
(part 2)
Tuesday, March 19, 2024
9:30 AM
Minicourse: Constructive Quantum Field Theory on manifolds

Nguyen Viet Dang
(
Sorbonne Université
)
Minicourse: Constructive Quantum Field Theory on manifolds
Nguyen Viet Dang
(
Sorbonne Université
)
9:30 AM  10:30 AM
Room: amphithéâtre Yvonne ChoquetBruhat
(part 3)
11:00 AM
Minicourse: Constructive Quantum Field Theory on manifolds

Nguyen Viet Dang
(
Sorbonne Université
)
Minicourse: Constructive Quantum Field Theory on manifolds
Nguyen Viet Dang
(
Sorbonne Université
)
11:00 AM  12:00 PM
Room: amphithéâtre Yvonne ChoquetBruhat
(part 4)
1:30 PM
Minicourse: Geometry of Killing horizons and applications to black hole physics

Eric Gourgoulhon
(
LUTH, Observatoire de Paris
)
Minicourse: Geometry of Killing horizons and applications to black hole physics
Eric Gourgoulhon
(
LUTH, Observatoire de Paris
)
1:30 PM  2:30 PM
Room: amphithéâtre Yvonne ChoquetBruhat
III. Stationary black holes 1. Stationary spacetimes 2. Black holes in stationary spacetimes 3. Topology theorems 4. Mass and angular momentum 5. Rigidity theorem: the event horizon as a Killing horizon 6. Smarr formula 7. Nohair theorems
3:00 PM
Minicourse: Geometry of Killing horizons and applications to black hole physics

Eric Gourgoulhon
(
LUTH, Observatoire de Paris
)
Minicourse: Geometry of Killing horizons and applications to black hole physics
Eric Gourgoulhon
(
LUTH, Observatoire de Paris
)
3:00 PM  4:00 PM
Room: amphithéâtre Yvonne ChoquetBruhat
IV. Degenerate Killing horizons and their nearhorizon geometry 1. The extremal ReissnerNordström example 2. The scri+ example 3. Nearhorizon geometry of generic extremal black holes
Wednesday, March 20, 2024
9:30 AM
Minicourse: Quantum Field Theory on black hole spacetimes

Stefan Hollands
(
Universität Leipzig
)
Minicourse: Quantum Field Theory on black hole spacetimes
Stefan Hollands
(
Universität Leipzig
)
9:30 AM  10:30 AM
Room: amphithéâtre Yvonne ChoquetBruhat
I will outline the algebraic formulation of linear quantum field theories on globally hyperbolic spacetimes. A characterization of the physically allowed states (Hadamard states) is provided in terms of their shortdistance behavior as well as in terms of wave front sets. The latter concept requires certain notions from microlocal analysis/distribution theory, which are provided in a concise manner. The notion of KMS state is introduced and the relevance of this notion for the Unruheffect in Rindler spacetime, and its counterparts in various other spacetimes with bifurcate Killing horizons, is explained. I will discuss physically relevant states on black hole spacetimes such as the Unruh and Boulware states, including their Hadamard property, and derive the presence of a steady, thermal flux of quantumstressenergy in the Unruh state (Hawking effect). Time permitting, I will outline the algebraic formulation of interacting quantum field theories on globally hyperbolic spacetimes, in the sense of formal power series. (part 1)
11:00 AM
Minicourse: Quantum Field Theory on black hole spacetimes

Stefan Hollands
(
Universität Leipzig
)
Minicourse: Quantum Field Theory on black hole spacetimes
Stefan Hollands
(
Universität Leipzig
)
11:00 AM  12:00 PM
Room: amphithéâtre Yvonne ChoquetBruhat
(part 2)
1:30 PM
Minicourse: Linear waves and spectral theory

Peter Hintz
(
ETH Zürich
)
Minicourse: Linear waves and spectral theory
Peter Hintz
(
ETH Zürich
)
1:30 PM  2:30 PM
Room: amphithéâtre Yvonne ChoquetBruhat
After an introduction to microlocal analysis, I will explain how to describe the longtime behavior of solutions of linear wave equations on spacetimes of interest in General Relativity using spectral theory and resonance expansions. Time permitting, I will also touch upon the asymptotically flat case (Schwarzschild, Kerr). (part 1)
3:00 PM
Minicourse: Linear waves and spectral theory

Peter Hintz
(
ETH Zürich
)
Minicourse: Linear waves and spectral theory
Peter Hintz
(
ETH Zürich
)
3:00 PM  4:00 PM
Room: amphithéâtre Yvonne ChoquetBruhat
(part 2)
Thursday, March 21, 2024
9:30 AM
Minicourse: Constructive Quantum Field Theory on manifolds

Nguyen Viet Dang
(
Sorbonne Université
)
Minicourse: Constructive Quantum Field Theory on manifolds
Nguyen Viet Dang
(
Sorbonne Université
)
9:30 AM  10:30 AM
Room: amphithéâtre Yvonne ChoquetBruhat
(part 5)
11:00 AM
Minicourse: Geometry of Killing horizons and applications to black hole physics

Eric Gourgoulhon
(
LUTH, Observatoire de Paris
)
Minicourse: Geometry of Killing horizons and applications to black hole physics
Eric Gourgoulhon
(
LUTH, Observatoire de Paris
)
11:00 AM  12:00 PM
Room: amphithéâtre Yvonne ChoquetBruhat
V. Handson session: exploring the extremal Kerr nearhorizon geometry with SageMath 1. Introduction to SageMath 2. The extremal Kerr throat 3. NHEK metric 4. Killing vectors and Lie algebra of the isometry group
1:30 PM
Minicourse: Quantum Field Theory on black hole spacetimes

Stefan Hollands
(
Universität Leipzig
)
Minicourse: Quantum Field Theory on black hole spacetimes
Stefan Hollands
(
Universität Leipzig
)
1:30 PM  2:30 PM
Room: amphithéâtre Yvonne ChoquetBruhat
(part 3)
3:00 PM
Minicourse: Quantum Field Theory on black hole spacetimes

Stefan Hollands
(
Universität Leipzig
)
Minicourse: Quantum Field Theory on black hole spacetimes
Stefan Hollands
(
Universität Leipzig
)
3:00 PM  4:00 PM
Room: amphithéâtre Yvonne ChoquetBruhat
(part 4)
Friday, March 22, 2024
9:30 AM
Minicourse: Quantum Field Theory on black hole spacetimes

Stefan Hollands
(
Universität Leipzig
)
Minicourse: Quantum Field Theory on black hole spacetimes
Stefan Hollands
(
Universität Leipzig
)
9:30 AM  10:30 AM
Room: amphithéâtre Yvonne ChoquetBruhat
(part 5)
11:00 AM
Minicourse: Linear waves and spectral theory

Peter Hintz
(
ETH Zürich
)
Minicourse: Linear waves and spectral theory
Peter Hintz
(
ETH Zürich
)
11:00 AM  12:00 PM
Room: amphithéâtre Yvonne ChoquetBruhat
(part 3)
1:30 PM
Minicourse: Linear waves and spectral theory

Peter Hintz
(
ETH Zürich
)
Minicourse: Linear waves and spectral theory
Peter Hintz
(
ETH Zürich
)
1:30 PM  2:30 PM
Room: amphithéâtre Yvonne ChoquetBruhat
(part 4)
3:00 PM
Minicourse: Linear waves and spectral theory

Peter Hintz
(
ETH Zürich
)
Minicourse: Linear waves and spectral theory
Peter Hintz
(
ETH Zürich
)
3:00 PM  4:00 PM
Room: amphithéâtre Yvonne ChoquetBruhat
(part 5)
Saturday, March 23, 2024
Sunday, March 24, 2024
Monday, March 25, 2024
9:30 AM
Estimates for rough wave maps on the Einstein cylinder via Peter—Weyl theory

Grigalius Taujanskas
(
University of Cambridge
)
Estimates for rough wave maps on the Einstein cylinder via Peter—Weyl theory
Grigalius Taujanskas
(
University of Cambridge
)
9:30 AM  10:30 AM
Room: amphithéâtre Yvonne ChoquetBruhat
Nonlinear wave equations of wave maps type are typically expected to be wellposed for initial data just above scaling critical regularity. For wave maps on Minkowski space, this is by now wellunderstood as a consequence of works of Klainerman—Machedon, Tataru, Tao, and others, and effectively relies on sharp null form estimates which exploit the special "null” structure of the nonlinearities. In Fourier space, these estimates capture cancellations between parallel propagating waves. I will introduce a new approach to obtain a wide range of analogous estimates on the Einstein cylinder, where traditional Fourier theory is unavailable, using instead the Lie group structure of SU(2), an emergent periodicity of the conformal wave equation on the Einstein cylinder, and PeterWeyl theory. The estimates we obtain hold for a slightly different set of exponents than in flat space, including edge cases which are forbidden in flat space, with an arbitrarily small loss which we trace down to the noncommutativity of SU(2). Time permitting, I will outline how the estimates may be used to show almost optimal wellposedness of wave maps equations on the Einstein cylinder.
11:00 AM
Semiclassical effects inside black holes

Marc Casals
(
Leipzig University
)
Semiclassical effects inside black holes
Marc Casals
(
Leipzig University
)
11:00 AM  12:00 PM
Room: amphithéâtre Yvonne ChoquetBruhat
All black holes in the Universe are believed to be rotating. This poses interesting questions, since rotating black hole solutions of Einstein’s equations of General Relativity possess a socalled Cauchy horizon in their interior, beyond which Einstein’s equations cease to be predictable (i.e., the Cauchy value problem is no longer wellposed). However, these exact solutions may not model sufficiently accurately black holes in Nature, which have classical matter in their neighbourhood and, furthermore, are inevitably surrounded by a quantum vacuum (which, in the exterior, is responsible for Hawking radiation). It is generally found that effects on Cauchy horizons from quantum fields are in fact dominant over those from classical matter. In this talk, we will present recent results on effects due to a quantum field on the Cauchy horizon of rotating (Kerr and Kerrde Sitter) black holes which are evaporating via the emission of Hawking radiation. In particular, we will show that the (renormalized) fluxes from a quantum scalar field generically diverge on the Cauchy horizon and cause latitudes of infinite twisting separating regions of infinite expansion and contraction for spheres approaching this horizon.
1:30 PM
Minicourse: A primer on celestial holography

Prahar Mitra
(
University of Amsterdam
)
Minicourse: A primer on celestial holography
Prahar Mitra
(
University of Amsterdam
)
1:30 PM  2:30 PM
Room: amphithéâtre Yvonne ChoquetBruhat
Holography in asymptotically flat spacetimes has received much attention recently and has been significantly developed along several different fronts. In one formulation known as celestial holography, quantum gravity in $d+2$dimensional asymptotically flat spacetimes can be reformulated as a conformal field theory that lives on the $d$dimensional celestial sphere. In this minilecture series, I will introduce the basics of celestial holography, starting with an identification of the relevant symmetries of the problem, Ward identities and their relationship to soft theorems, and ending with a discussion of celestial CFTs and their structure. (part 1)
3:00 PM
Minicourse: A primer on celestial holography

Prahar Mitra
(
University of Amsterdam
)
Minicourse: A primer on celestial holography
Prahar Mitra
(
University of Amsterdam
)
3:00 PM  4:00 PM
Room: amphithéâtre Yvonne ChoquetBruhat
(part 2)
Tuesday, March 26, 2024
11:00 AM
Scattering on selfdual black holes

Lionel Mason
(
The Mathematical Institute, University of Oxford
)
Scattering on selfdual black holes
Lionel Mason
(
The Mathematical Institute, University of Oxford
)
11:00 AM  12:00 PM
Room: amphithéâtre Yvonne ChoquetBruhat
Penrose's twistor theory demonstrated that the selfdual sector of Einstein's general relativity is completely integrable. This talk will explain how this can be exploited to generate efficient scattering formulae by developing a perturbation theory about a fully nonlinear selfdual sector rather than around flat space. The talk will focus on the example of a selfdual black hole background. Rather than exploit the twistor theory directly, we find that the complete integrability can be used to solve for linear fields on the bacground using some novel geometric structures, charged helicity raising and lowering operators, whose existence reflects the underlying simplicity of the selfdual sector in this case. As a first step, these generate analogues of momentum eigenstates on the background and are simple enough to complete their nonperturbative twopoint scattering off the background. I will briefly explain how the twistor theory can be used to to extend the construction to give formulae at all multiplicities.
1:30 PM
Minicourse: A primer on celestial holography

Prahar Mitra
(
University of Amsterdam
)
Minicourse: A primer on celestial holography
Prahar Mitra
(
University of Amsterdam
)
1:30 PM  2:30 PM
Room: amphithéâtre Yvonne ChoquetBruhat
(part 3)
3:00 PM
Minicourse: A primer on celestial holography

Prahar Mitra
(
University of Amsterdam
)
Minicourse: A primer on celestial holography
Prahar Mitra
(
University of Amsterdam
)
3:00 PM  4:00 PM
Room: amphithéâtre Yvonne ChoquetBruhat
(part 4)
Wednesday, March 27, 2024
11:00 AM
Sheaves for spacetime

Pierre Schapira
(
Univ Paris 6
)
Sheaves for spacetime
Pierre Schapira
(
Univ Paris 6
)
11:00 AM  12:00 PM
Room: amphithéâtre Yvonne ChoquetBruhat
We shall study the Cauchy problem on globally hyperbolic manifolds with the only tools of microlocal sheaf theory and the precise CauchyKowalevski theorem. A causal manifold is a manifold $M$ endowed with a closed convex proper cone $\lambda\subset T^*M$. On such a manifold, one defines the $\lambda$topology and the associated notions of a causal preorder and a causal path. One introduces the notion of a Gcausal manifold, those for which there exists a time function. On a Gmanifold, sheaves satisfying a suitable condition on their microsupport and defined on a neigborhood of a Cauchy hypersurface extend to the whole space. When the sheaf is the complex of hyperfunction solutions of a hyperbolic $\mathcal{D}$module, this proves that the Cauchy problem is globally wellposed. We will also describe a "shifted spacetime" associated with the quantization of an Hamiltonian isotopy. This talk is partly based on papers in collaboration with Benoît Jubin, Stéphane Guillermou and Masaki Kashiwara.
1:30 PM
Asymptotic symmetries and log soft theorems in gauge theories and gravity

Sangmin Choi
(
University of Amsterdam
)
Asymptotic symmetries and log soft theorems in gauge theories and gravity
Sangmin Choi
(
University of Amsterdam
)
1:30 PM  2:30 PM
Room: amphithéâtre Yvonne ChoquetBruhat
In the last few years, a remarkable link has been established between the soft theorems and asymptotic symmetries of quantum field theories: soft theorems are Ward identities of the asymptotic symmetry generators. In particular, the treelevel subleading soft theorems are the Ward identities of the subleading asymptotic symmetries of the theory, for instance divergent gauge transformation in QED and superrotation in gravity. However, it is known that the subleading soft theorems receive quantum corrections with logarithmic dependence on the soft photon/graviton energy. It is therefore natural to ask how the quantum effects affect the classical (treelevel) symmetry interpretation. In this talk, we explore this question in the context of scalar QED and perturbative quantum gravity, and show that the logarithmic soft theorems are the Ward identities of subleading asymptotic symmetries that arise from relaxed boundary conditions which take longrange interactions into account.
3:00 PM
Minicourse: A primer on celestial holography

Prahar Mitra
(
University of Amsterdam
)
Minicourse: A primer on celestial holography
Prahar Mitra
(
University of Amsterdam
)
3:00 PM  4:00 PM
Room: amphithéâtre Yvonne ChoquetBruhat
(part 5)
Thursday, March 28, 2024
10:15 AM
Modular Theory: How and Why

Vojkan Jakšić
(
McGill University
)
Modular Theory: How and Why
Vojkan Jakšić
(
McGill University
)
10:15 AM  11:00 AM
Room: amphithéâtre Yvonne ChoquetBruhat
In this talk I will review the TomitaTakesaki modular theory from both mathematical and physical perspective and discuss some recent developments in nonequilibrium quantum statistical mechanics of open quantum systems where this theory has played a central role. The talk is dedicated to the memory of Huzihiro Araki. [See also Araki's lecture at McGill in the links.] (part 1)
11:15 AM
Modular Theory: How and Why

Vojkan Jakšić
(
McGill University
)
Modular Theory: How and Why
Vojkan Jakšić
(
McGill University
)
11:15 AM  12:00 PM
Room: amphithéâtre Yvonne ChoquetBruhat
(part 2)
1:30 PM
Carrollian amplitudes in flat space holography

Romain Ruzziconi
(
University of Oxford
)
Carrollian amplitudes in flat space holography
Romain Ruzziconi
(
University of Oxford
)
1:30 PM  2:30 PM
Room: amphithéâtre Yvonne ChoquetBruhat
Carrollian holography aims to express gravity in asymptotically flat spacetime in terms of a dual Carrollian CFT living at null infinity. In this talk, I will review how Carrollian geometry arises at the conformal boundary of asymptotically flat spacetimes. I will then discuss some aspects of Carrollian holography and argue that this approach is naturally related to the AdS/CFT correspondence via a flat limit procedure. I will introduce the notion of Carrollian amplitude, which allows to encode massless scattering amplitudes into boundary correlators, and describe its connection to celestial amplitudes.
3:00 PM
Classical superselection sectors, memory and soft symmetries from Hamiltonian reduction by stages in gauge theory

Michele Schiavina
(
University of Pavia
)
Classical superselection sectors, memory and soft symmetries from Hamiltonian reduction by stages in gauge theory
Michele Schiavina
(
University of Pavia
)
3:00 PM  4:00 PM
Room: amphithéâtre Yvonne ChoquetBruhat
In recent years, increasing attention has been drawn to the behaviour of field theory with local (gauge) symmetries on manifolds with boundary and corners. On the physics side, this has led to the discovery of a relation between perturbative scattering results (e.g. Weinberg’s “soft photon” theorems) and certain soft/asymptotic/large gauge symmetries, with their associated conserved charges. However, on the mathematics side we have been lacking an exhaustive explanation of these phenomena. In this talk I will attempt to provide one, through an application of Hamiltonian reduction by stages to gauge moduli problems in the presence of higher codimension strata, which is enabled by the existence of a particular normal gauge subgroup, and it is natural from a physical standpoint. The “first stage” implements the constraint reduction/moduli space of the gauge theory. Conversely, the residual momentum map governing further stages has generally no physicallypreferred value, leading to the classical counterpart of the “superselection sectors” encountered in algebraic quantum field theory, here interpreted as symplectic leaves of the fullyreduced (Poisson) phase space. As an example within this framework, I will describe the Hamiltonian assignment to a null manifold with boundary in Yang—Mills theory, and show how it provides a purely Hamiltonian explanation of the emergence of soft symmetries, and how the electromagnetic memory (or a nonAbelian counterpart thereof) is recovered as (a part of) the residual momentum map. In passing, I will describe how the Ashtekar—Streubel phase space, usually treated as the true reduced phase space of the theory, is instead the result of a partial reduction. This is based on joint work with A. Riello.
Friday, March 29, 2024
11:00 AM
The renormalized volume of 3dimensional hyperbolic manifolds

JeanMarc Schlenker
(
Université du Luxembourg
)
The renormalized volume of 3dimensional hyperbolic manifolds
JeanMarc Schlenker
(
Université du Luxembourg
)
11:00 AM  12:00 PM
Room: amphithéâtre Yvonne ChoquetBruhat
Conformally compact Einstein manifolds have infinite volume, but a welldefined notion of renormalized volume, introduced by theoretical physicists. For 3dimensional hyperbolic manifolds, this notion has interesting relations to other quantities studied by geometers, such as the volume of the convex core and the bending lamination on its boundary. We will describe how the relation between the physics and the mathematics points of view can bring new perspectives on both sides.
1:30 PM
Stability of spacetimes with supersymmetric compactifications

Lars Andersson
(
BIMSA
)
Stability of spacetimes with supersymmetric compactifications
Lars Andersson
(
BIMSA
)
1:30 PM  2:30 PM
Room: amphithéâtre Yvonne ChoquetBruhat
Spacetimes with compact directions, which have special holonomy such as CalabiYau spaces, play an important role in supergravity and string theory. In this talk I will discuss the global, nonlinear stability for the vacuum Einstein equations on a spacetime which is a cartesian product of a high dimensional Minkowski space with a compact Ricci flat internal space with special holonomy. I will start by giving a brief overview of related stability problems which have received a lot of attention recently, including the black hole stability problem. This is based on joint work with Pieter Blue, Zoe Wyatt and ShingTung Yau.
Saturday, March 30, 2024
Sunday, March 31, 2024
Monday, April 1, 2024
Tuesday, April 2, 2024
11:00 AM
Conformal Kähler geometry and nonvacuum gravitational instantons

Bernardo Araneda
(
MPI (Albert Einstein Institute)
)
Conformal Kähler geometry and nonvacuum gravitational instantons
Bernardo Araneda
(
MPI (Albert Einstein Institute)
)
11:00 AM  12:00 PM
Room: amphithéâtre Yvonne ChoquetBruhat
Gravitational instantons are fourdimensional Riemannian geometries introduced by Hawking for the study of quantum fields on curved backgrounds and Euclidean Quantum Gravity. Their complete classification is a challenging open problem in geometry. After briefly reviewing recent developments in the Ricciflat case, we will give a framework based on complex geometry that leads to major simplifications in the study of nonRicciflat instantons. Applications include generalisations of the ChenTeo geometry (a recent counterexample to the Euclidean black hole uniqueness conjecture).
1:30 PM
Simplifying harmonic gauge perturbations around black holes

Igor Khavkine
(
Czech Academy of Sciences
)
Simplifying harmonic gauge perturbations around black holes
Igor Khavkine
(
Czech Academy of Sciences
)
1:30 PM  2:30 PM
Room: amphithéâtre Yvonne ChoquetBruhat
I will review a method of simplifying the separated equations of Maxwell and linear gravitational perturbations around a Schwarzschild black hole. The simplified form is a sparse upper triangular coupling of a system of ReggeWheeler equations. The method takes advantage of a specific notion of equivalence between differential equations and of the special structure of ODEs with rational coefficients. I will also discuss the prospects of applying similar methods to the Kerr black hole.
Wednesday, April 3, 2024
11:00 AM
Stringlocalized quantum field theory  some ideas and perspectives

Lucas Tavares Cardoso
(
Federal University of Santa Maria
)
Stringlocalized quantum field theory  some ideas and perspectives
Lucas Tavares Cardoso
(
Federal University of Santa Maria
)
11:00 AM  12:00 PM
Room: amphithéâtre Yvonne ChoquetBruhat
The construction of stringlocalized free fields was rigorously accomplished almost twenty years ago. In this approach, the fields are operators in some Hilbert space, and therefore there are no unphysical degrees of freedom such as ghosts. In addition to allowing the construction of the fields entirely in a Hilbert space, the stringlocalized fields exhibit, in general, a good behavior in the ultraviolet regime and, among other features, the class (representation) of stringlocalized fields with m = 0 and s = ∞ are possible candidates to consistently describe dark matter. The interaction picture is obtained perturbatively via the BogolyubovEpsteinGlaser scheme together with the requirement that the Smatrix be string independent. This talk is intended to show some of the distinguishing features of sQFT along with future perspectives.
1:30 PM
A spin correction to Coulomb interaction based on KerrNewmann solution

Sajad Aghapour
(
Max Planck Institute for Gravitational Physics (AEI)
)
A spin correction to Coulomb interaction based on KerrNewmann solution
Sajad Aghapour
(
Max Planck Institute for Gravitational Physics (AEI)
)
1:30 PM  2:30 PM
Room: amphithéâtre Yvonne ChoquetBruhat
The complex shift introduced by Appell and used by Sommerfeld and Synge in introducing a nontrivial electromagnetic field with a ring singularity from the Coulomb field has an intimate relation to the NewmanJanis transformation in the context of exact solutions of GR. Such a constructed electromagnetic field, called the magic field by LyndenBell, coincides with the electromagnetic sector of the KerrNewman solution of EinsteinMaxwell theory. The Riemann surface of the analytic continuation of the magic field matches the analytic extension of massless Kerr or zeroG limit of KerrNewman. This field is also referred to as the square root of Kerr in more recent works on doublecopy formalism. After briefly reviewing some of these points in this talk, I will report the results of calculating the interaction Lagrangian of two magic fields in a static situation, which will correct the Coulomb interaction with respect to the spin of the fields.
Thursday, April 4, 2024
11:00 AM
An Introduction to Quantum Fields and Local Measurements

Rainer Verch
(
Universität Leipzig
)
An Introduction to Quantum Fields and Local Measurements
Rainer Verch
(
Universität Leipzig
)
11:00 AM  12:00 PM
Room: amphithéâtre Yvonne ChoquetBruhat
An introduction to quantum field measurement in the local covariant framework of quantum field theory will be given. Concepts such as the local dynamical coupling between "system" and "probe" will be discussed, as well as selective and nonselective state updates following probe measurements. Furthermore, Sorkin’s impossible measurement scenario will be sketched, and it will be argued that the impossible measurements of this scenario are also present in classical relativistic field theory. The material of this talk is based on joint works with C.J. Fewster (arXiv:1810.06512 and 2304.13356) and with A. Much (arXiv:2308.16673).
1:30 PM
Microlocal analysis near null infinity on asymptotically flat spacetimes

András Vasy
(
Stanford University
)
Microlocal analysis near null infinity on asymptotically flat spacetimes
András Vasy
(
Stanford University
)
1:30 PM  2:30 PM
Room: amphithéâtre Yvonne ChoquetBruhat
There are a number of reasons due to which it is advantageous to have a phase space based, or microlocal, approach available for analyzing wave propagation. In this talk I will explain a microlocal framework for wave propagation on asymptotically flat spacetimes of arbitrary dimension which in particular includes operator corresponding to Lorentzian metrics arising from solutions of Einstein’s equations in the 4 spacetime dimensional setting. On the compactification of Minkowski space that underlies this, which is a manifold with corners (with the usual null infinity, scri, being a boundary hypersurface), the operators lie in a combination of Melrose’s totally characteristic (also called b), and Mazzeo’s edge pseudodifferential operator algebras. I will give an introduction via a simpler setting (which includes Minkowski space and a different class of perturbations), and then explain the reasons for, and complications with, moving to the present setting. Along the way, I will also briefly describe the related KleinGordon work of Ethan Sussman. This is joint work with Peter Hintz.
Friday, April 5, 2024
11:00 AM
Quantum fields on rotating black holes

Christiane Klein
(
Université Grenoble Alpes
)
Quantum fields on rotating black holes
Christiane Klein
(
Université Grenoble Alpes
)
11:00 AM  12:00 PM
Room: amphithéâtre Yvonne ChoquetBruhat
Since astrophysical black holes are expected to be rotating, one would like to study quantum fields on such spacetimes. In this talk, we lay some of the mathematical foundations for this endeavor. We construct a physically motivated state, the Unruh state, for the free scalar quantum field on Kerr de Sitter and show that it is a Hadamard state. Moreover, we demonstrate that a similar construction for fermions on Kerr results in a Hadamard state for any subextremal black hole, extending previous results for small angular momentum. Finally, we discuss the divergence of the stressenergy tensor of the quantum scalar field towards the Cauchy horizon. We show that the leading divergence has a universal, stateindependent behaviour, even in rotating black hole spacetimes, as long as there is a nonzero spectral gap for the corresponding equation of motion.
Saturday, April 6, 2024
Sunday, April 7, 2024
Monday, April 8, 2024
9:00 AM
Welcome / registration / coffee
Welcome / registration / coffee
9:00 AM  9:15 AM
Room: espace cafétéria (ground floor)
9:15 AM
The second law of black hole mechanics in effective field theory

Harvey Reall
(
University of Cambridge
)
The second law of black hole mechanics in effective field theory
Harvey Reall
(
University of Cambridge
)
9:15 AM  10:10 AM
Room: amphithéâtre Hermite
The laws of black hole mechanics are an important part of the identification of black holes as thermodynamic objects. If this is correct then these laws should be robust against the inclusion of higher derivative corrections to the Einstein equation. For the first law, this was confirmed by the work of Wald et al in the early 1990s, which provides a definition of the entropy of a stationary black hole solution of any diffeomorphism invariant theory. But it has remained an open problem to generalize this to obtain a definition of dynamical black hole entropy, that satisfies a second law of black hole mechanics. I shall describe a solution to this problem. The key ingredient is to treat higher derivative terms according to the rules of effective field theory.
10:10 AM
Coffee break
Coffee break
10:10 AM  10:40 AM
10:40 AM
The nonlinear stability of slowly rotating black holes

Sergiu Klainerman
(
Princeton University
)
The nonlinear stability of slowly rotating black holes
Sergiu Klainerman
(
Princeton University
)
10:40 AM  11:35 AM
Room: amphithéâtre Hermite
My talk will focus on the recent resolution of the Kerr stability conjecture for the particular case of slowly rotating Kerr black holes.
11:35 AM
Burnett's conjecture in General Relativity

Cécile Huneau
(
CNRS et Ecole Polytechnique
)
Burnett's conjecture in General Relativity
Cécile Huneau
(
CNRS et Ecole Polytechnique
)
11:35 AM  12:30 PM
Room: amphithéâtre Hermite
In this talk, I will present a work in collaboration with Jonathan Luk, on the behaviour of weak limits of solutions to Einstein equations. In 1989, Burnett conjectured that a metric, obtained as a uniform limit of solutions to Einstein vacuum equation, whose derivatives converge only weakly, is a solution to Einstein massless Vlasov equations. This conjecture has been back in the spotlight with the work of Green and Wald on perturbations in cosmology. In a recent work with Jonathan Luk, we prove this conjecture, without symmetry assumption, in generalized wave coordinates.
12:30 PM
Lunch break
Lunch break
12:30 PM  2:30 PM
2:30 PM
Null Infinity Is a Weakly Isolated Horizon!

Abhay Ashtekar
(
Penn State
)
Null Infinity Is a Weakly Isolated Horizon!
Abhay Ashtekar
(
Penn State
)
2:30 PM  3:25 PM
Room: amphithéâtre Hermite
Null infinity, $\mathcal{I}^+$, arises as a boundary of the Penrose conformal completion $(\hat{M}, \hat{g}_{ab})$ of an asymptotically flat physical spacetime $(M, g_{ab})$. I will begin by pointing out that $\mathcal{I}^+$ is a weakly isolated horizon (WIH) in $(\hat{M}, \hat{g}_{ab})$, and then show that all its familiar properties can be derived from the general WIH framework. This seems quite surprising because physics associated with black hole (and cosmological) WIHs $\Delta$ is very different from that extracted at $\mathcal{I}^+$. These differences can be directly traced back to the fact that while Einstein's equations hold at $\Delta$, conformal Einstein's equations hold at $\mathcal{I}^+$. In particular, the BMS group at $\mathcal{I}^+$ stems from the symmetry group of WIHs. There is also a unified procedure to arrive at fluxes and charges associated with the BMS symmetries at $\mathcal{I}^+$ and those associated with the symmetries at $\Delta$. This procedure differs from those commonly used in the literature and its novel elements seem interesting in their own right. This subtle interplay between geometry and physics is reminiscent of a musical fugue. The fact that is there is a single mathematical framework underlying $\Delta$ and $\mathcal{I}^+$ paves the way to explore the relation between horizon dynamics in the strong field region and waveforms at infinity. It should also be useful in the analysis of black hole evaporation in quantum gravity. This work was carried out in collaboration with Simone Speziale and supported by Eberly and Atherton Funds of Penn State and the DVRC program of the Perimeter Institute.
3:25 PM
Coffee break
Coffee break
3:25 PM  3:55 PM
3:55 PM
Black Holes Decohere Quantum Superpositions

Robert Wald
(
University of Chicago
)
Black Holes Decohere Quantum Superpositions
Robert Wald
(
University of Chicago
)
3:55 PM  4:50 PM
Room: amphithéâtre Hermite
We show that if a massive body is put in a quantum superposition of spatially separated states, the mere presence of a black hole in the vicinity of the body will eventually destroy the coherence of the superposition. This occurs because, in effect, the gravitational field of the body radiates soft gravitons into the black hole, allowing the black hole to harvest "which path'' information about the superposition. A similar effect occurs for quantum superpositions of electrically charged bodies. The effect is very closely related to the memory effect and infrared divergences at null infinity.
Tuesday, April 9, 2024
9:15 AM
The Euclidean vacuum state for linearized gravity on de Sitter spacetime

Christian Gérard
(
Université ParisSaclay
)
The Euclidean vacuum state for linearized gravity on de Sitter spacetime
Christian Gérard
(
Université ParisSaclay
)
9:15 AM  10:10 AM
Room: amphithéâtre Hermite
We will explain the construction of the euclidean vacuum state for linearized gravity on de Sitter spacetime by a rigorous version of Wick rotation. We will discuss issues related to gauge invariance, positivity and invariance under de Sitter isometries.
10:10 AM
Coffee break
Coffee break
10:10 AM  10:40 AM
10:40 AM
On attempts and progresses towards proving the de Sitter no hair theorem using mean curvature flow

Leonardo Senatore
(
ETH Zürich
)
On attempts and progresses towards proving the de Sitter no hair theorem using mean curvature flow
Leonardo Senatore
(
ETH Zürich
)
10:40 AM  11:35 AM
Room: amphithéâtre Hermite
I will review how mean curvature flow is providing progress towards proving the socalled de Sitter nohair theorem, concerning the onset of a de Sitter phase of the universe out of inhomogenous initial conditions. This is relevant for the initial condition of Inflation in our universe.
11:35 AM
Gluing variation

Piotr Chruściel
(
University of Vienna
)
Gluing variation
Piotr Chruściel
(
University of Vienna
)
11:35 AM  12:30 PM
Room: amphithéâtre Hermite
I will review various ways of constructing spacetimes of interest using spacelike and gluing constructions methods
12:30 PM
Lunch break
Lunch break
12:30 PM  2:30 PM
2:30 PM
Asymptotics of Dynamical Spacetimes and Radiation

Lydia Bieri
(
University of Michigan
)
Asymptotics of Dynamical Spacetimes and Radiation
Lydia Bieri
(
University of Michigan
)
2:30 PM  3:25 PM
Room: amphithéâtre Hermite
In this talk, I will discuss some results on the asymptotic behavior and radiation for a general class of spacetimes. This will include results on gravitational radiation and memory for sources that are not stationary outside of a compact set, but whose gravitational fields decay more slowly towards infinity. We will also show that angular momentum at future null infinity is well defined for asymptoticallyflat spacetimes with a term homogeneous of degree 1 in the initial data metric, that is it may include a nonisotropic mass term. Finally, we will also discuss peeling (that is, how peeling stops) for the Weyl curvature components at future null infinity for these spacetimes.
3:25 PM
Coffee break
Coffee break
3:25 PM  3:55 PM
3:55 PM
On the Feynman propagator on curved spacetimes

Jan Dereziński
(
University of Warsaw
)
On the Feynman propagator on curved spacetimes
Jan Dereziński
(
University of Warsaw
)
3:55 PM  4:50 PM
Room: amphithéâtre Yvonne ChoquetBruhat
The Feynman propagator is one of the main tools of Quantum Field Theory. I will review various definitions of this concept, including the operatortheoretic and outin Feynman propagator. I will discuss various examples of spacetimes: stationary, asymptotically stationary, FLRW, de Sitter and antide Sitter. I will consider both the stable and tachyonic case. Based on joint work with Christian Gass.
6:00 PM
Cocktail
Cocktail
6:00 PM  9:00 PM
Room: Cafeteria Space
Wednesday, April 10, 2024
9:15 AM
Secular growths and their relation to Equilibrium states in perturbative Quantum Field Theories

Nicola Pinamonti
(
University of Genova
)
Secular growths and their relation to Equilibrium states in perturbative Quantum Field Theories
Nicola Pinamonti
(
University of Genova
)
9:15 AM  10:10 AM
Room: amphithéâtre Hermite
During this talk we discuss the emergence of secular growths in the correlation functions of interacting quantum field theories when treated with perturbation methods. It is known in the literature that these effects are present if the interaction Lagrangian density changes adiabatically in a finite interval of time. If this happens, the perturbative approach cannot furnish reliable results in the evaluation of scattering amplitudes or in the evaluation of various expectation values. We show, during this talk, that these effects can be avoided for adiabatically switchedon interactions, if the spatial support of the interaction is compact and if the background state is suitably chosen. In particular, this is the case when the background state is chosen to be at equilibrium and when thermalisation occurs at late time. The same result holds also if the background state is only invariant under time translation or if the explicit time dependence is not too strong, in a precise sense which will be discussed in the talk. (based on Galanda, Pinamonti, Sangaletti [arXiv: 2312.00556])
10:10 AM
Coffee break
Coffee break
10:10 AM  10:40 AM
10:40 AM
Bounds for the local entropy

Roberto Longo
(
University of Rome Tor Vergata
)
Bounds for the local entropy
Roberto Longo
(
University of Rome Tor Vergata
)
10:40 AM  11:35 AM
Room: amphithéâtre Hermite
11:35 AM
Nonminimal coupling, negative null energy, and effective field theory

Eleni Alexandra Kontou
(
King's College London
)
Nonminimal coupling, negative null energy, and effective field theory
Eleni Alexandra Kontou
(
King's College London
)
11:35 AM  12:30 PM
Room: amphithéâtre Hermite
Even classical scalar fields, nonminimally coupled with the curvature, can violate energy conditions such as the null energy condition. In the context of quantum field theory, nonminimally coupled scalars can obey lower bounds, known as quantum energy inequalities, but these are always state dependent. In this talk I will discuss classical and quantum bounds on the null energy and consider possible violations. Further, I will examine the conformal transformation between Jordan and Einstein frames both classically and semiclassically. Finally, I will comment on extensions of this work and connections with selfinteracting fields.
12:30 PM
Lunch break
Lunch break
12:30 PM  2:30 PM
2:30 PM
Progress on the definition of asymptotically flat and de Sitter spacetimes

Geoffrey Compère
(
Université Libre de Bruxelles
)
Progress on the definition of asymptotically flat and de Sitter spacetimes
Geoffrey Compère
(
Université Libre de Bruxelles
)
2:30 PM  3:25 PM
Room: amphithéâtre Hermite
The definition of scattering in asymptotically flat spacetimes requires to consistently match its five asymptotic boundaries: past/future timelike infinity, past/future null infinity and spatial infinity. I will present a framework consistent with logarithmic corrections to soft theorems where a single BMS group acts on all boundaries and where individual ingoing/outgoing bodies are ascribed initial/final BMS charges. Using the postMinkowskian expansion, I will demonstrate that nonradiative regions are entirely characterized by a set of conserved celestial charges that consist of the GerochHansen multipole moments, the generalized BMS charges and additional nonstationary multipole moments. In the context of asymptotically de Sitter spacetimes, I will finally demonstrate that the presence of a quadrupole moment of any localized source in de Sitter leads to a fluctuating boundary metric that breaks the conformal asymptotic symmetry group. Dynamical Einstein gravity in de Sitter cannot therefore be modelled by a 3d CFT. Based on work performed with S. Gralla, H. Wei, R. Oliveri, A. Seraj, L. Blanchet, G. Faye, J. Hoque and E. Kutluk.
3:25 PM
Coffee break
Coffee break
3:25 PM  3:55 PM
3:55 PM
Metric reconstruction

Stefan Hollands
(
Universität Leipzig
)
Metric reconstruction
Stefan Hollands
(
Universität Leipzig
)
3:55 PM  4:50 PM
Room: amphithéâtre Hermite
I will review recent developments in metric reconstruction theory, i.e., the task of parameterizing GR in terms of a single complex scalar field. I will focus on the GHZ (after Green, Hollands, Zimmerman) procedure of solving the sourced linearized (or $n$th perturbative order) Einstein equations in Kerr in terms of a Hertz potential. Time permitting, I will also outline other reconstruction methods such as ones based on the Lorenz gauge due to Dolan et al., or the AAB method (after Aksteiner, Anderson, Bäckdahl).
5:15 PM
How to observe quantum effects on curved spacetimes?
How to observe quantum effects on curved spacetimes?
5:15 PM  6:15 PM
Room: amphithéâtre Darboux
Thursday, April 11, 2024
9:15 AM
The timelike tube theorem and analytic vectors in QFT

Alexander Strohmaier
(
Universität Hannover
)
The timelike tube theorem and analytic vectors in QFT
Alexander Strohmaier
(
Universität Hannover
)
9:15 AM  10:10 AM
Room: amphithéâtre Hermite
The BrosIagolnitzer analysis of analytic singularities in QFT can be generalised to analytic curved spacetimes via the notion of the analytic wavefront set and the analytic microsupport. I will start with an elementary introduction into the topic and basic definitions. I will give some physics intuition that motivates the introduction of analytic states and will show that one can prove the timelike tube theorem in quantum field theory on curved spacetimes under plausible assumptions. I will also discuss some modified notions of analytic singularities that capture the structure of the npoint functions at infinity. (Joint work with E. Witten)
10:10 AM
Coffee break
Coffee break
10:10 AM  10:40 AM
10:40 AM
Imaginary Liouville conformal field theory

Colin Guillarmou
(
Univ. Paris Saclay & CNRS
)
Imaginary Liouville conformal field theory
Colin Guillarmou
(
Univ. Paris Saclay & CNRS
)
10:40 AM  11:35 AM
Room: amphithéâtre Hermite
Conformal field theory in dim 2 allows to describe scaling limits of many statistical physics models, such as Ising model and its variants. CFT are parametrized by their central charge and conformal weights. We construct using probability (and in particular the compactified boson) a whole family of conformal field theories with central charge c<1 and discrete spectrum, which sets to be a good candidate to describe scaling limits of many statistical physics models, including nonunitary and logarithmic CFT, loop models. Joint work with Kupiainen and Rhodes.
11:35 AM
Wave propagators and traces on singular spaces

Jared Wunsch
(
Northwestern University
)
Wave propagators and traces on singular spaces
Jared Wunsch
(
Northwestern University
)
11:35 AM  12:30 PM
Room: amphithéâtre Hermite
I will give a survey of recent progress in understanding wave and Schrödinger propagators in the presence of various kinds of geometric and analytic singularities; these singularities have the effect of diffracting energy of waves interacting with them, and thus may have a significant effect on scattering phenomena. In some cases we are able to understand the effects of diffractive propagation on existence of scattering resonances; one of the important tools here is a trace formula. I will, as time permits, discuss such results for conic singularities (joint with Melrose, MelroseVasy, Baskin, Ford, Hillairet); for the DiracCoulomb problem (joint with Baskin, BaskinWrochna); for rotating cosmic string spacetimes (joint with Morgan); and for semiclassical Schrödinger operators with singular potentials (joint with Gannot, Galkowski, YangZou).
12:30 PM
Lunch break
Lunch break
12:30 PM  2:30 PM
2:30 PM
New proposal for Lorentzian renormalisation group flow equations on curved spacetimes

Kasia Rejzner
(
University of York
)
New proposal for Lorentzian renormalisation group flow equations on curved spacetimes
Kasia Rejzner
(
University of York
)
2:30 PM  3:25 PM
Room: amphithéâtre Hermite
In this talk I will present recent results obtained in collaboration with d’Angelo, Drago and Pinamonti. We proposed a new formulation of renormalisation group flow equations that work on arbitrary globally hyperbolic spacetimes and for any chosen Hadamard state. The examples treated so far include the scalar field, YangMills theories and gravity.
3:25 PM
Coffee break
Coffee break
3:25 PM  3:55 PM
3:55 PM
Scattering for wave equations with sources and slowly decaying data

Hans Lindblad
(
Johns Hopkins University
)
Scattering for wave equations with sources and slowly decaying data
Hans Lindblad
(
Johns Hopkins University
)
3:55 PM  4:50 PM
Room: amphithéâtre Hermite
We construct solutions with prescribed radiation fields for wave equations with polynomially decaying sources close to the lightcone. In this setting, which is motivated by semilinear wave equations satisfying the weak null condition, solutions to the forward problem have a logarithmic leading order term on the lightcone and nontrivial homogeneous asymptotics in the interior of the lightcone. The backward scattering solutions we construct from knowledge of the source and the radiation field at null infinity alone are given to second order by explicit asymptotic solutions which satisfy novel matching conditions close to the light cone. This requires a delicate analysis close to the light cone of the forward solution with sources on the light cone. We also relate the asymptotics of the radiation field towards spacelike infinity to explicit homogeneous solutions in the exterior of the light cone for slowly polynomially decaying data corresponding to mass, charge and angular momentum in the applications. The somewhat surprising discovery is that these data can cause the same logarithmic radiation field as the source term. This requires a delicate analysis of the forward homogeneous solution close to the light cone using the invertibility of the Funk transform. This is joint work with Volker Schlue.
Friday, April 12, 2024
9:15 AM
Interplay between Stochastic Partial Differential Equations and Quantum Field Theory on Curved Backgrounds

Claudio Dappiaggi
(
University of Pavia
)
Interplay between Stochastic Partial Differential Equations and Quantum Field Theory on Curved Backgrounds
Claudio Dappiaggi
(
University of Pavia
)
9:15 AM  10:10 AM
Room: amphithéâtre Hermite
We review a novel framework for the study of a large class of nonlinear stochastic partial differential equations (SPDEs), which is inspired by microlocal analysis and by the algebraic approach to quantum field theory (AQFT). In particular, we show that AQFT and SPDEs share similar problems, most notably the existence of pathological divergences. These are dealt with adapting to this framework the EpsteinGlaser renormalization procedure which is used in the analysis of locally covariant quantum field theories. As a concrete example we shall discuss the stochastic $\Phi^3_d$ model and we shall comment on its applicability to other models such as the stochastic nonlinear Schrödinger equation, the stochastic sineGordon equation as well as the stochastic Thirring equation. Based on joint works with A. Bonicelli, B. Costeri, N. Drago, P. Rinaldi and L. Zambotti
10:10 AM
Coffee break
Coffee break
10:10 AM  10:40 AM
10:40 AM
Double copy and soft limits in (A)dS

Arthur Lipstein
(
Durham University
)
Double copy and soft limits in (A)dS
Arthur Lipstein
(
Durham University
)
10:40 AM  11:35 AM
Room: amphithéâtre Hermite
The study of the double copy relating gluon to graviton amplitudes and their soft limits has been a major driving force in the study of scattering amplitudes in flat space. I will describe recent progress in generalising these ideas to (A)dS, which may have interesting implications for holography and cosmology.
11:35 AM
Local measurement theory for quantum fields

Christopher Fewster
(
University of York
)
Local measurement theory for quantum fields
Christopher Fewster
(
University of York
)
11:35 AM  12:30 PM
Room: amphithéâtre Hermite
Many presentations of quantum mechanics include a postulate that the state of a system undergoes an instantaneous change following a measurement. This is clearly incompatible with special and general relativity and raises questions concerning the description of measurement in quantum field theory (QFT). Attempts to extend measurement postulates to QFT by hand have produced pathologies, such as the "impossible measurements" described long ago by Sorkin. I will present a recent operational approach to these questions, which models measurement of one quantum field (the system) by coupling it to another (the probe). This is all accomplished in a modelindependent way within algebraic quantum field theory (AQFT). The resulting framework provides a description of measurement in QFT that is causal, covariant and consistent, and includes state update rules that are derived from the formalism, and works equally well in flat or curved spacetimes. As well as covering the basics of the formalism I will touch on some more recent developments, including asymptotic measurement schemes, and how one may describe Bell inequality violation in this framework. The talk is mostly based on joint works with Rainer Verch, Henning Bostelmann, Maximilian Ruep and Ian Jubb.
12:30 PM
Lunch break
Lunch break
12:30 PM  2:30 PM
2:30 PM
The Klein—Gordon equation on asymptotically flat spacetimes

Dean Baskin
(
Texas A&M University
)
The Klein—Gordon equation on asymptotically flat spacetimes
Dean Baskin
(
Texas A&M University
)
2:30 PM  3:25 PM
Room: amphithéâtre Hermite
We consider the Klein—Gordon equation on Minkowski space with a potential that decays suitably fast in spatial directions and approaches a limiting potential as $t$ tends to infinity. The aim of this talk is to describe a global construction of the Feynman inverse for this problem. This is joint work with Moritz Doll and Jesse GellRedman (Melbourne).
3:25 PM
Coffee break
Coffee break
3:25 PM  3:55 PM
3:55 PM
The Calderón and nonlinear scattering problems for wave equations

Spyros Alexakis
(
University of Toronto
)
The Calderón and nonlinear scattering problems for wave equations
Spyros Alexakis
(
University of Toronto
)
3:55 PM  4:50 PM
Room: amphithéâtre Hermite
We present results on reconstruction of linear and nonlinear wave operators from knowledge of their near field and far field effect on incoming waves. Connections with unique continuation and nonlinear Goursat problems will be made. Based on joint work with Ali Feizomohammadi, Lauri Oksanen, Hiroshi Isozaki, Matti Lassas, and Teemu Tyni.
Saturday, April 13, 2024
Sunday, April 14, 2024
Monday, April 15, 2024
1:30 PM
KaluzaKlein theories without a priori fibration hypotheses

Frédéric Hélein
(
Université Paris Cité, IMJPRG
)
KaluzaKlein theories without a priori fibration hypotheses
Frédéric Hélein
(
Université Paris Cité, IMJPRG
)
1:30 PM  2:30 PM
Room: amphithéâtre Yvonne ChoquetBruhat
I will present a theory based on a variational principle, the critical points of which lead to solutions of the EinsteinYangMills equations, in the spirit of KaluzaKlein theories. The novelty is that the a priori fibration hypothesis is not required: fields are defined on a "spacetime" $Y$ of dimension $4+r$ without a priori principal bundle structure, where $r$ is the dimension of the structure group. If this group is compact and simply connected solutions it allows to construct a 4dimensional manifold $X$ which can be interpreted as our spacetime, in such a way that $Y$ acquires a principal bundle structure over $X$ and produce solutions of the EinsteinYangMills system. If the structure group is $U(1)$ (the case which corresponds to the EinsteinMaxwell system) the situation is slightly degenerated and supplementary hypotheses are necessary.
Tuesday, April 16, 2024
11:00 AM
Leadingorder term expansion for the Teukolsky equation on subextremal Kerr black holes

Pascal Millet
(
Ecole Polytechnique
)
Leadingorder term expansion for the Teukolsky equation on subextremal Kerr black holes
Pascal Millet
(
Ecole Polytechnique
)
11:00 AM  12:00 PM
Room: amphithéâtre Yvonne ChoquetBruhat
The study of wave propagation on black hole spacetimes has been an intense field of research in the past decades. This interest has been driven by the stability problem for black holes and by questions related to scattering theory. On Kerr black holes, the analysis of Maxwell's equations and the equations of linearized gravity, can be simplified by introducing the Teukolsky equation, which offers the advantage of being scalar in nature. After explaining this reduction, I will present a result providing the large time leadingorder term for initially localized and regular solutions of the Teukolsky equation, valid for the full subextremal range of black hole parameters and for all spins. I will explain how such a development follows naturally from the precise analysis of the resolvent operator on the real axis. Recent advances in microlocal analysis are used to establish the existence and mapping properties of the resolvent.
1:30 PM
Horizonhorizon scattering and black hole thermodynamics

Albert Law
(
Stanford University
)
Horizonhorizon scattering and black hole thermodynamics
Albert Law
(
Stanford University
)
1:30 PM  2:30 PM
Room: amphithéâtre Yvonne ChoquetBruhat
The thermal canonical partition function for a free scalar field outside a black hole horizon is illdefined due to the continuous nature of the normal mode spectrum. In this talk, I will explain how nontrivial spectral information can be extracted from the nearhorizon asymptotics of the normal modes through a relativistic generalization of the KreinFriedelLloyd formula. These considerations lead to a family of welldefined renormalized canonical partition functions parametrized by a choice of reference scattering problem. Remarkably, for a specific choice of reference, the renormalized canonical partition function is equal to the 1loop Euclidean black hole determinant, leading to a precise statistical interpretation of the latter. Time permitting, I will comment on the generalizations to spinning fields and interacting theories. The talk is mostly based on joint works with Dionysios Anninos, Frederik Denef, Manvir Grewal, Klaas Parmentier, and Zimo Sun.
Wednesday, April 17, 2024
9:45 AM
9:45 AM  12:00 PM
Contributions
9:45 AM
An analogue of noninteracting quantum field theory in Riemannian signature

Mikhail Molodyk
(
Stanford University
)
11:00 AM
Functional Renormalization and the NashMoser theorem

Edoardo D'Angelo
(
Università di Genova
)
Thursday, April 18, 2024
Friday, April 19, 2024
Saturday, April 20, 2024
Sunday, April 21, 2024
Monday, April 22, 2024
11:00 AM
TBA

Ali Seraj
(
Queen Mary University of London
)
TBA
Ali Seraj
(
Queen Mary University of London
)
11:00 AM  12:00 PM
Room: amphithéâtre Yvonne ChoquetBruhat
Tuesday, April 23, 2024
11:00 AM
Local covariance in EpsteinGlaser renormalisation

Arne Hofmann
(
Universität Hannover
)
Local covariance in EpsteinGlaser renormalisation
Arne Hofmann
(
Universität Hannover
)
11:00 AM  12:00 PM
Room: amphithéâtre Yvonne ChoquetBruhat
In a seminal work from 2000, Brunetti and Fredenhagen built on the causal perturbation theory of Epstein and Glaser to prove the renormalisability of scalar field theory on curved spacetimes. Their construction was criticized in subsequent publications by Hollands and Wald for failing to satisfy local covariance. I will show that with appropriate modifications, local covariance can be achieved in the BrunettiFredenhagen construction, for distributions which resemble (classical) pseudodifferential operators. The crucial feature of such distributions is the existence of uniform asymptotic expansions.
1:30 PM
Antide Sitter space interacting with quantum fields

Elizabeth Winstanley
(
University of Sheffield
)
Antide Sitter space interacting with quantum fields
Elizabeth Winstanley
(
University of Sheffield
)
1:30 PM  2:30 PM
Room: amphithéâtre Yvonne ChoquetBruhat
We compute the renormalized expectation value of the stressenergy tensor operator (RSET) for a quantum scalar field on three and fourdimensional antide Sitter spacetime (adS). Since adS is not a globally hyperbolic spacetime, boundary conditions have to be applied to the field. We explore the effect of the boundary conditions on the RSET. The RSET then acts as a source term in the Einstein equations governing the quantumcorrected adS metric (QCadS). We describe some of the qualitative features of the QCadS spacetime solutions.
Wednesday, April 24, 2024
11:00 AM
Wick rotation in the lapse: admissible complex metrics and the Wick rotated heat kernel

Rudrajit Banerjee
(
Okinawa Institute of Science and Technology
)
Wick rotation in the lapse: admissible complex metrics and the Wick rotated heat kernel
Rudrajit Banerjee
(
Okinawa Institute of Science and Technology
)
11:00 AM  12:00 PM
Room: amphithéâtre Yvonne ChoquetBruhat
A Wick rotation in the lapse (not in time) is introduced for foliated metric geometries. This interpolates between Lorentzian and Riemannian metrics on the same underlying smooth real manifold, passing through "admissible" complex metrics dampening the exponential of the action of a real scalar field. Moreover, strictly away from the Lorentzian metric, the associated LaplaceBeltrami operator generates a "Wick rotated heat semigroup", an analytic semigroup generalizing the usual heat semigroup on a Riemannian manifold. I will discuss the properties of the Wick rotated heat semigroup, including: (i) existence and uniqueness, (ii) the existence and uniqueness of an integral kernel, the "Wick rotated heat kernel", (iii) the kernel's diagonal admits a small semigroup time asymptotic expansion, and (iv) when the d'Alembertian of the Lorentzian metric is essentially selfadjoint, the Wick rotated heat semigroup converges to the unitary Schrödinger group generated by the d'Alembertian in the strict Lorentzian limit. This talk is based on joint work with Max Niedermaier.
Thursday, April 25, 2024
Friday, April 26, 2024