(Georgia Institute of Technology, 2016-10-11)
Kuchment, Peter
The talk will survey some known results and
unresolved problems concerning analytic properties of
dispersion relations and their role in various spectral theory
problems for periodic operators of mathematical physics,
such as spectral structure, embedded impurity eigenvalues,
Greens function asymptotics, Liouville theorems, etc.
(Georgia Institute of Technology, 2016-10-11)
Brandão, Fernando
In this talk I will show that quantum many-body
states satisfying an area law for entanglement have a local
entanglement spectrum, i.e. the entanglement spectrum can
be approximated by the spectrum of a local model acting on
the boundary of the region. The result follows from a version
of the Hammersley-Clifford Theorem (which states that
classical Gibbs states are equivalent to Markov networks) for
quantum approximate Markov chains. In particular I'll argue
that those are in one-to-one correspondence to 1D quantum
Gibbs states
(Georgia Institute of Technology, 2016-10-10)
Zworski, Maciej
Microlocal analysis exploits mathematical manifestations
of the classical/quantum (particle/wave) correspondence and has
been a successful tool in spectral theory and partial differential
equations. We can say that these last two fields lie on the
quantum/wave side. Recently, microlocal methods have been applied to the study of
classical dynamical problems, in particular of chaotic (Anosov)
flows. I will illustrate this by proving that the order of vanishing of the
dynamical zeta function at zero for negatively curved surfaces is
given by the absolute value of the Euler characteristic (joint work
with S Dyatlov).