It has been known for some time that
a system with a filled band will have an integer quantum Hall conductance equal
to its Chern number, a toplogical index associated with the band. While this is
true for a system in a magnetic field with filled Landau Levels, even a system
in zero external field can exhibit the QHE if its band has a Chern number. I
review this issue and discuss a more recent question of whether a partially
filled Chern band can exhibit the Fractional QHE. I describe the work done with
Ganpathy Murthy in which we show how composite fermions, which were so useful
in explaining the usual FQHE, can be introduced here and with equal success by
adapting our Hamiltonian Theory of CFs developed for the FQHE in the continuum.
The
combinatorial problems associated with the counting of black hole states in
loop quantum gravity can be analyzed by using suitable generating functions.
These not only provide very useful tools for exact computations, but can also
be used to perform an statistical analysis of the black hole degeneracy
spectrum, study the interesting substructure found in the entropy of
microscopic black holes and its asymptotic behavior for large horizon areas.
The methods that will be described are relevant for the discussion of the
thermodynamic limit for black holes in the area canonical ensemble. This is an
important issue in order to understand sub-leading corrections to the
Bekenstein-Hawking law.
When nuclear matter is heated beyond a temperature of 2 trillion
degrees, it converts into a strongly coupled plasma of quarks and
gluons, the sQGP. Experiments using highly energetic collisions
between heavy nuclei have revealed that this new state of matter is a
nearly ideal, highly opaque liquid. A description based upon string
theory and black holes in five dimensions has made the quark- gluon
plasma an iconic example of a strongly coupled quantum system. In this
lecture I will survey the observed properties of the sQGP in the light
of the latest results from RHIC and LHC. On the theoretical side, I
will discuss the thermalization and entropy production problem and
origin and role of event-by-event fluctuations.
The spectrum of the cosmic microwave background (CMB) is known to be extremely close to a perfect blackbody. However, even within standard cosmology several processes occurring in the early Universe lead to distortions of the CMB at a level that might become observable in the future. This could open an exciting new window to early Universe physics. In my talk I will then explain in more detail why the cooling of matter in the early Universe causes a negative mu- and y-type distortion and how the damping of primordial small-scale perturbations before recombination could allow placing interesting constraints on different inflationary models.