Optimization is a broad area with ramifications in many disciplines, including machine learning, control theory, signal processing, robotics, computer vision, power systems, and quantum information. I will talk about some novel algorithmic and theoretical results in two broad classes of optimization problems. The first class of problems are semidefinite programs (SDP). I will present the first polynomial time guarantees for the Burer-Monteiro method, which is widely used for solving large scale SDPs. I will also discuss some general guarantees on the quality of SDP solutions for parameter estimation problems. The second class of problems I will consider are polynomial systems. I will introduce a novel technique for solving polynomial systems that, by taking advantage of graphical structure, is able to outperform existing techniques by orders of magnitude.

**Bio:**

Diego Cifuentes is an applied math instructor in the Massachusetts Institute of Technology (MIT). Previously he was a postdoctoral researcher at the Max Planck Institute for Mathematics in the Sciences, and before that he completed his Ph.D. in the Electrical Engineering and Computer Science department at MIT under the supervision of Pablo Parrilo. His research interests include mathematical optimization, computational algebraic geometry, and their applications in sciences and engineering.