In this talk, we will present advances in the geometric understanding of networks that link curvature to acquired robustness of dynamical systems. At the core of this work is the interplay of geometry, entropy, and optimal mass transport to that of functional robustness of complex systems. We first motivate these concepts in a visual setting by coupling the classical computational vision problems of segmentation, shape analysis, and pose estimation in a certain energy functional. From this, we then develop a connection that shows Ricci curvature is positively correlated with a system’s robustness or its ability to dynamically adapt. Compatible discrete notions and schemes are shown to illustrate the computational (parallelizable) advantages over related measures necessary for practical applications.

Romeil Sandhu is a post-doctoral fellow in the Applied Mathematics & Statistics / Computer Science Departments at Stony Brook University working closely with M.D. Anderson and Memorial Sloan Kettering Cancer Center. He received his B.S. M.S., and Ph.D. from the Georgia Institute of Technology in 2006, 2009, and 2010, respectively. Afterwards, he co-founded (and exited) a successful high tech defense startup supporting missile defense related issues and has been active participant in the defense community. He returned to academia to conduct research on network geometry. His current research focuses on the underlying relationship of geometry, statistics, and control to problems in systems biology, computational vision, machine learning, and medical imaging.