Monday, March 19 |
07:00 - 08:45 |
Breakfast ↓ Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building. (Vistas Dining Room) |
08:45 - 09:00 |
Introduction and Welcome by BIRS Station Manager (TCPL 201) |
09:00 - 09:45 |
Carlangelo Liverani: Deterministic walks in random environment ↓ I will consider a class of deterministic walks in random environment and discuss a strategy for studying
their long time behavior. I will describe some simple examples and discuss the possibility of
applying this strategy to the random Lorenz gas (work in collaboration with Romain Aimino) (TCPL 201) |
09:50 - 10:35 |
Peter Balint: A continuum model of mean field coupled circle maps ↓ We consider a model of globally coupled circle maps, the finite version
of which was studied in the works of Koiller-Young, Fernandez and Balint-Selley. In the
continuum version the state of the system is described by a density on
the circle. For a fairly general class of expanding circle maps we show that, for sufficiently
small coupling, there is a unique invariant density. For sufficiently strong coupling the
density converges to a Dirac mass that moves chaotically on the circle. This is joint work
with G. Keller, F. Selley and I.P. Toth. (TCPL 201) |
10:35 - 10:50 |
Group Photo ↓ Meet in foyer of TCPL to participate in the BIRS group photo. The photograph will be taken outdoors, so dress appropriately for the weather. Please don't be late, or you might not be in the official group photo! (TCPL Foyer) |
10:50 - 11:05 |
Coffee Break (TCPL Foyer) |
11:05 - 11:50 |
Cecilia Gonzalez-Tokman: results for non-autonomous dynamical systems. ↓ In this talk we discuss recent developments concerning stability properties
of non-autonomous dynamical systems, motivated by? the ergodic
theoretical study of random, forced or time-dependent systems
and their coherent structures. In the setting of random interval maps
we present results about stability of random absolutely continuous invariant
measures. In the context of multiplicative ergodic theory, we
discuss results on stability of Lyapunov exponents and Oseledets spaces
in nite and innite-dimensional settings. This is based on joint works
with Gary Froyland, Rua Murray and Anthony Quas. (TCPL 201) |
11:50 - 13:00 |
Lunch (Vistas Dining Room) |
13:00 - 14:00 |
Guided Tour of The Banff Centre ↓ Optional: Meet in the Corbett Hall Lounge for a guided tour of The Banff Centre campus. (Corbett Hall Lounge (CH 2110)) |
14:30 - 15:00 |
Coffee Break (TCPL Foyer) |
17:30 - 19:30 |
Dinner ↓ A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building. (Vistas Dining Room) |
19:30 - 20:15 |
Vadim Kaloshin: Can you hear the shape of a drum and deformational spectral rigidity of planar domains? ↓ M. Kac popularized the question {\em Can you hear the shape of a drum?}
Mathematically, consider a bounded planar domain Ω and the associated
Dirichlet problem Δu+λ2u=0 with u|∂Ω = 0. The set of
λs such that this equation has a solution, denoted L(Ω)
is called the Laplace spectrum of Ω.
Does Laplace spectrum determine Ω? In general, the answer is negative.
Consider the billiard problem inside ?. Call the length spectrum the
closure of the set of perimeters of all periodic orbits of the billiard. Due
to deep properties of the wave trace function, generically, the Laplace
spectrum determines the length spectrum. We show that any generic axis
symmetric planar domain with is dynamically spectrally rigid, i.e. can't be
deformed without changing the length spectrum. This partially answers a
question of P. Sarnak. This is joint works with J. De Simoi, A. Figalli, and
J. De Simoi, Q. Wei. (TCPL 201) |
20:20 - 21:05 |
Vered Rom-Kedar: Exponential Fermi accelerators in closed and open geometries and on energy equilibration ↓ In 1949, Fermi proposed a mechanism for the heating of particles
in cosmic rays. He suggested that on average, charged particles gain
energy from collisions with moving magnetic mirrors since they hit
the mirrors more frequently with heads on collisions. Fermi, Ulam
and their followers modeled this problem by studying the energy gain
of particles moving in billiards with slowly moving boundaries. Until
2010 several examples of such oscillating billiards leading to power-
law growth of the particles averaged energy were studied. In 2010
we constructed an oscillating billiard which produces exponential in
time growth of the particles energy [1]. The novel mechanism which
leads to such an exponential growth is robust and may be extended to
arbitrary dimension. Moreover, the exponential rate of the energy gain
may be predicted by utilizing adiabatic theory and probabilistic models
[2,3]. The extension of these results to billiards with mixed phase space
leads to the development of adiabatic theory for non-ergodic systems
[4]. Finally, such accelerators lead to a faster energy gain in open
systems, when particles are allowed to enter and exit them through
a small hole [5]. The implications of this mechanism on transport in
extended systems [6] and on equilibration of energy in closed systems like springy billiards will be discussed [7].
These are joint works, mainly with with K. Shah, V. Gelfreich and
D. Turaev [1-5],[7] and [6] is with M. Pinkovezky and T. Gilbert:
[1] K. Shah, D. Turaev and V. Rom-Kedar, Exponential energy
growth in a Fermi accelerator, Phys. Rev. E 81, 056205, 2010.
[2] V. Gelfreich, V. Rom-Kedar, K. Shah, D. Turaev, Robust expo-
nential accelerators, PRL 106, 074101, 2011. (TCPL 201) |