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The gravitational waves from neutron star binary systems carry unique information about their interiors, where matter is compressed by strong gravity to several times nuclear density and novel phases emerge. Measuring this information from the data relies on accurate models of the interplay of matter with strong-field, dynamical gravity. I will discuss various signatures in gravitational waves that contain information about the ground-state of dense matter, summarize what we have learned from recent measurements, and conclude with an outlook onto the challenges and prospects for the next years as gravitational-wave science continues to move towards an era of precision physics.

Binary black hole spins are among the key observables for gravitational wave astronomy. In particular, the spin orientations within the orbital plane can be used to identify spin-orbit resonances, where the black hole spins and the orbital angular momentum become locked into a fixed plane as the binary evolves. Stellar binaries can become trapped in these resonances if supernova natal recoils and stellar tides are large enough: therefore, observing these resonances in gravitational wave data can inform us about supernova and stellar astrophysics. However, the general expectation has been that current gravitational wave detectors, LIGO and Virgo, are not sensitive enough to measure the orbital-plane spin orientations. In this talk, I will show that this can be achieved by simply measuring the spins very close to the merger. This leads to a marked improvement in the spin constraints for several signals detected by LIGO-Virgo. Finally, I will show results combining many such signals to look for signatures of spin-orbit resonances in the astrophysical binary black hole population.

Quantum field theoretic techniques can be used to calculate classical gravitational scattering of black holes (or neutron stars) relevant for gravitational-wave observations. Two current frontiers are the inclusion of spin and finite-size effects. We introduce on-shell variables for Heavy Particle Effective Theories (HPETs) with the goal of extending Heavy Black Hole Effective Theory---the gravitational analog of Heavy Quark Effective Theory---to higher spins and facilitation its application to higher post-Minkowskian orders. These variables inherit the separation of spinless and spin-inclusive effects from the HPET fields, resulting in an explicit spin-multipole expansion of the three-point amplitude for any spin. For finite-size effects we apply the Hilbert series to classify and construct all tidal operators involving two powers of the curvature.

A compact accretion disk may be formed in the merger of two neutron stars or of a neutron star and a stellar-mass black hole. Outflows from such accretion disks have been identified as a major site of rapid neutron-capture (r-process) nucleosynthesis and as the source of 'red' kilonova emission following the first observed neutron-star merger GW170817. We present long-term general-relativistic radiation magnetohydrodynamic simulations of a typical post-merger accretion disk at initial accretion rates of ms post-merger. We include neutrino radiation transport that accounts for effects of neutrino fast flavor conversions dynamically. We find ubiquitous flavor oscillations that result in a significantly more neutron-rich outflow, providing lanthanide and 3rd-peak r-process abundances similar to solar abundances. This provides strong evidence that post-merger accretion disks are a major production site of heavy r-process elements. A similar flavor effect may allow for increased lanthanide production in collapsars.

Galaxies are remarkably diverse in their properties, ranging from irregular to disky to elliptical in morphology, and from blue to red in color. At the same time, when analyzed systematically, galaxy populations exhibit striking regularities, with clear trends with mass and redshift. How does this 'regular complexity' emerge from the hot Big Bang? I will present results from the FIRE simulations which shed some light onto the processes that shape galaxies. The FIRE zoom-in simulations resolve the multiphase interstellar medium of galaxies and model several different feedback processes (including Type II/Ia supernovae, stellar winds, and radiation) while including the cosmological environment. I will highlight recent results on the formation of disk galaxies, the 'burstiness' of star formation, and galactic winds. Our new results indicate that transitions in each of these important phenomena can be simultaneously explained by a phase transition in the inner circumgalactic medium, 'inner CGM virialization' (ICV), and arise from the interplay between feedback energy produced on small scales and the physics of halo gas on larger scales.

After a short introduction to the λ-model, I will discuss the construction of integrable deformations by employing an asymptotic limit on λ-deformations of non-compact coset CFTs. Specifically, I will focus on a 2D and a 3D example. After the asymptotic limit, the new models interpolate between a CFT with a linear dilaton and a hyperbolic space in two and three dimensions respectively. The existence of a new zoom-in limit in λ-deformed models will also be discussed.

The hexagon formalism provides a framework to calculate correlation functions in N=4 Super Yang-Mills theory using integrability. The basic idea is to decompose the correlation function into building blocks called hexagon form factors. These hexagon patches can be glued back together by dressing their non physical edges with virtual magnons and integrating over their respective rapidities. The approach will be demonstrated on the example of the one-loop correction to a correlation function of five BPS Operators of length two. Here it is necessary to glue three adjacent hexagon patches, which involves the scattering of two virtual magnons. We will calculate parts of this process analytically using a simplified form of the corresponding scattering matrix.

In the talk we discuss the renormalization of the electric charge, as defined in the Thomson limit, with the aim to express the charge renormalization constant in terms of self-energies of the photon-Z-boson system in an arbitrary R_xi-gauge to all perturbative orders. The derivation as carried out in the Standard Model holds in all spontaneously broken gauge theories with the SU(2)_w * U(1)_Y gauge group in the electroweak sector and is based on the application of charge universality to a fake fermion with infinitesimal weak hypercharge and vanishing weak isospin, which effectively decouples from all other particles. Charge universality, for instance, follows from the known universal form of the charge renormalization constant as derived within the background-field formalism. Finally, we briefly discuss the generalization of the described procedure to gauge theories with gauge group U(1)_Y * G with any Lie group G, only assuming that electromagnetic gauge symmetry is unbroken and mixes with U(1)_Y transformations in a non-trivial way.

I will discuss when a supergravity solution, belonging to a consistent truncation on an internal sphere, is guaranteed to have some degree of separation in its Hamilton-Jacobi equation. This talk is based on https://arxiv.org/abs/2102.12493, where it is shown that such separability can be guaranteed if sufficient isometries along the internal sphere are preserved, in addition to an appropriate restriction of the reduction gauge vectors. A classification of such sufficient 'separable isometries' may be of practical use in the generation of separable solutions within a given consistent truncation, which are conveniently amenable to scalar probe calculations. On the other hand, our results suggest that a supergravity solution with a separable massless Hamilton-Jacobi equation may be a tell tale sign that it belongs to an underlying consistent truncation, providing a simple diagnostic in the search for new consistent truncations, as occurred in the motivating example of https://arxiv.org/abs/2004.13031​​.​

One of the major challenges in computing higher-order corrections of collider observables is the treatment of infrared singularities. Local Unitarity (LU) is a novel representation of differential scattering cross-sections that locally realises the direct cancellation of infrared singularities exhibited by its real-emission and virtual degrees of freedom. In this talk I will introduce the key concepts behind LU and will show how it can be used to produce differential cross sections with the push of a button.

We first give a brief status of the field of multi-loop calculations, with focus on integrals with many mass scales and phenomenological applications. Then we discuss representations of loop integrals in Feynman parameter space and their evaluation with sector decomposition methods.This will lead us to asymptotic expansions of integrals, for example in the small mass limit or the high energy limit, also known as “expansion by regions”. We will discuss a geometric formulation of such expansions in integration parameter space and present the automation of such expansions within the program pySecDec.

Infrared problems in the evaluation of gauge-theory amplitudes and cross sections have been a focus of theoretical research for close to a century. Yet, new discoveries and new ideas continue to emerge, and high-precision phenomenology requires further sharpening of our tools. I will review our present understanding of the infrared structure of non-abelian scattering amplitudes, emphasising the ideas of universality, factorisation, evolution and resummation. I will briefly introduce new ideas for the analysis of soft divergences using conformal field theory tools, and finally I will discuss the problem of infrared subtraction for high-order predictions of complex collider observables.

The computation of master integrals is one of the key problems in modern precision high energy physics. In this talk, we would introduce the improved auxiliary mass flow method to numerically compute master integrals. This improved version has much better performance than the original one introduced several years ago in arXiv: 1711.09572, such that many cutting-edge problems are now computable in this framework. As examples, we calculate master integrals involved in two-loop electroweak correction to e+e- -> HZ, two-loop QCD corrections to 3j, W+2j, H+2j, ttbarH, 4j and three-loop QCD correction to ttbar production. Our tests show that the method might be the most powerful one among currently existing numerical methods.

After a short but gentle recap of noncommutative geometry we show that the spectral action, when perturbed by a gauge potential, can be written as a series of Chern-Simons actions and Yang-Mills actions of all orders. In the odd orders, generalized Chern--Simons forms are integrated against an odd $(b,B)$-cocycle, whereas, in the even orders, powers of the curvature are integrated against (b,B)-cocycles that are Hochschild cocycles as well. In both cases, the Hochschild cochains are derived from the Taylor series expansion of the spectral action tr(f(D+V)) in powers of V=pi_D(A), but unlike the Taylor expansion we expand in increasing order of the forms in A. As a consequence of our expansion and of the gauge invariance of the spectral action, we show that the odd (b,B)-cocycle pairs trivially with K_1.

In this talk, I review the definition and applications of EL∞-algebras given in arXiv:2106.00108. EL∞-algebras are generalizations of L∞-algebras comprising weak Lie ∞-algebras, and they have a number of applications within extended geometry. In particular, they clarify the higher symmetry structure of generalized tangent bundles and double/exceptional field theory. They also provide the algebraic origin for data needed in the definition of higher gauge theories such as the tensor hierarchy of gauged supergravity. This Lie ∞-algebraic perspective now provides a clear path towards finite gauge transformations and a global picture of these higher gauge theories.

On 7th April, the first results from the g-2 experiment at Fermilab were published and have attracted huge world-wide attention. In this talk, the Standard Model prediction of g-2 of the muon is reviewed, with emphasis on the determination of the hadronic contributions which are the limiting factor for its uncertainty. Recent developments, the current state of the discrepancy between experiment and theory as well as future prospects will be discussed.

The renormalization of the supersymmetric Wess-Zumino model is carried out to five loops in both the MSbar and momentum subtraction schemes. The model is the supersymmetric extension of scalar phi^3 theory but is renormalizable in four rather than six dimensions. The calculation is carried out in superspace meaning the D-algebra can be implemented automatically paving the way for the Mincer and Forcer packages to be employed to compute the Feynman integrals. Endowing the basic chirally symmetric theory with an O(N) symmetry means the five loop result can be checked against the known large N exponents. We also consider a generalization of the model with a tensor coupling similar to that used for percolation problems in non-supersymmetric phi^3 theory. In this case we reproduce the five loop part of Bellon and Schaposnik's 2008 construction of the Hopf algebra Schwinger-Dyson solution of the beta-function.

I will outline how (exceptional) generalised geometry secretly governs the physics of probe branes. Currents on the worldvolume naturally organise in the same multiplets appearing in the tensor hierarchy, and their current algebra takes a universal geometric form. The technical tool for this is an AKSZ-like construction of a Poisson algebra --- the brane phase space --- from the data of a QP manifold; i.e. from the L_infinity-algebra structure of gauge transformations of the (super)gravity background. This talk will be based on https://arxiv.org/abs/2103.08608

In this talk I will present recent results on the complete two-loop corrections in massless QCD for the production of two photons and a jet. The full colour structure of the amplitude is taken into account. In particular, we analytically compute all two-loop helicity amplitudes for the quark-antiquark, quark-gluon, and antiquark-gluon channel, and check them with an independent calculation of the polarisation-summed interference with the tree amplitude.

In the theory of renormalisation of quantum field theories (a la Connes and Kreimer), character groups of certain Hopf algebras appear as “renormalization groups”. Here the Hopf algebra encodes the combinatorics underlying renormalisation, while the group hosts objects and equations of interest (such as time ordered exponentials and objects related to the Birkhoff factorization). The aim of this talk is to discuss the infinite-dimensional Lie group structure of the renormalization groups. Note that these groups are not naturally modelled on Banach spaces, so we will start with an introduction to what we actually mean by “infinite-dimensional Lie group”. No prior knowledge will be assumed as we review the basic concepts (calculus beyond Banach spaces, infinite dimensional Lie groups) and discuss some key properties of these infinite-dimensional groups.

I will discuss recent progress towards understanding geometric and holographic aspects of electromagnetic duality in four-dimensional supergravity. More concretely, I will focus on the connection between electromagnetic duality and the existence of new classes of S-fold backgrounds of type IIB supergravity of the form AdS4 x S1 x S5 which are conjectured to correspond to new strongly coupled three-dimensional CFT’s on a localised interface of SYM. I will discuss holographic RG flows on the D3-brane that generically connect anisotropic deformations of SYM in the UV to various S-fold CFT’s in the IR with different amounts of supersymmetry and flavour symmetries. Lastly, a geometric interpretation of axionic deformations will be provided in terms of monodromies on the internal S5 when moving around the S1.

I will review the GENEVA framework, that combines the NNLL resummation of large Sudakov logarithms at small values of the jet resolution variable with multiple NLO matrix-element corrections to larger values, to give a complete description at the next higher perturbative accuracy in the strong coupling constant at both small and large jet resolution scales. The resulting NNLO event generator matched to parton showers allowed us to obtain results for several color-singlet processes, displaying good agreement in comparison with LHC data. Possible extensions of the method towards more complicated final states will also be discussed.

n recent years much progress has been made in the field of non-relativistic physics. In particular, in this talk I will focus on the journey going from non-relativistic particles to strings and finally to membranes. I will discuss how these theories can be obtained in different ways, e.g. via limiting procedures or via embedding in the more general frameworks of Double Field Theory (DFT) and Exceptional Field Theory (ExFT). These provide tools that are especially useful for understanding the symmetries and degrees of freedom of the theories. An example is given by the scalar Poisson equation which, as we will see, cannot be obtained by variation of an action. DFT/ExFT explain naturally how and why this equation cannot be derived from an action principle.

Recent flavor data show a reinforced set of deviations from the Standard Model predictions, pointing to violations of lepton flavor universality. I will critically review these data and discuss their theoretical interpretation, including their possible connection to the hierarchical pattern of fermions masses and mixing angles. To this end, I will first interpret the data following an effective field theory approach and later discuss possible UV completions. Complementary constraints and implications for future measurements will be also discussed.

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After a short review of some salient features of E7 and E8 exceptional field theories, I will formulate their E11 generalisation. This exceptional field theory for the Kac-Moody group E11 combines consistently ideas of Peter West, Olaf Hohm, Henning Samtleben and many others. I will explain in particular how one recovers the eleven-dimensional supergravity Lagrangian, together with an infinity of non-linear duality equations for higher rank tensors including the dual graviton. This is a work in collaboration with Axel Kleinschmidt and Ergin Sezgin.

I report on work in progress with Ömer Gürdoğan, Erik Panzer and Matteo Parisi on the analytic structure of Feynman integrals in the parametric representation. More generally, we consider integrals of (relative) meromorphic differential forms over relative cycles, both living in the complement of a subspace arrangement in a compact complex manifold. If the form and/or the cycle depend on additional parameters (e.g. masses, momenta in the Feynman case), such integrals define complex-valued functions on the space of parameters. Our goal is to study the singularities (branch points, discontinuities) of these functions using the classical framework developed by Pham et al. (based on the work of Landau, Leray, Thom, Picard, Lefschetz etc.). In the relative case, however, the necessary tools are at most implicitly contained in the existing literature, if at all. I will describe how to fill this gap, i.e. our proposed setup for a 'relative Picard-Lefschetz theory', and show how a careful analysis of the involved geometry and topology leads to a nice conjecture on the iterated structure of the singularities of such functions, generalising the symbol calculus in the case of polylogarithms.

Upon dimensional reduction to two spacetime dimensions, (super)gravity exhibits an infinite-dimensional duality symmetry based on an affine Lie algebra. I will review the construction of the associated exceptional field theory which, in the maximally supersymmetric case, provides a (formally) E9-covariant reformulation of eleven-dimensional and type IIB supergravity. I will present two equivalent descriptions of its dynamics, which both rely on a pseudo-Lagrangian supplemented by a twisted self-duality equation, and highlight features which do not appear in other exceptional field theories.

Generalizing the point-like interactions of standard ``local'' QFT to combinatorially non-local interactions preserves locality in the sense of renormalization. The crucial difference is that residues come with an additional graph structure. Still, the standard Hopf-algebraic structure of (perturbative) renormalization applies. I show how this facilitates renormalization in the case of the BPHZ momentum scheme and give an outlook on non-perturbative applications.

I will review recent breakthroughs in understanding on-shell heterotic moduli from the past decade, many of which required thinking in terms of generalised geometry, doubled field theory and L-infinity algebras. In most of these formulations an extra set of End(TX)-valued are needed for the description to make sense. These unphysical fields are often given the interpretation of field redefinitions. I will take some modest steps towards an understanding of the moduli problem without these spurious degrees of freedom. In particular, I will describe the cohomology which counts the infinitesimal massless modes.

I will review recent progress on the perturbative renormalization of quantum gravity: Following a suggestion of Kreimer (2007) and results of van Suijlekom (2007), we study the relationship between gravitational Slavnov--Taylor identities and Hopf ideals [DP, 2019]. This includes some combinatorics with the superficial degree of divergence and the extension of coproduct identities to the non-renormalizable case. We proceed by displaying gravitational Feynman rules for arbitrary vertex valence and for a one-parameter quadratic de Donder gauge fixing [DP, 2020]. In particular, we study the longitudinal and transversal properties of the gravitational Feynman rules using the respective projection tensors [DP, in prep.]. Specifically, we comment on the relationship between the two commonly used metric decompositions, the deviation of the flat background metric and the inverse metric density decomposition. This leads us to define an intermediate metric decomposition, whose transversal structure is symmetric and thus similar to the situation in Quantum Yang--Mills Theory. We close with a comment on the respective Feynman graph cohomology, as defined by Kreimer et al. (2013) in the context of Quantum Yang--Mills Theory.

The AdS/CFT correspondence is a powerful tool for studying strongly coupled QFTs by performing computations in string theory and its low energy limit, supergravity. I will review Exceptional Field Theory, a formalism that unifies gravitational and flux degrees of freedom of supergravity, and thereby makes a large exceptional symmetry group manifest. This large symmetry group simplifies many complicated calculations in AdS backgrounds, such as constructing consistent truncations or computing the spectrum of linearised fluctuations around AdS vacua. I will show how this can be used to gain insights into dstrongly coupled QFTs. Finally, it time permits, I will discuss applications to non-supersymmetric AdS vacua.

I will report on recent progress with Bouchard, Chidambaram and Creutzig establishing that Whittaker vectors (also called Gaiotto vectors and representing instanton partition function on equivariant C^2) and the Nekrasov partition function (of instantons on equivariant P^2) for N = 2 supersymmetric gauge theory with gauge group SU(n) can be computed by the topological recursion. The starting point is a form of the Alday-Gaiotto-Tachikawa conjecture established by Schiffman-Vasserot and Braverman-Nakajima-Finkelberg and stating that the cohomology of a suitable compactification of the moduli space of G-bundles on P^2 carries an action of the W(gl_r) algebra and the fundamental class is a Whittaker vector for this action. Our approach suggests a route to prove rigorously that the all-order hbar = -epsilon_1 epsilon_2 expansion of the Whittaker vector partition function can be extracted (by means of the topological recursion) from the Seiberg-Witten curve.

The interest in the analytical structure of Feynman integrals dates back to the 1950s and Landau's famous approach. And due to various methods based on "unitarity cuts", interest in the singularities of Feynman integrals has unabated to this day. However, many heuristically motivated statements from this time have still lacked a solid mathematical basis. This is not least due to the fact that many of the necessary mathematical methods were only developed later. Recently, more efforts have been made to compensate for this lack of mathematical foundation. In this talk, we will consider the singularities of the Feynman integral from the perspective of Gelfand-Kapranov-Zelevinsky (GKZ) hypergeometric systems and describe them as A-discriminants. The advantage of this approach is that we can draw on a large arsenal of already known properties of this GKZ theory. After a short introduction to the methods of GKZ, we will present a few of these properties.

In the talk I will describe the concept of G-algebroid, which generalises both Lie and Courant algebroids, as well as the Leibniz algebroids used in the description of exceptional generalised geometry (at least for n<7). I will discuss a classification result in the "M-theoretic exact" case and then employ G-algebroids to define and study a general concept of "Poisson-Lie duality", recovering in particular the recently introduced Poisson-Lie U-duality. This is a joint work with Mark Bugden, Ondrej Hulik, and Daniel Waldram.

Exactly solvable models and holography; Listening to the shape of string theory's extra dimensions; Atomic systems for timing and sensing applications

Proposed in 1954 by Gell-Mann, Goldberger, and Thirring, crossing symmetry postulates that particles are indistinguishable from anti-particles traveling back in time. Its elusive proof amounts to demonstrating that scattering matrices in different crossing channels are boundary values of the same analytic function, as a consequence of physical axioms such as causality, locality, or unitarity. In this talk we report on the progress in proving crossing symmetry on-shell within the framework of perturbative quantum field theory. We derive bounds on internal masses above which scattering amplitudes are crossing-symmetric to all loop orders. They are valid for four- and five-point processes, or to all multiplicity if one allows deformations of momenta into higher dimensions at intermediate steps. As usual we will have our informal coffee meeting before the talk to simulate a coffee corner discussion. The zoom room will already be open from 3:30pm on. Feel free to join any time before the talk. Passcode upon request.

W-algebras associated to simple Lie algebras are non-linear generalisations of the Virasoro algebra, from which certain CFTs can be defined. Using a formalism of Kontsevich and Soibelman and representation theory of W-algebras via free fields (when this exist), one can construct from them systems of PDEs whose solution is computed by a topological recursion. Such solutions carry information about 2d (worldsheet) geometry, and topological recursion mean this information is reached by induction on the Euler characteristic that resembles a cutting/pasting approach. They are sometimes expressible as integrals on the moduli space of complex curves or as topological string A-model amplitudes (for certain target spaces), and gives suitable definition of topological string B-model for certain type of complex 1d singularities. I will give an overview of these connections, and describe if time permits sketch a more recent link (ongoing work) to Nekrasov partition functions in 5d gauge theories (in which W-algebra are known to appear since Alday-Gaiotto-Tachikawa proposal). This is based on joint works with Andersen, Chekhov, Orantin, Bouchard, Chidambaram, Creutzig, Noshchenko, Kramer, Schüler.

High energy particle collisions are an ideal framework for accessing new information on matter constituents and forces of Nature. Advances in Theoretical Physics depend on our ability to describe the scattering processes among elementary particles at very high accuracy. Theoretical Physicists calculate scattering amplitudes, numbers that are related to the probabilities of different aftermath of particle scattering, which encode the chance that a given set of particles will turn into certain other particles after an impact. Feynman graphs are a convenient way to represent particle collisions. The mathematical methods required to describe scattering events which take place from the smallest to the largest scale of the Universe benefit from concepts borrowed from the rich research in mathematical disciplines, such as (differential and algebraic) Geometry, Topology and Number Theory. In this seminar, I elaborate on the diagrammatic approach to Fundamental Interactions via Scattering Amplitudes and Feynman integrals, and on their algebraic properties which have been recently understood to be ruled by Intersection Numbers: a novel connection between Physics and Mathematics.

We will discuss the deformation theory of nearly G2-manifolds. After defining nearly G2-manifolds, we will describe some identities for 2 and 3-forms on such manifolds. We willintroduce a Dirac type operator which will be used to completely describe the cohomology of nearly G2-manifolds. Along the way, we will give a different proof of a result of Alexandrov-Semmelman on the space of infinitesimal deformation of nearlyG2structures. Finally, wewill prove that the infinitesimal deformations of the homogeneous nearly G2-structure on the Aloff–Wallach space are obstructed to second order. The talk is based on a joint workwith Ragini Singhal (University of Waterloo).

We will start by discussing a flow of isometric G2-structures. We consider the negativegradient flow of the energy functional restricted to the class of G2-structures inducing agiven Riemannian metric. We will discuss various analytic aspects of the flow includingglobal and local derivative estimates, a compactness theorem and a monotonicity formulafor the solutions. After defining an entropy functional we will prove that low entropy initialdata lead to solutions that exist for all time and converge smoothly to a G2-structure with divergence free torsion. We will also discuss finite time singularities and the singular set ofthe solutions. Finally, we will discuss the isometric flow ”coupled with the Ricci flow of the underlying metric, which again is a flow of G2-structures (and is a specific example of a familyof flows of G2-structures which we have introduced), and discuss some of its properties. This is a based on two separate joint works with Panagiotis Gianniotis (University of Athens)and Spiro Karigiannis (University of Waterloo)

Composite Higgs models are Beyond the Standard Model approaches involving a strongly coupled sector in which the Higgs particle is a Goldstone boson of a spontaneously broken symmetry, in analogy to pions in QCD. I will discuss gauge/gravity dual descriptions of explicit realizations of composite Higgs models using insights from non-conformal examples of the AdS/CFT correspondence. I will explain how to calculate particle masses and decay constants for proposed Sp(4) and SU(4) gauge theories. The results obtained compare favourably to lattice gauge theory studies and go beyond those due to a greater flexibility in choosing the fermion content. That content changes the running of the couplings and its choice can lead to sizable changes in the bound state masses. The `top partners’ present in composite Higgs are modelled by dual fermionic fields in the bulk. Including suitable higher dimension operators can ensure a top mass consistent with the Standard Model.

The anomalous magnetic moment of the muon serves as a low-energy precision test of the Standard Model of particle physics. The White Paper (arXiv:2006.04822) recently published in Physics Reports concludes that a tension of 3.7 standard deviations persists between the direct measurement and the Standard Model prediction of the anomalous magnetic moment of the muon. A new direct measurement is expected very soon by the E989 experiment at Fermilab. On the theory side, the uncertainty of the SM prediction is quasi-saturated by the hadronic contributions. I will focus on the effort by the lattice QCD community to compute these hadronic contributions and compare these calculations to phenomenological determinations.

With Run II, the LHC experiment already reached an unprecedented level of precision compared to previous hadron colliders. The amount of data collected in Run III and the High-Luminosity run will increase quickly and dramatically. I will discuss specific challenges to theorists that must be overcome to provide predictions that have the precision necessary to match the accuracy of data. A few novel ideas to exploit this precision directly or indirectly will also be discussed.

The nascent field of gravitational wave (GW) science will be an interdisciplinary subject — enriching different branches of physics — yet the associated computational challenges are enormous. Faithful theoretical templates are a compulsory ingredient for data analysis and reliable physical interpretation of the signals. Yet, while current templates for compact binary sources may be sufficient for detection and crude parameter estimation, they are still too coarse for precision physics with GW data. We then find ourselves in a situation in which, for key processes within empirical reach, theoretical uncertainties may dominate. To move forward, and profit the most from GW observations, more accurate waveforms will be needed. This will be critical, as I will discuss, to study the equation of state of neutron stars and the nature of black holes; as well as potentially successful searches for exotic compact objects and putative ultra-light (dark matter) particles in the Universe. The ‘effective field theory approach’ to the binary inspiral problem in general relativity — which my collaborators and I have developed — has been instrumental for the construction of the state-of-the-art GW template bank. I will review how these and other novel techniques borrowed from particle physics have transformed the study of the two-body problem in gravity, providing key new results and paving the road forward to a new era of foundational investigations in physics through GW precision data.

In the talk, the energy-momentum (also "stress-energy") tensor will be presented as crucial current density for the gravitational field. With its property of being conserved it necessarily generates a massless spin-2 gauge field which, by considering gauge and coordinate transformations becomes part of the spacetime metric. Beyond, the energy-momentum tensor is delivering deep insight into gravitation in thermodynamics, particularly interrelations between heat current, viscosity, temperature, entropy and entropy production under themselves and with respect to gravity will be discussed.

QED radiative corrections to hadronic observables are generally rather small but they become phenomenologically relevant when the target precision is at the percent level. This is the case of leptonic and semileptonic decays of light and heavy pseudoscalar mesons. On the one hand, QED radiative corrections to hadronic observables can be calculated with the required non-perturbative accuracy by using lattice techniques. On the other hand, the inclusion of electromagnetic interactions in a lattice calculation is a challenging problem because QED is a long-range unconfined interaction and numerical simulations necessarily require a finite volume. The problem is particularly delicate in the case of QED radiative corrections to decay rates because of the appearance of infrared divergences (proportional to the logarithm of the lattice volume) at intermediate stages of the calculations. In this talk I will briefly review the recent theoretical advances that opened the way to realistic non-perturbative simulations of QCD+QED, discuss a method that allows to calculate QED radiative corrections to hadronic decay rates and present the results of a non-perturbative calculation of the leptonic decay rates P-> l nu (gamma) in the case of light (P=pi,K) and charmed (P=D,Ds) pseudoscalar mesons.

The status of string theory will be examined, and what is known and what is unknown about the theory will be discussed. String theory has special duality symmetries that do not occur in conventional field theories, and some of the implications of these will be explored, and the implications for the nature of space-time will be investigated.

Weak capture transfer occurs when a particle becomes captured into orbit about one of the primary mass points of the three or four-body problem, temporarily. Capture in this case is defined when the Kepler two-body energy of a particle with respect to the primary is negative. This was first numerically demonstrated by Belbruno (EB) in 1986. This capture occurs in a region about the primary called a weak stability boundary (WSB). It was proven by EB (2005) that the WSB contains within it a hyperbolic invariant set, giving rise to chaotic motion. Although crudely numerically estimated in 1986, numerical work by Gomez (2007) gave deeper insights into its makeup yielding surprising results as to its complexity. Further insights in the makeup of this region were made in a series of studies (Gidea,Topputo, EB). The relationship of weak capture to permanent capture and the work of Sitnikov in the 1960s is discussed. Weak capture transfer has important applications. One such transfer was used in 1991 by EB and Miller to rescue an errand Japanese lunar probe and successfully send it to the Moon. This same transfer class was used in 2011 for NASA’s lunar Grail mission and another type was used by ESAs lunar SMART 1 mission in 2004. One such transfer is currently being used in a mission to Mercury for ESA’s BepiColombo mission. A new result that is described is the existence of a weak capture transfer to Mars. This promises to have interesting applications. A lunar gateway is also discussed based on recent work. If there is time, an exciting new application of weak capture to quantum mechanics is discussed.

Gravitational wave observations provide a new and unique window into the early universe. I will start by explaining why this is the case, and give an overview of new physics scenarios that give rise to a stochastic gravitational wave background in the early universe, and therefore may be testable by future gravitational wave observations. Then I will focus on the audible axion scenario, a class of axion models whose cosmological evolution leaves an observable imprint in the gravitational wave background. This allows a new and unique probe of very high scale axions, with symmetry breaking scales close to the GUT or string scale.

The Swampland program aims to distinguish effective field theories that can be consistently completed into quantum gravity in the ultraviolet from those which cannot. It has lead to a number of proposals, or conjectures, regarding the required properties of effective theories. I will review some of the evidence for these and propose that they arise due to a particular aspect of duality where propagating fields in the infrared are emergent from the collective properties of infinite towers of states. Time permitting, I will discuss some applications of the conjectures, in particular to accelerating cosmologies and to massive spin-2 fields.

Dyson-Schwinger equations are the quantum analogues of the equations of motion and so are physically very important and useful. In their diagrammatic form they also show some nice discrete mathematical structures. For example, diagrammatically they generate certain classes of Feynman diagrams and so act like combinatorial specifications, and they are compatible with algebraic structures on Feynman diagrams, like renormalization Hopf algebras. In this colloquium I will overview the physics and the math of this and close with a different combinatorial expansion that can go beyond naive Feynman diagrammatics and solve some Dyson-Schwinger equations using an unusual expansion indexed by rooted connected chord diagrams.

In the planar limit of a large number of colors, N=4 super Yang-Mills theory is integrable, and remarkable advances have been made in determining operator anomalous dimensions and more to all loop orders. In this talk I'll describe recent progress in constructing scattering amplitudes in this theory to high loop order. Planar N=4 amplitudes are dual to light-like polygonal Wilson-loops, and are only nontrivial for six or more gluons. The spaces of functions to which the amplitudes belong are so restrictive that only a few constraints are needed to simply write down the answer, through seven loops in the six-gluon case and four loops in the seven-gluon case. The results are multi-variate functions of the kinematics, which can be analyzed in various limits in order to study how high loop order amplitudes factorize. One can also extrapolate from weak to strong coupling, and compare with the AdS/CFT dual description available there.

This talk is about integrability of planar N=4 super Yang-Mills theory. I will review the notion of integrability in the AdS/CFT context and what it means for planar scattering and Wilson loops including selected results. I will then present a concrete notion of the corresponding Yangian symmetry in this model, show that it holds true, and discuss the (perturbative) implications for correlation functions and Wilson loops.