Abstract: In the talk I will describe what is known and (mostly)
unknown about asymptotic statistical topology and geometry of zero
sets of random spherical harmonics of large degree. I plan to
discuss (a) several provoking open questions and (b)...
Abstract: An open problem is to prove that for any (or at least any
generic) Riemannian metric, there is some sequence of
eigenfunctions of the Laplacian for which the number of nodal
domains tends to infinity. It sounds easy but as yet there are...
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...
