Amplitudes, Strong-Field Gravity and Resummation

7 Apr 2026, 09:00 → 17 Apr 2026, 19:00 Europe/Stockholm

Albano Building 3

Lucile Cangemi (University of Edinburgh), Paolo Di Vecchia (Stockholm University, Nordita), Riccardo Gonzo (University of Edinburgh), Chris Kavanagh (University College Dublin), Adam Pound (University of Southampton), Geraint Pratten (University of Birmingham)

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Program at a glance (7-17 April 2026)

 

Click to view full poster (PDF)

The program is structured as follows:

• Week 1 [April 7–10, 2026 (4 days)]: The PhD school will focus on foundations and tools for gravitational self-force, amplitudes, self-force EFT, resummation strategies and data analysis relevant to waveform modelling. Theoretical lectures will be complemented by hands-on programming sessions and dedicated tutorials.

• Week 2 [April 13–17, 2026 (5 days)]: Workshop focused on uniting the weak-field (PM) and strong-field (GSF) approaches to the two-body problem, as well resummation strategies relevant for gravitational-wave phenomenology. Individual talks will be complemented by discussion sessions to promote cross-community interaction and constructive debates.

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PhD School (7-10 April 2026)

Topics will include:

1) Scattering amplitudes and the EFT approach to self-force

Lecturers: Nabha Shah (NBI) & Chia-Hsien Shen (Uppsala Univ. and NTU, Taiwan)

2) Introduction to gravitational self-force theory

Lecturers: Leor Barack (Univ. of Southampton) and Barry Wardell (UCD)

3) Introduction to Numerical Relativity, Resummation strategies and Data Analysis

Lecturer: Patricia Schmidt (Univ. of Birmingham)  and Geraint Pratten (Univ. of Birmingham)  

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Workshop (13-17 April 2026)

There is pressing need for high-precision models of gravitational waveforms from binary black hole mergers, driven by the increasing sensitivity of gravitational-wave detectors. The central theme of this program is how to leverage particle physics methods when calculating processes relevant to gravitational-wave phenomenology. In particular, the workshop focuses on uniting two key perturbative approaches — post-Minkowskian (PM) theory, effective for weak-field, widely separated systems, and gravitational self-force (GSF) theory, suited to extreme-mass-ratio systems in strong fields. Crucial to combining these tools is understanding the resummation of the perturbative series. We aim to bring together both experts and younger theorists from these communities, fostering new collaborations and combining our efforts to address the pressing questions at the interface between these fields.

Invited speakers: [* To be confirmed]

D. Akpinar (University of Edinburgh), L. Bohnenblust (Humboldt University), C-H. Chang (NTU), T. Damour (IHES), A. Georgoudis (QMUL), J. Hoogeveen (Humboldt University), M. Khalaf (Hebrew University), D. Kosower (IphT), K. Lee (APCTP, Pohang), O. Long (AEI, Potsdam), J. Mathews (National University of Singapore), A. Nagar (INFN, Torino),  H. Pfeiffer (AEI, Potsdam), J. Plefka (Humboldt University), R. Porto (DESY), T. Rahnuma (APCTP, Pohang), P. Rettegno (INFN, Torino), R. Russo (QMUL), J. Steinhoff (AEI, Potsdam), C-H. Shen (Uppsala University), M. van de Meent (NBI), A. Vaswani (University of Southampton), N. Warburton (UCD).

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Venue

The program will be hosted by Nordita in Stockholm (Sweden) from 7th - 17th April 2026. 

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Application/Registration

Due to limited space, registration will be moderated for both the PhD school and the workshop. You may apply to the PhD school only, the workshop only, or both. Registration to be considered for on-site participation will close on 31 January 2026; after this date, registrants will receive an on-site/remote participation confirmation from the organizers.

Remote participation: All talks will be livestreamed via Zoom, and recordings will be made available to registered participants who cannot attend in person.

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Organizers

• Lucile Cangemi — University of Edinburgh, United Kingdom

• Paolo Di Vecchia — Nordita, Sweden

• Riccardo Gonzo — Queen Mary University of London, United Kingdom

• Chris Kavanagh — University College Dublin, Ireland

• Adam Pound — University of Southampton, United Kingdom

• Geraint Pratten — University of Birmingham, United Kingdom

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Funding sources: 

This workshop is partially supported by the UKRI/ERC grant GWModels.

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Sponsored by:

 

Nordita_poster_final.jpg

Nordita_poster_final.pdf

Tuesday 7 April

09:00 → 09:30 Registration

09:30 → 11:00 Amplitudes and EFT approach

Speaker: Chia-Hsien Shen

Nordita_lecture_1.pdf

Nordita_tutorial.pdf

11:00 → 11:30 Coffee break

11:30 → 13:00 Intro to black hole perturbation theory and self-force

Speaker: Leor Barack

BHPT.pdf

13:00 → 14:30 Lunch

14:30 → 16:00 NR, EOB and Data Analysis

Speaker: Patricia Schmidt

Nordita-NR.pdf

16:00 → 17:00 Free discussion

17:00 → 18:00 Reception

Wednesday 8 April

09:30 → 11:00 NR, EOB and Data Analysis

Speaker: Geraint Pratten

nordita - introduction to eob.pdf

11:00 → 11:30 Coffee break

11:30 → 13:00 Amplitudes and EFT approach

Speaker: Chia-Hsien Shen

Nordita_lecture_2.pdf

13:00 → 14:30 Lunch

14:30 → 15:30 BHPT Tutorial

Speaker: Barry Wardell

15:30 → 16:00 Coffee break

16:00 → 17:00 Gong Show

Gong_show.pdf

Thursday 9 April

09:30 → 11:00 Intro to black hole perturbation theory and self-force

Speaker: Leor Barack

11:00 → 11:30 Coffee break

11:30 → 13:00 NR, EOB and Data Analysis

Speaker: Patricia Schmidt

Nordita-GWDA.pdf

13:00 → 14:30 Lunch

14:30 → 15:30 Intro to self-force EFT

Speaker: Nabha Shah

15:30 → 16:00 Coffee break

16:00 → 17:30 Intro to black hole perturbation theory and self-force

Speaker: Leor Barack

19:00 → 21:00 Dinner Restaurang Kvarnen (Tjärhovsgatan 4, 116 21 Stockholm, Sweden)

Friday 10 April

09:30 → 11:30 Intro to Self-force EFT

Speaker: Nabha Shah

11:30 → 12:00 Coffee break

12:00 → 13:00 BHPT Tutorial

Speaker: Barry Wardell

13:00 → 14:30 Lunch

14:30 → 16:00 Hands-on session: NR, EOB and Data Analysis

Speaker: Patricia Schmidt

16:00 → 16:30 Closing remarks and goodbye

Monday 13 April

09:00 → 09:30 Registration

09:30 → 10:10 High-Precision Dynamics and Waveforms in Two-Body Scattering

Speaker: Thibault Damour

DamourNorditaStockholm.pdf

10:10 → 10:40 Coffee Break

10:40 → 11:20 Amplitudes for Gravitational Waves

I review relativistic perturbative computations relevant to gravitational-waves physics.

Speaker: David Kosower

Amplitudes for Gravitational Waves (Amplitudes, Strong-Field Gravity, and Resummation, Stockhom, Apr 13, 2026).pptx

11:20 → 12:00 WEFT at fifth post N/M order

I review recent developments in the WEFT approach to compact binary dynamics, both in the PN and PM domains, to fifth order in the perturbative expansion.

Speaker: Rafael Porto

12:00 → 13:30 Lunch

13:30 → 14:10 Numerical Simulations of Binary Black Hole Encounters

Binary black hole encounters are the general-relativisic
generalization of the Newtonian two-body problem, and represent the
majorit of observed gravitational waves (GW). Precise knowledge about
the interaction between two black holes and the emitted GWs are of
high importance for finding and analysing GW signals, as well as to
deepen the understanding of the structure and solutions of Einstein's
equations. Such knowledge is obtained by numerical calculations and
perturbation methods like post-Newtonian and post-Minkowskian
expansions, as well as the gravitational self-force formalism, and the
last years have seen rich new results in the overlap between different
methods. This talk summarizes recent advances in numerical relativity
for binary black holes on eccentric and hyperbolic orbits, and for
high mass-ratio. It then elucidates how numerical relativity and
perturbation methods combine in the quest to understand properties of
general relativity and to support gravitational wave science.

Speaker: Harald Pfeiffer

26Apr_Stockholm.pdf

14:10 → 14:40 Coffee Break

14:40 → 16:10 Discussion session

Speaker: Jan Plefka

17:00 → 18:00 Reception

Tuesday 14 April

09:30 → 10:10 Gravitational radiation from hyperbolic orbits: comparison between SF, PM, PN and NR

In this talk will present the latest gravitational self-force (GSF) calculations for the radiation from hyperbolic orbits. In the first part of the talk I will focus on the radiated energy and comparisons with post-Minkowskian (PM), post-Newtonian and numerical relativity results as described in arXiv:2512.02274. In the secondary part I will present preliminary results for the radiated angular momentum and the gravitational wave memory.

Speaker: Niels Warburton

Warburton-Nordita.pdf

10:10 → 10:40 Coffee Break

10:40 → 11:20 Hybrid Self-Force and Post-Newtonian Waveform models - an opportunity for Post-Minkowskian Theory?

In this talk, I’ll give an overview of self-force-based hybrid gravitational wave models that incorporate results from post-Newtonian theory. I’ll highlight that the hybridisation procedure is carefully designed with intuition from common resummations in post-Newtonian and post-Minkowskian theory. I’ll conclude with a sketch of the opportunity for these hybrid models to incorporate scattering results from post-Minkowskian theory.

Speaker: Josh Mathews

Nordita_Apr_26_Josh_Mathews.pdf

11:20 → 12:00 Post-Minkowskian theory, Numerical Relativity and Effective-One-Body models

The analysis of gravitational-wave events requires fast and accurate theoretical predictions. I focus on Effective-One-Body (EOB) models informed by Post-Minkowskian (PM) results and Numerical Relativity (NR) simulations. I compare analytical and numerical results for binary scatterings, including spin and tidal effects. Finally, I discuss the use of PM results for bound systems by means of a Lagrangian formalism.

Speaker: Piero Rettegno (Polytechnic University of Turin)

Nordita_Rettegno.pdf

12:00 → 13:30 Lunch

13:30 → 14:10 Perturbative QFT for Gravitational Waves: Nonlocal-in-time dynamics @ 5PM

In recent years, techniques from perturbative quantum field theory have driven significant progress in the Post-Minkowskian (PM) expansion of binary black hole dynamics. A key challenge in this framework arises from conservative, nonlocal-in-time contributions, which obstruct a straightforward analytic continuation from scattering states to bound orbits via the boundary-to-bound (B2B) dictionary. In this talk, I will present a practical resolution based on a hybrid subtract-and-add scheme that consistently combines PM, Post-Newtonian (PN), and self-force (SF) results. This approach enables the controlled treatment of nonlocal effects and yields new state-of-the-art results for the conservative dynamics at 5PM order, including contributions up to 10th order in the self-force expansion.

Speaker: Gregor Kälin

https://2026-nordita-bb70dc.gitlab.io/

14:10 → 14:40 Coffee Break

14:40 → 16:10 Discussion session

Speaker: Jan Steinhoff

16:30 → 18:00 Poster session

Wednesday 15 April

09:30 → 10:10 When eccentricities "tick up''

The dissipation of energy and angular momentum through the emission of gravitational waves dampens the eccentricity of compact binaries. This is a well-known fact in gravitational wave theory. However, there is a notable well-documented exception to this rule: in extreme mass-ratio inspirals the eccentricity will initially decrease during the inspiral, but will ``tick-up'' just before the binary transitions to its final plunge. We here give a simple explanation for this behaviour, showing that this the expected universal behaviour for eccentric systems transitioning through a last stable orbit.

Speaker: Maarten van de Meent

mvdm_NORDITA_2026.pdf

10:10 → 10:40 Coffee Break

10:40 → 11:20 Modelling black hole scattering using comoving hyperboloidal coordinates

In recent years, the gravitational wave community has seen growing
interest in modelling scattering events between 2 black holes (BH) since such
events serve to better probe regions of strong gravity close to the primary BH.
While some progress on this has been made using the post-Minkowskian
approximation using techniques from effective field theory and scattering
amplitudes, a complimentary approach is to use the Gravitational Self Force (GSF)
which is more suited to analysing motion in the strong field. In this talk, I describe
how these events can be modelled for self-force applications using a numerical
scheme based on hyperboloidal slices that are comoving with the smaller particle.
Furthermore, I will show how this scheme circumvents the divergences that
plagued earlier time-domain implementations.

Speaker: Aditya Vaswani

AV_Nordita2026.pdf

11:20 → 12:00 Black hole scattering in the strong-field regime: Merging post-Minkowskian theory with numerical methods

Recent advances in modelling unbound binary black hole interactions have been driven by the application of scattering amplitude methods to generate results within the post-Minkowskian (PM) expansion. However, this expansion breaks down when approaching the strong-field regime, where large curvature effects become non-negligible. In this talk, I will show how data from numerical relativity simulations and self-force (SF) calculations can be used as benchmarks to validate state-of-the-art PM expressions. Additionally, I will show how strong-field SF information can be used to resum the PM series, providing accurate predictions for scattering angles and radiative quantities across all separations.

Speaker: Oliver Long

Oliver Long Nordita.pdf

12:00 → 12:10 Group picture

12:10 → 13:30 Lunch

13:30 → 14:10 Waveform modeling within the effective one body approach: new perspectives

I will briefly summarize the status of effective-one-body (EOB) based waveforms for generic binaries (spin precession, eccentricity, scattering) and then suggest new avenues for theoretical development coming from both the post-Minkowskian approach and from (revisited) black hole perturbation theory.

Speaker: Alessandro Nagar

14:10 → 14:40 Coffee Break

14:40 → 16:10 Discussion session (Chris Kavanagh)

19:00 → 21:00 Dinner Restaurang Kvarnen (Tjärhovsgatan 4, 116 21 Stockholm, Sweden)

Thursday 16 April

09:30 → 10:10 Dissipative observables for black hole scattering

I will use Black Hole Perturbation Theory (BHPT) to study dissipative observables such as the radiative and absorbed fluxes of energy and angular momentum. I will focus on the case of black hole scattering in the Post-Minkowskian regime and discuss to what extent it
is possible to reconstruct the full observables from the BHPT expansion.

Speaker: Rodolfo Russo

160426.pdf

10:10 → 10:40 Coffee Break

10:40 → 11:20 Surfing the shockwave with black hole response theory

In this talk, we develop a black-hole response formulation of worldline quantum field theory (WQFT) tailored to the gravitational self-force (SF) expansion. By integrating out the primary black hole’s worldline and graviton fluctuations, we obtain an effective action built from black-hole response functions. In this, the one-point response function encodes the exact background metric, the two-point response function describes the scattering of a gravitational wave off the black hole, and higher-point functions provide effective vertices for a systematic gravitational SF expansion.
As a first application, we consider a massless primary source, corresponding to the Aichelburg-Sexl shockwave or an ultra-boosted black hole. We show that the one-point response resums to the exact shockwave metric. Next, we discuss the computation of the exact in G two-point response by resumming the full post-Minkowskian series. We conclude with an outlook on how to obtain the 1SF impulse and waveform in the high-energy regime with this framework.

Speaker: Lara Bohnenblust

NORDITA_LaraBohnenblust.pdf

11:20 → 12:00 Non linear memory from reverse unitarity

I will present a recent computation of the nonlinear gravitational-wave memory in two-body scattering, using scattering amplitudes and soft theorems in the weak-field post-Minkowskian regime. The effect first appears at NNLO PM, and I will show how its evaluation reduces to simpler, lower-point cut two-loop integrals.

Speaker: Alessandro Georgoudis

12:00 → 13:30 Lunch

13:30 → 14:10 Gravitational Sommerfeld Effects

In the effective field theory (EFT) description of compact binary inspirals, the radiated gravitational waveform receives universal corrections from gravitational background, the so-called "tail" effects, that resum into the "Sommerfeld factor". We derive a closed-form expression for the Sommerfeld factor and present a systematic framework to compute it at high orders by combining EFT with black hole perturbation theory, including induced tidal responses. We prove that the phase of the Sommerfeld factor is exactly half of the elastic Compton scattering phase shift when tidal interactions are conservative. We further establish a new renormalization group equation for the radiative multipole moments. These high-order perturbative results provide new avenues for improving waveform resummation.

Speaker: Chih-Hao Chang

Nordita Talk - Gravitational Sommerfelf Effect.pdf

14:10 → 14:40 Coffee Break

14:40 → 16:10 Discussion session (Chia-Hsien Shen)

Friday 17 April

09:30 → 10:10 Self-Force From Response Theory

We develop an efficient framework for the computation of gravitational Self-Force (SF) dynamics with Worldline Quantum Field Theory (WQFT). This “response theory” constructs an effective action for the self-forced secondary, expanded in terms of response functions. These response functions encode all SF dynamics and are interpreted as classical off-shell n-point graviton correlation functions. We discuss in length how SF dynamics may be obtained from response functions, when supplemented by 0SF dynamics. The framework is then explicitly applied to gravitational scattering in the Aichelburg-Sexl background describing a massless black hole. The prerequisite 0SF dynamics is explicitly computed, and promising work towards 1SF discussed.

Speaker: Jitze Hoogeveen

SF from response theory.pdf

10:10 → 10:40 Coffee Break

10:40 → 11:20 Kerr Black Hole Scattering: An On-Shell Approach to Conserved Quantities and Integrability

Amplitudes and worldline methods have emerged as powerful tools for studying the gravitational two-body problem. In particular, they have enabled major progress in the computation of scattering observables for spinning black holes at high post-Minkowskian orders. In this talk, we will build on these developments to investigate the integrability properties of Kerr black hole scattering, both in the probe limit and beyond. We will begin by reviewing the radial action and the recently introduced Dirac bracket formalism, which together motivate a notion of asymptotic integrability. Using these tools, we will show that this integrability persists to higher orders in spin than previously established. Finally, we will discuss spin-shift symmetry, a striking and still not fully understood property of spinning amplitudes, and show how, when combined with integrability constraints, it leads to a powerful bootstrap of the radial action.

Speaker: Dogan Akpinar

Nordita2026.pdf

11:20 → 12:00 Analytical Fluxes from Generic Schwarzschild Geodesics

In this talk, I present an analytic method for computing gravitational-wave fluxes from bound Schwarzschild geodesics with arbitrary eccentricity. Our approach systematically expands the Fourier coefficients of the emitted radiation in a Chebyshev basis, allowing them to be reduced to sums of Keplerian-like Fourier coefficients previously derived in the Quantum Spectral Method. Because the construction does not rely on a small-eccentricity expansion, it applies to a broad range of bound eccentric orbits. As an illustration, we implement the method using a 15PN-expanded input and find that it reproduces the total flux for the validation case (p,e)=(12.5,0.5) to relative accuracy 10^{-5}, while for the stronger-field orbit (p,e)=(10,0.8) it yields weighted mode-by-mode errors below 10^{-6} for the selected dominant modes analyzed. These results provide an analytic route to frequency-domain flux calculations relevant to EMRI modelling.

Speaker: Majed Khalaf

Nordita_presentation.pdf

12:00 → 13:30 Lunch

13:30 → 14:10 Metric of a Star: A Recursive multipolar Post-Minkowskian Construction

We construct the exterior metric of a stationary compact source within the multipolar post-Minkowskian (MPM) formalism and develop a recursive momentum-space reformulation of the construction. The MPM framework solves the Einstein equations outside a compact source perturbatively in Newton's constant, decomposing the metric into symmetric trace-free mass and current multipole moments. In this momentum space, the multipolar structure emerges naturally from the recursive field equations, simplifying tensor structures and clarifying how multipole moments enter at successive PM orders. Crucially, the nonlinearities of the Einstein equations reduce in this picture to the iterative evaluation of bubble integrals, making explicit the nonlinear multipolar interactions, including monopole–quadrupole, quadrupole-quadrupole, and higher-order couplings. As a consistency check, we match the generic multipolar solution to the Kerr metric generated independently by a similar recursive formulation, verifying that the construction reproduces the correct Kerr multipole structure, which includes its infinite tower of moments, and thus captures the nonlinear structure of rotating vacuum solutions.

Speaker: Tabasum Rahnuma

Nordita26_Tabasum.pdf

14:10 → 15:40 Discussion session (Kanghoon Lee)

15:40 → 16:10 Closing remarks and goodbye