## David Dynerman

University of Wisconsin, Madison

*Describing geometry and symmetry of cryo-EM datasets using algebra*

Cryo-electron microscopy (cryo-EM) is a microscopy technique used to discover the 3D structure of molecules from very noisy images. We discuss how algebra can describe two aspects of cryo-EM datasets.

First, we'll describe common lines datasets. Common lines are lines of intersection between cryo-EM images in 3D. They are a crucial ingredient in some 2D->3D reconstruction algorithms, and they can be characterized by polynomial equalities and inequalities. Second, we'll discuss how 3D symmetries of a molecule can be detected from only 2D cryo-EM images, without performing full 3D reconstruction.

This talk is a presentation to Eva Nogales' lab. The Nogales lab uses cryo-EM to investigate the structure of proteins. The math content of the talk is geared towards biophysicists, while mathematicians might enjoy learning a little bit about cryo-EM and some of the challenges it poses.