- Series
- Job Candidate Talk
- Time
- Tuesday, March 3, 2020 - 11:00am for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Joe Kileel – Program in Applied and Computational Mathematics, Princeton University – https://web.math.princeton.edu/~jkileel/
- Organizer
- Prasad Tetali
Perspectives from numerical optimization and computational algebra are
brought to bear on a scientific application and a data science
application. In the first part of the talk, I will discuss
cryo-electron microscopy (cryo-EM), an imaging technique to determine
the 3-D shape of macromolecules from many noisy 2-D projections,
recognized by the 2017 Chemistry Nobel Prize. Mathematically, cryo-EM
presents a particularly rich inverse problem, with unknown
orientations, extreme noise, big data and conformational
heterogeneity. In particular, this motivates a general framework for
statistical estimation under compact group actions, connecting
information theory and group invariant theory. In the second part of
the talk, I will discuss tensor rank decomposition, a higher-order
variant of PCA broadly applicable in data science. A fast algorithm
is introduced and analyzed, combining ideas of Sylvester and the power
method.