Talks

Positivity properties of scattering amplitudes are typically related to unitarity and causality. However, in some cases positivity properties can also arise from deeper underlying structures. In these lectures, we will discuss infinitely many positivity constraints that certain amplitudes and their derivatives obey called completely monotonicity in the mathematics literature.
In the first lecture, we will discuss completely monotone functions and some of their properties. We shall then show why some objects such scalar Feynman integrals admit this property via integral representations. In the second lecture, we will discuss the connection between complete monotonicity and positive geometries.

We discuss the newly introduced hidden zeros in a class of scattering amplitudes. We relate their existence to color-kinematics duality and the double copy. Further we also discuss splitting of the scattering amplitude near these zeros and show how such behaviour can be seen as a result of a residue theorem after a complex shift. Similar shifts allow us to calculate amplitudes of related theories as well.

Positivity properties of scattering amplitudes are typically related to unitarity and causality. However, in some cases positivity properties can also arise from deeper underlying structures. In these lectures, we will discuss infinitely many positivity constraints that certain amplitudes and their derivatives obey called completely monotonicity in the mathematics literature.
In the first lecture, we will discuss completely monotone functions and some of their properties. We shall then show why some objects such scalar Feynman integrals admit this property via integral representations. In the second lecture, we will discuss the connection between complete monotonicity and positive geometries.

I will give a brief review of some recent progress regarding mathematical aspects of three closely-related quantities in N=4 SYM theory: half-BPS correlators, the square of amplitudes and energy correlators.

Various models of physics beyond the Standard Model predict the existence of ultralight bosons. These particles can be produced through superradiant instabilities, which create boson clouds around rotating black holes, forming so-called "gravitational atoms". In this talk, I review a series of papers that study the interaction between a gravitational atom and a binary companion. The companion can induce transitions between bound states of the cloud (resonances), as well as transitions from bound to unbound states (ionization). These processes back-react on the binary’s dynamics and leave characteristic imprints on the emitted gravitational waves (GWs), providing direct information about the mass of the boson and the state of the cloud. However, some of the resonances may destroy the cloud before the binary enters the frequency band of future gravitational wave detectors. This destruction leaves a mark on the binary’s eccentricity and inclination, which can be identified through a statistical analysis of a population of binary black holes.

We prove the equivalence between two traditional approaches to the classical mechanics of a massive spinning particle in special relativity. One is the spherical top model of Hanson and Regge, recast in a Hamiltonian formulation with improved treatment of covariant spin constraints. The other is the massive twistor model, slightly generalized to incorporate the Regge trajectory relating the mass to the total spin angular momentum. We establish the equivalence by computing the Dirac brackets of the physical phase space carrying three translation and three rotation degrees of freedom. Lorentz covariance and little group covariance uniquely determine the structure of the physical phase space. We comment briefly on how to couple the twistor particle to electromagnetic or gravitational backgrounds.