Abstract: In the 1970s Berry conjectured that the behavior of high
energy, quantum-chaotic billiard systems could be well modeled by
random waves. That is random combinations of the plane waves e^{ik
·x}. On manifolds it is more natural to...
$C^r$ closing lemma is an important statement in the theory of
dynamical systems, which implies that for a $C^r$ generic system
the union of periodic orbits is dense in the nonwondering domain.
$C^1$ closing lemma is proved in many classes of...
Abstract: I will discuss recent results regarding the problem of
counting intersections of eigenfunction nodal sets with real
analytic curves H and the connection to eigenfunction restriction
bounds over H.
We present joint work with Jan Maas showing that Quantum Markov
semigroups satisfying a detailed balance condition are gradient
flow for quantum relative entropy, and use this prove some
conjectured inequalities arising in quantum information theory...
Abstract: The classical Liouville theorem says that if a harmonic
function on the plane is bounded then it is a constant. At the same
time for any angle on the plane, there exist non-constant harmonic
functions that are bounded outside the angle...
We provide a duality framework for Bayesian Mechanism Design.
Specifically, we show that the dual problem to revenue maximization
is a search over virtual transformations. This approach
yields a unified view of several recent breakthroughs in...
Abstract: We present a sequence of positive quadratic forms
associated with harmonic functions on Abelian groups. We show how
the positivity property recovers the polynomial Liouville property
and we prove a three spheres theorem in terms of random...
