The Distinguished Colloquium Series in Interdisciplinary and Applied Mathematics is made possible with the generous support of the Columbia Engineering Dean, Mary C. Boyce. Lectures take place at various times during the academic year.

**Thursday, November 7, 2019**

4:00 PM, Room 750 Costa Engineering, CEPSR

530 W. 120th Street

(reception at 3:15 PM in the APAM Department, 200 Mudd)

Amit Singer

Professor, Department of Mathematics

Program in Applied and Computational Mathematics (PACM)

Center for Statistics and Machine Learning (CSML)

Princeton University

**Title: **Mathematics of Cryo-Electron Microscopy** **

**Abstract:** Single-particle electron cryomicroscopy (cryo-EM) is becoming an increasingly popular technique for elucidating the three-dimensional structure of proteins and other biologically significant complexes at near-atomic resolution. Unlike X-ray crystallography, single-particle cryo-EM is an entirely general imaging method that does not require crystallization and can capture molecules in their native states.

In single-particle cryo-EM, the three-dimensional molecular structure needs to be determined from many noisy two-dimensional tomographic projections of individual molecules, whose orientations and positions are unknown. The high level of noise and the unknown pose parameters are two key elements that make reconstruction a challenging computational problem. Even more challenging is the inference of structural variability and flexible motions when the individual molecules being imaged are in different conformational states.

This lecture discusses computational methods for structure determination by single-particle cryo-EM and their guiding mathematical principles including statistical inference, machine learning, and signal processing that also play a significant role in many other data science applications.

**Biography:** Amit Singer is one of the leaders in the mathematical analysis of noisy data provided by cryo-EM.

Singer is a professor of mathematics and a member of the executive committee of the Program in Applied and Computational Mathematics (PACM) at Princeton University. He joined Princeton as an assistant professor in 2008. From 2005 to 2008 he was a Gibbs Assistant Professor in Applied Mathematics at the Department of Mathematics, Yale University.

Singer received his B.Sc. degree in Physics and Mathematics and his Ph.D. degree in applied mathematics from Tel Aviv University, Israel, in 1997 and 2005, respectively. He was awarded the Moore Investigator in Data-Driven Discovery Award (2014), the Simons Investigator Award (2012), the Presidential Early Career Award for Scientists and Engineers (2010), the Alfred P. Sloan Research Fellowship (2010) and the Haim Nessyahu Prize in Mathematics (2007). His current research in applied mathematics focuses on theoretical and computational aspects of data science, and on developing computational methods for structural biology.

Singer works on a broad range of problems in applied mathematics, solving specific applied problems and employing sophisticated theory to allow the solution of general classes of problems. Among the areas to which he has contributed are diffusion maps, cryo-electron microscopy, random graph theory, sensor networks, graph Laplacians, and diffusion processes. His recent work in electron microscopy combines representation theory with a novel network construction to provide reconstructions of structural information on molecules from noisy two-dimensional images of populations of the molecule. He works with a widely varied group of collaborators and graduate students in several disciplines. His work is increasing the range of applicable mathematics.

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*This seminar is co-sponsored by the Center for Computing Systems for Data-driven Science, in the Data Science Institute, at Columbia University.*

** Organizing Committee:
**Qiang Du (APAM)

Don Goldfarb (IEOR)

Eitan Grinspun (Computer Science / APAM)

Ioannis Karatzas (Mathematics)

Andrei Okounkov (Mathematics)

Michael I. Weinstein (APAM / Mathematics)

For information, please contact Professor M.I. Weinstein, miw2103@columbia.edu.

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**Distinguished Colloquium Series in Interdisciplinary and Applied Mathematics Archive**