Talks

I will review the recent progress on the application of the Amplituhedron framework to study IR finite quantities in the planar N=4 SYM theory. This includes the negative geometry expansion for the Wilson loops and the deformed Amplituhedron which connects to the Coulomb branch amplitudes.

In a classical scattering problem, the classical eikonal is defined as the generator of the canonical transformation that maps in-states to out-states. It can be regarded as the classical limit of the log of the quantum S-matrix. In a classical analog of the Born approximation in quantum mechanics, the classical eikonal admits an expansion in oriented tree graphs, where oriented edges denote retarded/advanced worldline propagators. The Magnus expansion, which takes the log of a time-ordered exponential integral, offers an efficient method to compute the coefficients of the tree graphs to all orders. In a relativistic setting, our methods can be applied to the post-Minkowskian (PM) expansion for gravitational binaries in the worldline formalism. Importantly, the Magnus expansion yields a finite eikonal, while the naïve eikonal based on the time-symmetric propagator is infrared-divergent from 3PM on.

I will review the recent progress on the application of the Amplituhedron framework to study IR finite quantities in the planar N=4 SYM theory. This includes the negative geometry expansion for the Wilson loops and the deformed Amplituhedron which connects to the Coulomb branch amplitudes.

In this talk we will review the amplituhedron, the correlahedron, and the relations between them. We will explore the generalisation of the definition of positive geometry required for it (and also for the loop amplituhedron). We will show the equivalence between the correlahedron and a recently defined geometry for four-point correlators. Finally we will discuss the non maximally nilpotent case.

In these lectures, we will discuss two different approaches to on-shell recursion relations that are used to construct scattering amplitudes of various massless theories. The first lecture, based on soft limits of amplitudes, will be on theories resulting from spontaneous (super-)symmetry breaking. The second lecture will focus on the mathematical structures or building blocks that result from BCFW recursion of maximally supersymmetric gluons and gravitons.

Scattering amplitudes in N=4 supersymmetric Yang-Mills theory can be computed using the BCFW recursion. There are many ways of running the recursion and hence many formulas for a single amplitude. The amplituhedron, defined by Arkani-Hamed and Trnka, is a remarkable geometric object which encodes N=4 SYM amplitudes and their many formulas. I will give an introduction to the (tree-level) amplituhedron and the mathematics behind it, such as the positive Grassmannian. Time permitting, I will discuss recent developments involving the structure of the amplituhedron, such as the surprising "cluster adjacency" phenomenon.

In these two lectures we will go over some applications of nonlinear algebra to physics. In the first lecture we will take a look at the CHY scattering equations in order to see what algebraic statistics and theoretical physics have in common. In the second lecture, we will consider a classical algebraic variety, the Grassmannian. We will discuss its basic properties and see several contexts in which the Grassmannian appears in positive geometry and physics.

In these two lectures we will go over some applications of nonlinear algebra to physics. In the first lecture we will take a look at the CHY scattering equations in order to see what algebraic statistics and theoretical physics have in common. In the second lecture, we will consider a classical algebraic variety, the Grassmannian. We will discuss its basic properties and see several contexts in which the Grassmannian appears in positive geometry and physics.

Scattering amplitudes in N=4 supersymmetric Yang-Mills theory can be computed using the BCFW recursion. There are many ways of running the recursion and hence many formulas for a single amplitude. The amplituhedron, defined by Arkani-Hamed and Trnka, is a remarkable geometric object which encodes N=4 SYM amplitudes and their many formulas. I will give an introduction to the (tree-level) amplituhedron and the mathematics behind it, such as the positive Grassmannian. Time permitting, I will discuss recent developments involving the structure of the amplituhedron, such as the surprising "cluster adjacency" phenomenon.