Tuesday, January 23, 2018
Time  Items 

All day 

4:00pm 
01/23/2018  4:00pm to 5:00pm Cryoelectron microscopy (cryoEM) is an imagingtechnology that is revolutionizing structural biology, enabling reconstruction of molecules at nearatomic resolution. CryoEM produces a large number of very noisy twodimensional tomographic projection images of a molecule, taken at unknown viewing directions. The extreme levels of noise make classical tasks in statistics and signal processing, such as alignment, detection and classification, impossible. I will start the talk by studying the multireference alignment problem, which can be interpreted as a simplified model for cryoEM. In multireference alignment, we aim to estimate multiple signals from their circularlytranslated, unlabeled, copies. In high noise regimes, the measurements cannot be alignedor clustered. Nonetheless, accurate estimation can be achieved using nonconvex optimization by considering the invarariants of the problem. Then, I will introduce the analog invariants of the cryoEM problem and focus on two applications, called 2D classification and ab initio modeling. Location: 01/23/2018  4:15pm to 5:15pm This talk will illustrate some patterns in the homology of the configuration space Fk(M), the space of ordered ktuples of distinct points in a manifold M. For a fixed manifold M, as k increases, we might expectthe topology of these configuration spaces to become increasingly complicated. Church and others showed, however, that when M is connected and open, there is a representationtheoretic sense in which the homology groups of these spaces stabilize. In this talk I will explain these stability patterns, and describe higherorder stability phenomena  relationships between unstable homology classes in different degrees  establishedin recent work joint with Jeremy Miller. This project was inspired by workinprogress of GalatiusKupersRandalWilliams. Location: 