Talks

In this mini course, I shall introduce the basic concepts in 2D topological orders by studying simple models of topological orders and then introduce topological quantum computing based on Fibonacci anyons. Here is the (not perfectly ordered) syllabus.                      

•        Overview of topological phases of matter
•        Z2 toric code model: the simplest model of 2D topological orders
•        Quick generalization to the quantum double model
•        Anyons, topological entanglement entropy, S and T matrices
•        Fusion and braiding of anyons: quantum dimensions, pentagon and hexagon identities
•        Fibonacci anyons
•        Topological quantum computing.

In this talk I will show the equivalence of several different tests of the Jacobi identity for celestial currents at tree level, in particular finding a simple, practical condition on hard momentum space 4-point amplitudes in any EFT. Along the way I will clarify the role of the order of soft and collinear limits in obstructing the Jacobi identity for soft insertions and I will argue that, despite their current-algebra-like properties, soft insertions as formulated in this talk cannot be interpreted as local operators in celestial conformal field theory.

Zoom link:  https://pitp.zoom.us/j/99642885302?pwd=dWZhbzZUYnBuSlJ3UzBhSHdqdzVKdz09

Inflationary cosmology is notoriously past geodesically incomplete in many situations. However, it is generally unknown whether the geodesic incompleteness implies the existence of an initial spacetime curvature singularity or whether the spacetime may be extended beyond its null past boundary. In homogeneous and isotropic cosmology with flat spatial sections, we classify which past inflationary histories have a scalar curvature singularity and which might be extendible/non-singular. We derive rigorous extendibility criteria of various regularity classes for quasi-de Sitter spacetimes that evolve from infinite proper time in the past. Beyond homogeneity and isotropy, we show that continuous extensions respecting the Einstein field equations with a perfect fluid must have the equation of state of a de Sitter universe asymptotically. An interpretation of our results is that past-eternal inflationary scenarios are most likely physically singular, except in very special situations.

Zoom link:  https://pitp.zoom.us/j/98334550627?pwd=UnR3eUxZRFZpeEZoOGEwNkJuc0M0UT09