- David Borthwick
"Geometric bounds on resonances"
For
conformally compact manifolds which are hyperbolic outside a compact
set, we have upper and lower global bounds on the resonance counting
function, with exponent given by the dimension, but relatively little
is known about the geometric content of the constants in these
bounds. We'll discuss a method that can yield this information,
and present some applications.
- Kiril Datchev
"Resonance free regions for manifolds with hyperbolic ends"
- Alexander Gamburd
"Uniform spectral gap bounds and applications" (3h minicourse)
- Sébastien
Gouëzel (Rennes)
"Small eigenvalues of the (foliated) laplacian in Teichmüller space"
- Harald Helfgott
"Title"
Abstract
- Frédéric Hérau
"Hypocoercivity for some linear kinetic equations with a boundary"
We
consider the Fokker-Planck equation or the linear Boltzmann equation in
a domain with a possible external potential and with specular
reflexion conditions at the boundary. We show existence and uniqueness
of a weak solution in weighted adapted spaces, and prove explicit
exponential time decay to the equilibrium. The proof of existence and
uniqueness follows a purely hilbertian method. Hypocoercivity
estimates are a consequence of coercivity of the collision part
of the equation, of coercivity in the space variable of a Witten
Laplacian, and of an explicit "cross operator" mixing velocity
and space variables. This is a joint work with D. Le Peutrec.
- Victor Ivrii
"2D- and 3D-Magnetic Schrödinger Operator: Short Loops and Pointwise Spectral Asymptotics"
For
Schrödinger operator with a strong magnetic field I am considering
asymptotics of e(x,x,τ) (no spatial averaging) as μ→∞, h→+0 where
e(x,y,τ) is the Schwartz kernel of the spectral projector, h and μ are
semiclassical and binding parameters respectively. In pointwise
asymptotics not only periodic trajectories but also loops are
important. And they are plentiful here as for k=±1,±2,±3,… there is a
loop after k wingings!
- Dmitry Jakobson
"Extremal metrics for manifolds and graphs"
- Alex Kontorovitch
"On Zaremba's Conjecture"
It
is well-known that modular multiplication is "random". This concept is
useful for many applications, such as generatingpseudorandom sequences
or good lattice points for multi-dimensional quasi-Monte Carlo
integration. Zaremba's theorem quantifies the quality of this
"randomness" in terms of certain Diophantine properties of the modulus
and multiplier, related to continued fraction expansions. His 40-year
old conjecture predicts the ubiquity of moduli and multipliers for
which this Diophantine property is uniform. In joint work with Jean
Bourgain, we use recent advances in the Affine Sieve, as well as
spectral gap technology for the "congruence" Ruelle transfer operator,
to make progress on this problem.
- Carlangelo Liverani
"Ruelle Zeta functions for Anosov flows"
I will illustrate some results on the Ruelle zeta function for Anosov
flows. In particular we prove that the Ruelle zeta function is
meromorphic in the entire complex plane for smooth Anosov flows. (Work in collaboration with P.Giulietti and M.Pollicott).
- Dieter Mayer
"Behaviour of the zeros of the Selberg zeta function for Gamma_0(4) under a character deformation"
- Clément Mouhot
"Factorization of non-symmetric operators and application to spectral gap estimates"
- Marc Peigné
"On some exotic Schottky groups in variable curvature"
We
construct a Cartan-Hadamard manifold with pinched negative
curvature whose group of isometries possesses
divergent discrete free subgroups with parabolic
elements that do not satisfy the so-called
``parabolic gap condition''. This construction relies on the
comparaison between the Poincar\'e series of these free
groups and the potential of some transfer operator which appears
naturally in this context.
- Peter Perry
"Generic lower bounds on the resonance counting function for manifolds hyperbolic near infinity"
- Vesselin Petkov
"Asymptotics of the periods of closed trajectories for hyperbolic flows"
- Thomas Roblin
"Distributions invariantes par le feuilletage horosphérique"
- Masato Tsujii
"Spectrum of transfer operators" (3h minicourse)
My
plan is to speak about spectrum of transfer operators for hyperbolic
diffeomorphisms, contact Anosov flows, prequantum transfer operators
for Anosov diffeomorphisms.
- Steve Zelditch
"An explicit conjugation between classical and quantum mechanics on a compact hyperbolic manifold."