The scalable optimization of sensor and actuator placements remains an open challenge in estimation and control. In general, determining optimal sensor locations amounts to an intractable brute-force search among all candidate locations. My works exploits linear dimensionality reduction tools, including SVD and balanced model reduction, to bypass this combinatorial search. Sensor and actuator locations are computed using efficient matrix pivoting operations on the resulting low-dimensional representations, allowing runtime to scale only linearly with the number of candidate locations. Results are demonstrated on high-dimensional examples from imaging, fluids and control with thousands of candidate locations, and are comparable to placements computed using more expensive methods. If time permits, recent directions in nonlinear dimensionality reduction for forecasting will be discussed.

I will give a proof of S.Y.  Cheng's conjecture  that a bounded strongly pseudoconvex domain in C^n has  its Bergman metric being Einstein if and only if it is holomorphically equivalent to the ball.

One of the major results in the study of 3-manifolds is the fact that most 3-manifolds have a finite cover that fibers over S1. One may ask what is the counterpart of this result for other classes of manifolds. In this talk we will discuss the case of smooth projective varieties (or more generally Kaehler manifolds) and present some geometric and group-theoretic aspects of  "virtual algebraic fibrations" of their fundamental groups.