Talks

In gauge theories, there is an inherent tension between locality and gauge invariance.   This is precisely expressed by the failure to factorize the physical Hilbert space into local tensor products.   The extended Hilbert space offers a resolution to this problem by embedding physical states into a larger Hilbert space containing gauge variant degrees of freedom.  For two dimensional TQFT's, we show how this extension fits inside the framework of extended quantum field theory, as described by the Moore-Segal axioms.  These are sewing axioms that impose a sort of spacetime covariance for the extended Hilbert space.   For the case of two-dimensional Yang Mills and it's string theory dual, we show how this framework leads to exact calculations of multi-interval modular flow,  ,negativity, and entanglement entropy.  Moreover, we given an axiomatic formulation of the "entanglement brane", which nicely compliments the worldsheet description given in previous work.

We perform a full (3+1)-dimensional numerical simulation of the axion field around the QCD epoch. Our aim is to fully resolve large dynamical non-linear effects in the inhomogenous axion field. These effects are important as they lead to large overdensities in the field at late times. Those overdensities will eventually evolve into axion minicluster, which have various phenomenological implications like microlensing events. It is therefore important to have a reliable estimate of the number of overdensities and their mass relation.

The 8-vertex model and the XYZ spin chain have been found to emerge from gauge theories in various ways, such as 4d and 2d Nekrasov-Shatashvili correspondences, the action of surface operators on the supersymmetric indices of class-Sk theories, and correlators of line operators in 4d Chern-Simons theory.  I will explain how string theory unifies these phenomena.  This is based on my work with Kevin Costello [arXiv:1810.01970].

Positive geometries are real semialgebraic spaces that are
equipped with a meromorphic ``canonical form" whose residues reflect
the boundary structure of the space.  Familiar examples include
polytopes and the positive parts of toric varieties.  A central, but
conjectural, example is the amplituhedron of Arkani-Hamed and Trnka.
In this case, the canonical form should essentially be the tree
amplitude of N=4 super Yang-Mills.

I will talk about the definition and examples of positive geometries,
and discuss what is known about the geometry and combinatorics of the
amplituhedron.  The talk will be based on various joint works with
Arkani-Hamed, Bai, Galashin, and Karp.

Mermin-Wagner theorem, Goldstone's theorem, quantum thermalization and eigenstate thermalization hypothesis using Mathematica (Pedro's Notebook)

The unexpected diversity of planetary systems has posed challenges to our classical understanding of planetary formation. For instance, Jupiter sized planets have been detected with short orbital periods of a few days in misaligned orbits with respect to the spin-axis of their host stars. I will first describe the statistical implication of detecting misaligned hot Jupiters and will suggest how dynamical interactions between an outer perturber and the inner planet, can naturally lead to the formation of such misaligned hot Jupiters. Next, I will discuss a similar dynamical process in the outer Solar System, far away from our Sun, which could cause the observed clustering of extreme trans-Neptunian objects. This can constrain properties of a possible outer planet, Planet Nine, in our own Solar System.