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

## Functional inequalities and gradient flow for quantum evolution

## Mirror symmetry via Berkovich geometry II: the non-archimedean SYZ fibration

## Post Concert Discussion

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

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

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.

## Harmonic functions - positivity and convexity

The talk is based on a joint work with Gabor Lippner.

## Friends Lunch with a Member

Reuben Jonathan Miller, Friends of the Institute for Advanced Study Member