Equidistribution of random waves on shrinking balls

Melissa Tacy
Australian National University
February 17, 2017
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 randomize over the eigenfunctions of the Laplace-Beltrami operator. In this talk I will present results showing that such random waves equidistribute on balls that shrink with the eigenvalue. This is joint work with Xiaolong Han.

$C^\infty$ closing lemma for three-dimensional Reeb flows via embedded contact homology

Kei Irie
Kyoto University
February 16, 2017
$C^r$ 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 dynamical systems, however $C^r$ closing lemma with $r > 1$ is proved only for few cases. In this talk, I'll prove $C^\infty$ closing lemma for Reeb flows on closed contact three-manifolds. The proof uses recent developments in quantitative aspects of embedded contact homology (ECH).

Post Concert Discussion

Gamelan Galak Tika and David Lang
February 10, 2017
Edward T. Cone Concert Series: February 10, 2017

A concert of new and traditional Balinese music will be performed by Boston’s large percussion orchestra, Gamelan Galak Tika. An ensemble comprised of gongs, metallophones and hand drums, cymbals, vocals, bamboo flutes and spiked fiddles, Gamelan Galak Tika is approximately thirty members strong, drawing membership from the Massachusetts Institute of Technology students, staff and community. A concert talk with David Lang and the artists will follow the Friday, February 10 performance.

An improvement of Liouville theorem for discrete harmonic functions

Eugenia Malinnikova
Norwegian University of Science and Technology
February 14, 2017
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.
The situation is different for discrete harmonic functions on Z^2. We show that the following improved version of the Liouville theorem holds. If a discrete harmonic function is bounded on 99% of the plane then it is constant. It is a report on a joint work (in progress) with L. Buhovsky, A. Logunov and M. Sodin.

A unified duality-based approach to Bayesian mechanism design

Matt Weinberg
Princeton University
February 14, 2017

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 algorithmic mechanism design, and enables some new breakthroughs as well. In this talk, I'll:

1) Provide a brief overview of the challenges of multi-dimensional mechanism design.

2) Construct a duality framework to resolve these problems.