Øresund seminar, Spring 2013: afternoon April 12, 2013, in Lund
Speakers: Antti KUPIAINEN (Helsinki), Carsten Lunde PETERSEN (Roskilde),
Amol SASANE (Lund), Sara Maad SASANE (Lund)
(For more details see the
Seminar Page in Lund and the the Calendar of
Lund Center for Mathematical Sciences)
Øresund seminar, Fall 2012
Friday November 30, 2012
Institute for Mathematical Sciences - Copenhagen University
Auditorium 10
Schedule: (Titles and abstracts below)
13:30-14:20 Viviane Baladi
14:30-15:20 Magnus Aspenberg
coffee break
16:00-16:50 Wen Deng
17:00-17:50 Kurt Johansson
Organisation:
V. Baladi (contact organiser), J.-Ph. Solovej - in Copenhagen
N. Dencker, S. Pott - in Lund
Viviane Baladi (Copenhagen University)
Natural boundaries for dynamically defined power series
Ruelle transfer operators are linear operators associated to dynamical
systems. For systems with enough smoothness and hyperbolicity,
they have "nice spectrum" (i.e. a spectral gap) on a "suitable"
Banach space.
The susceptibility function describes how the "physical"
invariant measure of a dynamical system behaves under
perturbations of the dynamics. For certain simple systems
with bifurcations, the susceptibility function corresponds
to the resolvent of a transfer operator acting on a vector
which is just a snippet too big to fit in the "suitable"
Banach space.
In a recent work with S Marmi and D Sauzin, we found that,
although the transfer operator forced to deal with
this singular snippet suffers a meltdown, this
meltdown leads to a natural boundary for the susceptibility
function via a rather graceful mechanism. For this, we apply
a very elegant recent work of J Breuer and B Simon.
Magnus Aspenberg (Lund, LTH):
On Misiurewicz maps for rational functions on the Riemann sphere
Misiurewicz maps in complex dynamics are non-hyperbolic maps
without parabolic periodic points and such that the critial set on the
Julia set is non-recurrent. I will sketch the techniques of proving
measure-theoretic theorems about these maps. For instance, we prove that
they have measure zero but full Hausdorff dimension. Also they can be
perturbed into hyperbolic maps.
The next natural step would be to extend these results to the so-called
semi-hyperbolic maps studied by Carleson, Jones and Yoccoz.
Semi-hyperbolicity is weaker than the Misiurewicz condition above; each
critical point on the Julia set is non-recurrent instead of the whole
critical set.
Wen Deng (Lund, LU): Pseudospectrum for Oseen vortices operators
Oseen vortices are self-similar solutions to the vorticity equation in
R^2, and
it was proved by T.Gallay and C.E.Wayne in 2005 that these solutions are
stable for
any value of the circulation Reynolds number. The linearization of the
system around
an Oseen vortex naturally gives rise to a non-self-adjoint operator. In this
talk,
we shall discuss spectral and pseudospectral properties of the linearized
operator
in the fast rotation limit. In particular, we give some resolvent estimate
for the
operator along the imaginary axis, which are also optimal.
Kurt Johansson (KTH Stockholm): Scaling limits for random matrices and discrete models
I will give an overview of scaling limits for the eigenvalues of
random matrices, like the local bulk and edge statistics described by the
sine and Airy kernels respectively. These and related limits also occur in
many discrete probability models and a central problem in the area is that
of the universality of these scaling limits.
Information for external participants
External participants will be welcome in the lounge
in the 4-th floor of the Mathematics building
(Universitetsparken 5) to have their (self-bought)
lunch between 12:30 and 13:30. Sandwiches
can be bought e.g. in the ground floor of the Mathematics
building, you can also get a hot meal there
and bring the plate upstairs (they may have run out of sandwiches
if you arrive a bit late, bringing your own sandwich is
an option). Auditorium 10 is accessible from the first-floor
vandrehallen in the building (take the stairs on the right from ground floor of
vandrehallen, after having completely passed the cafeteria).
The best way to come to Mathematics is to go
to Nørreport (subway or train station) then take
a bus (184, 185 or 150S) at Nørreport, and
get off at stop Universitetsparken. (Bus 43 does not run on Nov 30.
Bus 42 does not stop at Universitetstparken on Nov 30.) Finding the building
Universitetsparken 5 (containing Mathematics,
but also Chemistry) the first time is then best
accomplished by having studied the Googlemap beforehand
(one convenient access is from Nørreallé).
For access information, see also the red pointer on the map
given here
Viviane Baladi
DMA - ENS - CNRS