Tue, 23 Jun 2020
12:00

Cluster patterns in Landau and Leading Singularities via the Amplituhedron

Matteo Parisi
(Oxford)
Abstract

In this talk I will present some recent explorations of cluster-algebraic patterns in the building blocks of scattering amplitudes in N = 4 super Yang-Mills theory. In particular, I will first briefly introduce the main characters on stage, i.e. Leading Singularities, Landau singularities, the amplituhedron and cluster algebras. I will then present my main conjecture, "LL-adjacency", which makes all the above characters play together: given a maximal cut of a loop amplitude, Landau singularities and poles of each Yangian invariant appearing in any representation of the corresponding Leading Singularities can be found together in a cluster.  I will explain how the conjecture has been tested for all one-loop amplitudes up to 9 points using cluster algebraic and amplituhedron-based methods.  Finally, I will discuss implications for computing loop amplitudes and their singularity structure, and open research directions.

This is based on the joint work with Ömer Gürdoğan (arXiv: 2005.07154).

Hawking Points in the Cosmic Microwave Background - a challenge to the concept of Inflation

For thirty years Oxford Mathematician Roger Penrose has challenged one of the key planks of Cosmology, namely the concept of Inflation, now over 40 years old, according to which our universe expanded at an enormous rate immediately after the Big Bang. Instead, fifteen years ago, Penrose proposed a counter-concept of Conformal Cyclic Cosmology by which Inflation is moved to before the Big Bang and which introduces the idea of preceding aeons.

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