Representation theoretic patterns in three dimensional cryo-electron

microscopy

Speaker: Ronny Hadani (UTexas at Austin)

Three dimensional cryo-electron microscopy (3D cryo-EM, for short) is the

problem of determining the three dimensional structure of a large molecule

from the set of images, taken by an electron microscope, of randomly

oriented and positioned identical molecular particles which are frozen in

a thin layer of ice. A solution to this problem is of particular interest,

since it promises to be an entirely general technique which does not

require crystallization or other special preparation stages. Present

approaches to the problem fail with particles that are too small, cryo-EM

images that are too noisy or at resolutions where the signal-to-noise

ratio becomes too small.

The focus of my talk is the intrinsic reconstitution algorithm, due to

Singer and Shkolnisky, which constitutes a basic step for the solution of

the 3D cryo-EM problem and whose main appealing property is its remarkable

numerical stability to noise. My goal is to give an introductory

explanation of the mathematical principles underlying this novel

algorithmic approach, while hinting about how they apply to other

fundamental problems in cryo-EM and beyond. Along the way, I will describe

the mathematical model underlying the experimental set-up, specifying the

main computational problems/technical difficulties that should be resolved

as part of three dimensional structure determination from cryo-EM images.

Finally, to put things in a broader mathematical perspective, I will

briefly mention the general picture: explaining how other fundamental

algorithmic problems of Cryo-EM (and beyond) can be formulated and

effectively solved in similar mathematical framework.

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Short Bio

Ronny Hadani is an associate professor in the math department at

University of Texas at Austin. Before that he was a L.E Dickson

postoctoral fellow at University of Chicago. He did his PhD in pure

mathematics at Tel-Aviv University under the supervision of Prof. Joseph

Bernstein. He did his Master degree in computer science at the Weizmann

Institute of Science. His field of expertise is representation theory and

harmonic analysis with applications to signal processing, communication

and computational science.