The presence of additional light fields during inflation
can source isocurvature fluctuations, which can cause the curvature
perturbation $\zeta$, and its statistics to evolve on superhorizon scales. I
will demonstrate that if these fluctuations have not completely decayed before
the onset of perturbative reheating, then primordial observables such as the
level of non--Gaussianity can develop substantial reheating dependant
corrections. I will argue that for inflationary models where an adiabatic
condition is not reached before the relevant fields begin to decay, we must be
careful in our interpretation of any observational constraints that place
bounds on the statistics of $\zeta$.
Two types of topological phases have attracted a lot of
attention in condensed matter physics:
symmetry protected
topological(SPT) phases and topologically ordered phases.
On the one hand, SPT phases are protected by given global symmetries while
there is no topological order in the bulk. On the other hand, topologically
ordered phases do not require symmetry and feature topological ground state
degeneracy. In this talk, I present a
classification of phases with both topological orders and global symmetries,
equipped with local bosonic exactly solvable models. This classification, in
some sense, organizes previous pieces of understandings on SPT phases,
topological orders, symmetry fractionalizations, into a single framework.
Solution of the exactly solvable models and measurable consequences will be
discussed.
In
quantum information theory, random techniques have proven to be very useful.
For example, many questions related to the problem of the additivity of
entropies of quantum channels rely on fine properties of concentration of
measure.
In
this talk, I will show that very different techniques of random matrix theory
can complement quite efficiently more classical random techniques. I will spend
some time on discussing the Weingarten calculus approach, and the operator norm
approach. Both techniques have been initially used in free probability theory,
and I will give some new applications of these techniques to quantum
information theory.