Single particle cryo-EM is an increasingly popular technique for determining 3-D molecular structures at high resolution. The 2017 Nobel Prize in Chemistry was awarded to three of the pioneers of cryo-EM, and already in the early stages of the global pandemic, cryo-EM was successfully applied to image the SARS-CoV-2 spike protein. We will discuss the mathematical principles and computational methods for reconstruction using cryo-EM, focusing on its sample complexity (i.e., the number of images required for reconstruction as a function of the signal-to-noise ratio) and reconstruction of flexible molecules.

The classical uniformization theorem for Riemann surfaces is well-established for both compact and non-compact connected surfaces. However,  in the discrete setting, the discrete uniformization theorem is only known for closed polyhedral surfaces.  This talk will propose a discrete uniformization problem for all surfaces and relate it to the classical Weyl problem in the hyperbolic 3-space and the Cauchy-Alexandrov rigidity theorem on convex polytopes.  Some of our progress will be discussed,  including a discrete Schwarz-Pick-Ahlfors lemma and its application.  This is joint work with Yanwen Luo.

Please join us for pre-seminar Tea