In this talk I will discuss a new lower bound for the off-diagonal Ramsey numbers $R(3,k)$. For this, we develop a version of the triangle-free process that is significantly easier to analyse than the original process. We then 'seed' this process with a carefully chosen graph and show that it results in a denser graph that is still sufficiently pseudo-random to have small independence number.

This is joint work with Marcelo Campos, Matthew Jenssen and Marcus Michelen.

I will present a novel correspondence between the gravitational phase space at null infinity and the subleading phase space for finite-distance null hypersurfaces, such as black hole horizons. Utilizing the Newman-Penrose formalism and an off-shell Weyl transformation, this construction transfers key structures from asymptotic boundaries to null surfaces in the bulk—for instance, a notion of radiation. Imposing self-duality conditions, I will identify the celestial symmetries and construct their canonical generators for finite-distance null hypersurfaces. This framework provides new observables for black hole physics.

String-inspired methods have revealed deep connections between seemingly unrelated field theories. A striking example is the double copy structure, rooted in the string theory Kawai–Lewellen–Tye (KLT) relations. In this talk, we will explore how a variety of theories—including colored scalars, pions, and gluons—emerge from a single, unifying object: the KLT kernel. We will argue that this kernel is not only a powerful computational tool, but also a conceptually rich structure worthy of independent study.

Based mainly on https://arxiv.org/abs/1610.04230 and the recent work https://arxiv.org/abs/2505.01501.