Triangle Seminars

Abstract:
The late-time gravitational-wave signal from a binary black hole merger is dominated by quasinormal ringing, a spectrum of damped oscillations whose complex frequencies, in linear perturbation theory, depend only on the remnant’s mass and spin. These modes encode a unique spectral fingerprint of the final black hole, and current observations already hint at the presence of overtones.
To fully exploit these signals, we must develop a framework for quasinormal mode (QNM) interactions. The ringdown follows a highly nonlinear merger phase, and although numerical simulations suggest that a linear superposition of modes models the signal well, the connection to a fully nonlinear description remains unclear. A key difficulty is that Kerr QNMs do not form a complete orthogonal basis. Moreover, their spatial wavefunctions diverge at both the bifurcation sphere and spatial infinity, complicating the construction of canonical inner products on standard Cauchy hypersurfaces. Thus, it remains unclear how to project onto QNMs to study nonlinear mode mixing. In this talk, I will present bilinear forms that serve as inner-product analogues for Weyl scalars, constructed from conserved currents and symmetry operators. I will discuss their key properties on hyperboloidal slices, using the Schwarzschild spacetime as a model example. This work is in collaboration with Rodrigo Panosso Macedo, Christiana Pantelidou, and Laura Sberna.

Abstract:
Primordial gravitational waves offer a rare opportunity to probe physics at energies far beyond the reach of terrestrial experiments, opening a unique window onto the very early universe. In this talk, I will explore how inflationary models beyond the simplest single-field picture can generate distinctive gravitational-wave signatures, and what this means for testing inflation with current and future interferometers. I will also discuss how anisotropies in the gravitational-wave energy density could become a powerful new probe of the inflationary era, with the potential to disentangle an inflationary background from those produced by other cosmic processes.

Abstract:
Solutions to general relativity with a negative cosmological constant have received significant attention due to the conjectured AdS/CFT correspondence, a particularly well-understood example of which is exhibited in 2+1 dimensions.
I will review known vacuum solutions to general relativity with a negative cosmological constant in 2+1 dimensions and discuss the difficulties in defining mass, which are resolved via minimisation using a positive energy theorem. I will present a gluing theorem for vacuum time-symmetric general-relativistic initial data sets in two spatial dimensions. By gluing two given time-symmetric vacuum initial data sets at conformal infinity, we obtain new time-symmetric vacuum initial data sets. I will sketch the derivation of the mass formulae of the resulting manifolds. Our gluing theorem yields complete manifolds with any mass aspect function, which are smooth except for one conical singularity.

Abstract:
Fields Medalist Prof. Manjul Bhargava will give a talk on his recent proof of van der Waerden's Conjecture.

Abstract:
We review a construction of two-dimensional chiral algebras inside four-dimensional conformal theories with 8 or more supercharges. While the chiral algebra is not unitarity, it inherits an extra structure from the fact that the parent four-dimensional theory is unitarity. We discuss this extra structure and use it to obtain constraints on which chiral algebras arise from four dimensions, as well as constraints on four-dimensional theories.

Abstract:
In holographic CFT's, such as N=4 SYM, it is natural to organise the spectrum in single and multi particle states. By now we have a wealth of information about 4-point correlators with BPS single particle states, but much less is known about 4-point correlators involving multi particle states. I will discuss how we can calculate such correlators at strong coupling by using various techniques: bootstrap, OPE's of higher point functions and a bulk approach based on 1/2-BPS asymptotically AdS supergravity solutions. I will provide explicit results for various families of 4-point correlators with one or two 1/2-BPS multi particle states in the context of the AdS5/N=4 SYM duality.

Abstract:
I will describe the use of methods of arithmetic geometry to find gauge theories in 4 dimensions that are free of anomalies. In many cases, it is possible to find all such theories.

Abstract:
In this talk, we present a bootstrap construction of planar two-loop
six-point scattering amplitudes in QCD theory, focusing on their maximal
transcendental weight components. From an analysis of on-shell diagrams,
we identify a complete and conformally-invariant set of leading
singularities. Combining these results with recent advances in
understanding the relevant hexagonal function space from canonical
differential equation, we can uniquely determine the maximal weight
parts of helicity amplitudes by imposing correct physical limits. We
especially present a detailed picture of two-loop six-point amplitudes
at the symbol level in pure Yang–Mills theory. It also reveals a
remarkably small and tightly constrained function alphabet, hinting at a
deeper organizing principle similar to that observed in maximally
supersymmetric Yang–Mills theory.