PACM Colloquium

PACM Colloquium: Jianfeng Lu, Duke University

Title: Diagrammatic algorithms for open quantum systems

Simulating open quantum systems is challenging due to its high dimensionality. The recently proposed inchworm algorithm provides an efficient strategy to reduce the bath degree of freedom based on diagrammatic resummation techniques. In this talk, we will discuss some recent progress in mathematical understanding of such diagrammatic algorithms. In particular, we will introduce a new algorithm for open quantum systems based on an integral-differential equation formulation.

PACM Colloquium: Gunther Uhlmann, University of Washington

Travel Time Tomography and Boundary Rigidity

We will consider the inverse problem of determining the speed or index of refraction of a medium by measuring the travel times of waves going through the medium. This problem arises in global seismology in an attempt to determine the inner structure of the Earth by measuring travel times of earthquakes. It has also several applications in optics and medical imaging among others. 

Joint PACM-EE Colloquium: Yury Polyanskiy, MIT

Tight sample complexity bounds via dualizing LeCam's method

In this talk we consider a general question of estimating linear functional of the distribution based on the noisy samples from it. We discover that the (two-point) LeCam lower bound is in fact achievable by optimizing bias-variance tradeoff of an empirical-mean type of estimator. We extend the method to certain symmetric functionals of high-dimensional parametric models.

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